Mixing
Number Spiral Problem
Clash Royale CLAN TAG#URR8PPP
up vote
24
down vote
favorite
A number spiral is an infinite grid whose upper-left square has number 1. Here are the first five layers of the spiral:
Your task is to find out the number in row y and column x.
Example:
Input: 2 3
Out : 8
Input: 1 1
Out : 1
Input: 4 2
Out : 15
Note:
- Any programming language is allowed.
- This is a code-golf challenge so shortest code wins.
- Best of Luck!
Source: https://cses.fi/problemset/task/1071
code-golf math
asked Aug 17 at 15:24
Agile_Eagle
328114
 |Â
show 4 more comments
up vote
24
down vote
favorite
A number spiral is an infinite grid whose upper-left square has number 1. Here are the first five layers of the spiral:
Your task is to find out the number in row y and column x.
Example:
Input: 2 3
Out : 8
Input: 1 1
Out : 1
Input: 4 2
Out : 15
Note:
- Any programming language is allowed.
- This is a code-golf challenge so shortest code wins.
- Best of Luck!
Source: https://cses.fi/problemset/task/1071
code-golf math
asked Aug 17 at 15:24
Agile_Eagle
328114
1
It looks like your inputs are 1 indexed (coordinates start at 1,1) (although this has to be intuited from the test cases) can we use 0 indexing (coordinates start at 0,0)?
– W W
Aug 17 at 16:26
4
What is the reasoning for this?
– W W
Aug 17 at 16:30
3
Nice challenge, but I don't really like that you force it to be 1-indexed... +1 anyway...
– Stewie Griffin
Aug 18 at 8:30
7
I think it's absolutely fine for the coordinates to start at (1, 1), especially if the program is posted that way on CSES, and the OP doesn't need to justify this. I think golfers here are getting a little too used to somewhat arbitrary freedoms.
– Lynn
Aug 18 at 12:57
2
@Lynn I second that
– Agile_Eagle
Aug 18 at 12:58
 |Â
show 4 more comments
up vote
24
down vote
favorite
up vote
24
down vote
favorite
A number spiral is an infinite grid whose upper-left square has number 1. Here are the first five layers of the spiral:
Your task is to find out the number in row y and column x.
Example:
Input: 2 3
Out : 8
Input: 1 1
Out : 1
Input: 4 2
Out : 15
Note:
- Any programming language is allowed.
- This is a code-golf challenge so shortest code wins.
- Best of Luck!
Source: https://cses.fi/problemset/task/1071
code-golf math
asked Aug 17 at 15:24
Agile_Eagle
328114
A number spiral is an infinite grid whose upper-left square has number 1. Here are the first five layers of the spiral:
Your task is to find out the number in row y and column x.
Example:
Input: 2 3
Out : 8
Input: 1 1
Out : 1
Input: 4 2
Out : 15
Note:
- Any programming language is allowed.
- This is a code-golf challenge so shortest code wins.
- Best of Luck!
Source: https://cses.fi/problemset/task/1071
code-golf math
asked Aug 17 at 15:24
Agile_Eagle
328114
asked Aug 17 at 15:24
Agile_Eagle
328114
asked Aug 17 at 15:24
Agile_Eagle
328114
asked Aug 17 at 15:24
Agile_Eagle
328114
328114
1
It looks like your inputs are 1 indexed (coordinates start at 1,1) (although this has to be intuited from the test cases) can we use 0 indexing (coordinates start at 0,0)?
– W W
Aug 17 at 16:26
4
What is the reasoning for this?
– W W
Aug 17 at 16:30
3
Nice challenge, but I don't really like that you force it to be 1-indexed... +1 anyway...
– Stewie Griffin
Aug 18 at 8:30
7
I think it's absolutely fine for the coordinates to start at (1, 1), especially if the program is posted that way on CSES, and the OP doesn't need to justify this. I think golfers here are getting a little too used to somewhat arbitrary freedoms.
– Lynn
Aug 18 at 12:57
2
@Lynn I second that
– Agile_Eagle
Aug 18 at 12:58
 |Â
show 4 more comments
1
It looks like your inputs are 1 indexed (coordinates start at 1,1) (although this has to be intuited from the test cases) can we use 0 indexing (coordinates start at 0,0)?
– W W
Aug 17 at 16:26
4
What is the reasoning for this?
– W W
Aug 17 at 16:30
3
Nice challenge, but I don't really like that you force it to be 1-indexed... +1 anyway...
– Stewie Griffin
Aug 18 at 8:30
7
I think it's absolutely fine for the coordinates to start at (1, 1), especially if the program is posted that way on CSES, and the OP doesn't need to justify this. I think golfers here are getting a little too used to somewhat arbitrary freedoms.
– Lynn
Aug 18 at 12:57
2
@Lynn I second that
– Agile_Eagle
Aug 18 at 12:58
1
1
It looks like your inputs are 1 indexed (coordinates start at 1,1) (although this has to be intuited from the test cases) can we use 0 indexing (coordinates start at 0,0)?
– W W
Aug 17 at 16:26
It looks like your inputs are 1 indexed (coordinates start at 1,1) (although this has to be intuited from the test cases) can we use 0 indexing (coordinates start at 0,0)?
– W W
Aug 17 at 16:26
4
4
What is the reasoning for this?
– W W
Aug 17 at 16:30
What is the reasoning for this?
– W W
Aug 17 at 16:30
3
3
Nice challenge, but I don't really like that you force it to be 1-indexed... +1 anyway...
– Stewie Griffin
Aug 18 at 8:30
Nice challenge, but I don't really like that you force it to be 1-indexed... +1 anyway...
– Stewie Griffin
Aug 18 at 8:30
7
7
I think it's absolutely fine for the coordinates to start at (1, 1), especially if the program is posted that way on CSES, and the OP doesn't need to justify this. I think golfers here are getting a little too used to somewhat arbitrary freedoms.
– Lynn
Aug 18 at 12:57
I think it's absolutely fine for the coordinates to start at (1, 1), especially if the program is posted that way on CSES, and the OP doesn't need to justify this. I think golfers here are getting a little too used to somewhat arbitrary freedoms.
– Lynn
Aug 18 at 12:57
2
2
@Lynn I second that
– Agile_Eagle
Aug 18 at 12:58
@Lynn I second that
– Agile_Eagle
Aug 18 at 12:58
 |Â
show 4 more comments
14 Answers
14
active
oldest
votes
up vote
19
down vote
C (gcc), Â 44Â 43 bytes
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?y-x:x-y)-z;
Try it online!
The spiral has several "arms":
12345
22345
33345
44445
55555
The position $(x, y)$ is located on arm $max(x, y)$ (assigned to variable z). Then, the largest number on arm $n$ is $n^2$, which alternates between being in the bottom left and top right position on the arm. Subtracting $x$ from $y$ gives the sequence $-n+1, -n+2, ldots, -1, 0, 1, ldots, n-1, n-2$ moving along arm $n$, so we choose the appropriate sign based on the parity of $n$, adjust by $n-1$ to get a sequence starting at 0, and subtract this value from $n^2$.
Thanks to Mr. Xcoder for saving a byte.
answered Aug 17 at 15:42
Doorknob♦
53.1k15111339
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?x-y:y-x)-z;saves 1 byte.
– Mr. Xcoder
Aug 17 at 15:52
@Mr.Xcoder Neat trick, thanks!
– Doorknob♦
Aug 17 at 15:55
Crossed out 44 is still regular 44 ;(
– Mr. Xcoder
Aug 17 at 16:11
3
@RobertS. Yes, that is what the function I defined does (in the Code section on TIO). For instance,f(1, 1)returns the value1. The Footer section loops through x=1 through 5 and y=1 through 5, calls the function for all such values, and prints its output in a grid, to demonstrate that the function is correct for all inputs shown in the question.
– Doorknob♦
Aug 17 at 19:38
1
@Agile_Eagle The function does return the number (it couldn't output the spiral - it doesn't even have any loops!).
– Doorknob♦
Aug 17 at 19:40
 |Â
show 6 more comments
up vote
7
down vote
Python, Â 54Â Â 50Â 49 bytes
def f(a,b):M=max(a,b);return(a-b)*(-1)**M+M*M-M+1
-4 bytes thanks to @ChasBrown
-1 bytes thanks to @Shaggy
Try it Online!
First time golfing! I'm more than aware this is not optimal, but whatever.
Essentially runs on the same principle as @Doorknob C code.
answered Aug 17 at 20:49
Rushabh Mehta
522119
2
Welcome to PPCG! In this case you can save 4 bytes using thedef f(a,b):approach, see here.
– Chas Brown
Aug 17 at 21:21
@ChasBrown Very interesting, thank you!
– Rushabh Mehta
Aug 17 at 21:21
@Shaggy Thank you! I've posted a few challenges, but never been good enough to golf
– Rushabh Mehta
Aug 17 at 22:32
In that case, then, welcome to Golf! :) I'm not a Python guy but I'm pretty sureM**2can be replaced withM*M.
– Shaggy
Aug 17 at 22:36
@Shaggy Thank you! Will fix right now
– Rushabh Mehta
Aug 17 at 22:37
add a comment |Â
up vote
7
down vote
MATL, 15 bytes
X>ttq*QwoEqGd*+
Try it online!
Collect and print as a matrix
How?
Edit: Same technique as @Doorknob's answer, just arrived at differently.
The difference between the diagonal elements of the spiral is the arithmetic sequence $ 0, 2, 4, 6, 8, ldots $. Sum of $ n $ terms of this is $ n(n - 1) $ (by the usual AP formula). This sum, incremented by 1, gives the diagonal element at position $ (n, n) $.
Given $ (x, y) $, we find the maximum of these two, which is the "layer" of the spiral that this point belongs to. Then, we find the diagonal value of that layer as $ v = n(n-1) + 1 $. For even layers, the value at $ (x, y) $ is then $ v + x - y $, for odd layers $ v - x + y $.
X> % Get the maximum of the input coordinates, say n
ttq* % Duplicate that and multiply by n-1
Q % Add 1 to that. This is the diagonal value v at layer n
wo % Bring the original n on top and check if it's odd (1 or 0)
Eq % Change 1 or 0 to 1 or -1
Gd % Push input (x, y) again, get y - x
* % Multiply by 1 or -1
% For odd layers, no change. For even layers, y-x becomes x-y
+ % Add that to the diagonal value v
% Implicit output
Alternate 21 byte solution:
Pdt|Gs+ttqq*4/QJb^b*+
Try it online!
Collect and print as a matrix
From the above, we know that the function we want is
$$ f = m * (m - 1) + 1 + (-1)^m * (x - y) $$
where $ m = max(x, y) $.
Some basic calculation will show that one expression for max of two numbers is
$$ m = max(x, y) = fracx + y + abs(x - y)2 $$
Plugging one into another, we find that one alternate form for $ f $ is:
$$ f = (x-y)cdot i^k + frac14((k-2)cdot k) + 1 $$
where $ k = abs(x-y) + x + y $.
This is the function the solution implements.
answered Aug 17 at 21:07
sundar
4,656829
add a comment |Â
up vote
5
down vote
Japt, 16 bytes
Adapted from Doorknob's solution over a few beers.
wV
nU²ÒNr"n-"gUv
Try it
Explanation
:Implicit input of integers U=x and V=y
wV :Maximum of U & V
n :Reassign to U
U² :U squared
Ò :-~
"n-" :Literal string
Uv :Is U divisible by 2? Return 0 or 1
g :Get the character in the string at that index
Nr :Reduce the array of inputs by that, where n is inverse subtraction (XnY = Y-X)
n :Subtract U from the result of the above
answered Aug 17 at 22:26
Shaggy
16.2k21559
add a comment |Â
up vote
3
down vote
Pyth, 20 bytes
A~Qh.MZQh-+*-GH^_1Q*
Test suite
An almost literal translation of Rushabh Mehta's answer.
Explanation:
A~Qh.MZQh-+*-GH^_1Q* | Full code
A~Qh.MZQh-+*-GH^_1Q*QQQ | Code with implicit variables filled
| Assign Q as the evaluated input (implicit)
A | Assign [G,H] as
~Q | Q, then assign Q as
h.MZQ | Q's maximal value.
| Print (implicit)
h-+*-GH^_1Q*QQQ | (G-H)*(-1)^Q+Q*Q-Q+1
answered Aug 18 at 2:59
hakr14
1,03529
add a comment |Â
up vote
2
down vote
Jelly, 13 bytes
»Ḃ-*×_‘+»×’$¥
Try it online!
Uses Doorknob's method. Way too long.
answered Aug 17 at 16:40
Mr. Xcoder
30.2k757193
Alternative:»á¸‚-*×_‘+»²_»Ê‹
– Mr. Xcoder
Aug 17 at 16:41
add a comment |Â
up vote
2
down vote
Jelly, 13 12 bytes
ṀḂḤ’×I+²_’ṀƲ
Try it online!
Computes the diagonal term with ²_’Ṁ and adds/subtracts to the correct index value with ṀḂḤ’×I.
answered Aug 18 at 2:48
dylnan
3,4982526
add a comment |Â
up vote
2
down vote
Brain-Flak, 76 bytes
(((<>))<>[(())]<([()])<>>)<>(()([()])()<><([])><><><>)
Try it online!
answered Aug 18 at 17:08
Nitrodon
6,3011620
add a comment |Â
up vote
2
down vote
05AB1E, 12 11 bytes
ZÃÂ<*>Ã…Â GR}Â¥+
-1 byte thanks to @Emigna changing Èi to G.
Port of @sundar's MATL answer, so make sure to upvote him!
Try it online or verify all test cases.
Explanation:
Z # Get the maximum of the (implicit) input-coordinate
# i.e. [4,5] → 5
à# Triplicate this maximum
< # Decrease it by 1
# i.e. 5 - 1 → 4
* # Multiply it
# i.e. 5 * 4 → 20
> # Increase it by 1
# i.e. 20 + 1 → 21
Ã…Â # Triple swap the top threes values on the stack (a,b,c to c,a,b)
# i.e. [4,5], 5, 21 → 21, [4,5], 5
G } # Loop n amount of times
R # Reverse the input-coordinate each iteration
# i.e. 5 and [4,5] → [5,4]→[4,5]→[5,4]→[4,5] → [5,4]
Â¥ # Calculate the delta of the coordinate
# [5,4] → [1]
+ # And add it to the earlier calculate value (output the result implicitly)
# 21 + [1] → [22]
answered Aug 20 at 8:37
Kevin Cruijssen
29.4k549162
1
Èicould beG.
– Emigna
Aug 20 at 10:39
@Emigna Oh smart, thanks! :D
– Kevin Cruijssen
Aug 20 at 11:01
add a comment |Â
up vote
0
down vote
Pascal (FPC), 90 bytes
uses math;var x,y,z:word;begin read(x,y);z:=max(x,y);write(z*z-z+1+(1and z*2-1)*(y-x))end.
Try it online!
Port of Doorknob's answer, but sundar's answer gave me idea for z mod 2*2-1 which I transformed into 1and z*2-1 to remove space.
answered Aug 17 at 22:38
AlexRacer
57928
add a comment |Â
up vote
0
down vote
Mathematica 34 bytes
x = 5, 8;
so:
m = Max[x];
Subtract @@ x (-1)^m + m^2 - m + 1
(*
54
*)
answered Aug 18 at 0:31
David G. Stork
1637
add a comment |Â
up vote
0
down vote
Julia 1.0, 35 bytes
xy=(m=max(x,y))*~-m+1+(-1)^m*(x-y)
Try it online!
answered Aug 18 at 8:12
sundar
4,656829
add a comment |Â
up vote
0
down vote
JavaScript (ES6), 46 bytes
f=(r,c,x)=>r<c?f(c,r,1):r%2-!x?r*r-c+1:--r*r+c
answered Aug 19 at 11:36
James
1313
add a comment |Â
up vote
0
down vote
Java (JDK 10), 39 bytes
x->y->(y-x)*((y=x>y?x:y)%2*2-1)+y*y-y+1
Try it online!
Credits
- Port of Doorknob's answer.
answered Aug 20 at 11:09
Olivier Grégoire
7,48311739
add a comment |Â
14 Answers
14
active
oldest
votes
14 Answers
14
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
19
down vote
C (gcc), Â 44Â 43 bytes
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?y-x:x-y)-z;
Try it online!
The spiral has several "arms":
12345
22345
33345
44445
55555
The position $(x, y)$ is located on arm $max(x, y)$ (assigned to variable z). Then, the largest number on arm $n$ is $n^2$, which alternates between being in the bottom left and top right position on the arm. Subtracting $x$ from $y$ gives the sequence $-n+1, -n+2, ldots, -1, 0, 1, ldots, n-1, n-2$ moving along arm $n$, so we choose the appropriate sign based on the parity of $n$, adjust by $n-1$ to get a sequence starting at 0, and subtract this value from $n^2$.
Thanks to Mr. Xcoder for saving a byte.
answered Aug 17 at 15:42
Doorknob♦
53.1k15111339
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?x-y:y-x)-z;saves 1 byte.
– Mr. Xcoder
Aug 17 at 15:52
@Mr.Xcoder Neat trick, thanks!
– Doorknob♦
Aug 17 at 15:55
Crossed out 44 is still regular 44 ;(
– Mr. Xcoder
Aug 17 at 16:11
3
@RobertS. Yes, that is what the function I defined does (in the Code section on TIO). For instance,f(1, 1)returns the value1. The Footer section loops through x=1 through 5 and y=1 through 5, calls the function for all such values, and prints its output in a grid, to demonstrate that the function is correct for all inputs shown in the question.
– Doorknob♦
Aug 17 at 19:38
1
@Agile_Eagle The function does return the number (it couldn't output the spiral - it doesn't even have any loops!).
– Doorknob♦
Aug 17 at 19:40
 |Â
show 6 more comments
up vote
19
down vote
C (gcc), Â 44Â 43 bytes
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?y-x:x-y)-z;
Try it online!
The spiral has several "arms":
12345
22345
33345
44445
55555
The position $(x, y)$ is located on arm $max(x, y)$ (assigned to variable z). Then, the largest number on arm $n$ is $n^2$, which alternates between being in the bottom left and top right position on the arm. Subtracting $x$ from $y$ gives the sequence $-n+1, -n+2, ldots, -1, 0, 1, ldots, n-1, n-2$ moving along arm $n$, so we choose the appropriate sign based on the parity of $n$, adjust by $n-1$ to get a sequence starting at 0, and subtract this value from $n^2$.
Thanks to Mr. Xcoder for saving a byte.
answered Aug 17 at 15:42
Doorknob♦
53.1k15111339
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?x-y:y-x)-z;saves 1 byte.
– Mr. Xcoder
Aug 17 at 15:52
@Mr.Xcoder Neat trick, thanks!
– Doorknob♦
Aug 17 at 15:55
Crossed out 44 is still regular 44 ;(
– Mr. Xcoder
Aug 17 at 16:11
3
@RobertS. Yes, that is what the function I defined does (in the Code section on TIO). For instance,f(1, 1)returns the value1. The Footer section loops through x=1 through 5 and y=1 through 5, calls the function for all such values, and prints its output in a grid, to demonstrate that the function is correct for all inputs shown in the question.
– Doorknob♦
Aug 17 at 19:38
1
@Agile_Eagle The function does return the number (it couldn't output the spiral - it doesn't even have any loops!).
– Doorknob♦
Aug 17 at 19:40
 |Â
show 6 more comments
up vote
19
down vote
up vote
19
down vote
C (gcc), Â 44Â 43 bytes
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?y-x:x-y)-z;
Try it online!
The spiral has several "arms":
12345
22345
33345
44445
55555
The position $(x, y)$ is located on arm $max(x, y)$ (assigned to variable z). Then, the largest number on arm $n$ is $n^2$, which alternates between being in the bottom left and top right position on the arm. Subtracting $x$ from $y$ gives the sequence $-n+1, -n+2, ldots, -1, 0, 1, ldots, n-1, n-2$ moving along arm $n$, so we choose the appropriate sign based on the parity of $n$, adjust by $n-1$ to get a sequence starting at 0, and subtract this value from $n^2$.
Thanks to Mr. Xcoder for saving a byte.
answered Aug 17 at 15:42
Doorknob♦
53.1k15111339
C (gcc), Â 44Â 43 bytes
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?y-x:x-y)-z;
Try it online!
The spiral has several "arms":
12345
22345
33345
44445
55555
The position $(x, y)$ is located on arm $max(x, y)$ (assigned to variable z). Then, the largest number on arm $n$ is $n^2$, which alternates between being in the bottom left and top right position on the arm. Subtracting $x$ from $y$ gives the sequence $-n+1, -n+2, ldots, -1, 0, 1, ldots, n-1, n-2$ moving along arm $n$, so we choose the appropriate sign based on the parity of $n$, adjust by $n-1$ to get a sequence starting at 0, and subtract this value from $n^2$.
Thanks to Mr. Xcoder for saving a byte.
answered Aug 17 at 15:42
Doorknob♦
53.1k15111339
edited Aug 17 at 21:25
answered Aug 17 at 15:42
Doorknob♦
53.1k15111339
answered Aug 17 at 15:42
Doorknob♦
53.1k15111339
answered Aug 17 at 15:42
Doorknob♦
53.1k15111339
53.1k15111339
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?x-y:y-x)-z;saves 1 byte.
– Mr. Xcoder
Aug 17 at 15:52
@Mr.Xcoder Neat trick, thanks!
– Doorknob♦
Aug 17 at 15:55
Crossed out 44 is still regular 44 ;(
– Mr. Xcoder
Aug 17 at 16:11
3
@RobertS. Yes, that is what the function I defined does (in the Code section on TIO). For instance,f(1, 1)returns the value1. The Footer section loops through x=1 through 5 and y=1 through 5, calls the function for all such values, and prints its output in a grid, to demonstrate that the function is correct for all inputs shown in the question.
– Doorknob♦
Aug 17 at 19:38
1
@Agile_Eagle The function does return the number (it couldn't output the spiral - it doesn't even have any loops!).
– Doorknob♦
Aug 17 at 19:40
 |Â
show 6 more comments
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?x-y:y-x)-z;saves 1 byte.
– Mr. Xcoder
Aug 17 at 15:52
@Mr.Xcoder Neat trick, thanks!
– Doorknob♦
Aug 17 at 15:55
Crossed out 44 is still regular 44 ;(
– Mr. Xcoder
Aug 17 at 16:11
3
@RobertS. Yes, that is what the function I defined does (in the Code section on TIO). For instance,f(1, 1)returns the value1. The Footer section loops through x=1 through 5 and y=1 through 5, calls the function for all such values, and prints its output in a grid, to demonstrate that the function is correct for all inputs shown in the question.
– Doorknob♦
Aug 17 at 19:38
1
@Agile_Eagle The function does return the number (it couldn't output the spiral - it doesn't even have any loops!).
– Doorknob♦
Aug 17 at 19:40
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?x-y:y-x)-z; saves 1 byte.– Mr. Xcoder
Aug 17 at 15:52
f(x,y,z)z=x>y?x:y;z=z*z-~(z%2?x-y:y-x)-z; saves 1 byte.– Mr. Xcoder
Aug 17 at 15:52
@Mr.Xcoder Neat trick, thanks!
– Doorknob♦
Aug 17 at 15:55
@Mr.Xcoder Neat trick, thanks!
– Doorknob♦
Aug 17 at 15:55
Crossed out 44 is still regular 44 ;(
– Mr. Xcoder
Aug 17 at 16:11
Crossed out 44 is still regular 44 ;(
– Mr. Xcoder
Aug 17 at 16:11
3
3
@RobertS. Yes, that is what the function I defined does (in the Code section on TIO). For instance,
f(1, 1) returns the value 1. The Footer section loops through x=1 through 5 and y=1 through 5, calls the function for all such values, and prints its output in a grid, to demonstrate that the function is correct for all inputs shown in the question.– Doorknob♦
Aug 17 at 19:38
@RobertS. Yes, that is what the function I defined does (in the Code section on TIO). For instance,
f(1, 1) returns the value 1. The Footer section loops through x=1 through 5 and y=1 through 5, calls the function for all such values, and prints its output in a grid, to demonstrate that the function is correct for all inputs shown in the question.– Doorknob♦
Aug 17 at 19:38
1
1
@Agile_Eagle The function does return the number (it couldn't output the spiral - it doesn't even have any loops!).
– Doorknob♦
Aug 17 at 19:40
@Agile_Eagle The function does return the number (it couldn't output the spiral - it doesn't even have any loops!).
– Doorknob♦
Aug 17 at 19:40
 |Â
show 6 more comments
up vote
7
down vote
Python, Â 54Â Â 50Â 49 bytes
def f(a,b):M=max(a,b);return(a-b)*(-1)**M+M*M-M+1
-4 bytes thanks to @ChasBrown
-1 bytes thanks to @Shaggy
Try it Online!
First time golfing! I'm more than aware this is not optimal, but whatever.
Essentially runs on the same principle as @Doorknob C code.
answered Aug 17 at 20:49
Rushabh Mehta
522119
2
Welcome to PPCG! In this case you can save 4 bytes using thedef f(a,b):approach, see here.
– Chas Brown
Aug 17 at 21:21
@ChasBrown Very interesting, thank you!
– Rushabh Mehta
Aug 17 at 21:21
@Shaggy Thank you! I've posted a few challenges, but never been good enough to golf
– Rushabh Mehta
Aug 17 at 22:32
In that case, then, welcome to Golf! :) I'm not a Python guy but I'm pretty sureM**2can be replaced withM*M.
– Shaggy
Aug 17 at 22:36
@Shaggy Thank you! Will fix right now
– Rushabh Mehta
Aug 17 at 22:37
add a comment |Â
up vote
7
down vote
Python, Â 54Â Â 50Â 49 bytes
def f(a,b):M=max(a,b);return(a-b)*(-1)**M+M*M-M+1
-4 bytes thanks to @ChasBrown
-1 bytes thanks to @Shaggy
Try it Online!
First time golfing! I'm more than aware this is not optimal, but whatever.
Essentially runs on the same principle as @Doorknob C code.
answered Aug 17 at 20:49
Rushabh Mehta
522119
2
Welcome to PPCG! In this case you can save 4 bytes using thedef f(a,b):approach, see here.
– Chas Brown
Aug 17 at 21:21
@ChasBrown Very interesting, thank you!
– Rushabh Mehta
Aug 17 at 21:21
@Shaggy Thank you! I've posted a few challenges, but never been good enough to golf
– Rushabh Mehta
Aug 17 at 22:32
In that case, then, welcome to Golf! :) I'm not a Python guy but I'm pretty sureM**2can be replaced withM*M.
– Shaggy
Aug 17 at 22:36
@Shaggy Thank you! Will fix right now
– Rushabh Mehta
Aug 17 at 22:37
add a comment |Â
up vote
7
down vote
up vote
7
down vote
Python, Â 54Â Â 50Â 49 bytes
def f(a,b):M=max(a,b);return(a-b)*(-1)**M+M*M-M+1
-4 bytes thanks to @ChasBrown
-1 bytes thanks to @Shaggy
Try it Online!
First time golfing! I'm more than aware this is not optimal, but whatever.
Essentially runs on the same principle as @Doorknob C code.
answered Aug 17 at 20:49
Rushabh Mehta
522119
Python, Â 54Â Â 50Â 49 bytes
def f(a,b):M=max(a,b);return(a-b)*(-1)**M+M*M-M+1
-4 bytes thanks to @ChasBrown
-1 bytes thanks to @Shaggy
Try it Online!
First time golfing! I'm more than aware this is not optimal, but whatever.
Essentially runs on the same principle as @Doorknob C code.
answered Aug 17 at 20:49
Rushabh Mehta
522119
edited Aug 17 at 22:39
answered Aug 17 at 20:49
Rushabh Mehta
522119
answered Aug 17 at 20:49
Rushabh Mehta
522119
answered Aug 17 at 20:49
Rushabh Mehta
522119
522119
2
Welcome to PPCG! In this case you can save 4 bytes using thedef f(a,b):approach, see here.
– Chas Brown
Aug 17 at 21:21
@ChasBrown Very interesting, thank you!
– Rushabh Mehta
Aug 17 at 21:21
@Shaggy Thank you! I've posted a few challenges, but never been good enough to golf
– Rushabh Mehta
Aug 17 at 22:32
In that case, then, welcome to Golf! :) I'm not a Python guy but I'm pretty sureM**2can be replaced withM*M.
– Shaggy
Aug 17 at 22:36
@Shaggy Thank you! Will fix right now
– Rushabh Mehta
Aug 17 at 22:37
add a comment |Â
2
Welcome to PPCG! In this case you can save 4 bytes using thedef f(a,b):approach, see here.
– Chas Brown
Aug 17 at 21:21
@ChasBrown Very interesting, thank you!
– Rushabh Mehta
Aug 17 at 21:21
@Shaggy Thank you! I've posted a few challenges, but never been good enough to golf
– Rushabh Mehta
Aug 17 at 22:32
In that case, then, welcome to Golf! :) I'm not a Python guy but I'm pretty sureM**2can be replaced withM*M.
– Shaggy
Aug 17 at 22:36
@Shaggy Thank you! Will fix right now
– Rushabh Mehta
Aug 17 at 22:37
2
2
Welcome to PPCG! In this case you can save 4 bytes using the
def f(a,b): approach, see here.– Chas Brown
Aug 17 at 21:21
Welcome to PPCG! In this case you can save 4 bytes using the
def f(a,b): approach, see here.– Chas Brown
Aug 17 at 21:21
@ChasBrown Very interesting, thank you!
– Rushabh Mehta
Aug 17 at 21:21
@ChasBrown Very interesting, thank you!
– Rushabh Mehta
Aug 17 at 21:21
@Shaggy Thank you! I've posted a few challenges, but never been good enough to golf
– Rushabh Mehta
Aug 17 at 22:32
@Shaggy Thank you! I've posted a few challenges, but never been good enough to golf
– Rushabh Mehta
Aug 17 at 22:32
In that case, then, welcome to Golf! :) I'm not a Python guy but I'm pretty sure
M**2 can be replaced with M*M.– Shaggy
Aug 17 at 22:36
In that case, then, welcome to Golf! :) I'm not a Python guy but I'm pretty sure
M**2 can be replaced with M*M.– Shaggy
Aug 17 at 22:36
@Shaggy Thank you! Will fix right now
– Rushabh Mehta
Aug 17 at 22:37
@Shaggy Thank you! Will fix right now
– Rushabh Mehta
Aug 17 at 22:37
add a comment |Â
up vote
7
down vote
MATL, 15 bytes
X>ttq*QwoEqGd*+
Try it online!
Collect and print as a matrix
How?
Edit: Same technique as @Doorknob's answer, just arrived at differently.
The difference between the diagonal elements of the spiral is the arithmetic sequence $ 0, 2, 4, 6, 8, ldots $. Sum of $ n $ terms of this is $ n(n - 1) $ (by the usual AP formula). This sum, incremented by 1, gives the diagonal element at position $ (n, n) $.
Given $ (x, y) $, we find the maximum of these two, which is the "layer" of the spiral that this point belongs to. Then, we find the diagonal value of that layer as $ v = n(n-1) + 1 $. For even layers, the value at $ (x, y) $ is then $ v + x - y $, for odd layers $ v - x + y $.
X> % Get the maximum of the input coordinates, say n
ttq* % Duplicate that and multiply by n-1
Q % Add 1 to that. This is the diagonal value v at layer n
wo % Bring the original n on top and check if it's odd (1 or 0)
Eq % Change 1 or 0 to 1 or -1
Gd % Push input (x, y) again, get y - x
* % Multiply by 1 or -1
% For odd layers, no change. For even layers, y-x becomes x-y
+ % Add that to the diagonal value v
% Implicit output
Alternate 21 byte solution:
Pdt|Gs+ttqq*4/QJb^b*+
Try it online!
Collect and print as a matrix
From the above, we know that the function we want is
$$ f = m * (m - 1) + 1 + (-1)^m * (x - y) $$
where $ m = max(x, y) $.
Some basic calculation will show that one expression for max of two numbers is
$$ m = max(x, y) = fracx + y + abs(x - y)2 $$
Plugging one into another, we find that one alternate form for $ f $ is:
$$ f = (x-y)cdot i^k + frac14((k-2)cdot k) + 1 $$
where $ k = abs(x-y) + x + y $.
This is the function the solution implements.
answered Aug 17 at 21:07
sundar
4,656829
add a comment |Â
up vote
7
down vote
MATL, 15 bytes
X>ttq*QwoEqGd*+
Try it online!
Collect and print as a matrix
How?
Edit: Same technique as @Doorknob's answer, just arrived at differently.
The difference between the diagonal elements of the spiral is the arithmetic sequence $ 0, 2, 4, 6, 8, ldots $. Sum of $ n $ terms of this is $ n(n - 1) $ (by the usual AP formula). This sum, incremented by 1, gives the diagonal element at position $ (n, n) $.
Given $ (x, y) $, we find the maximum of these two, which is the "layer" of the spiral that this point belongs to. Then, we find the diagonal value of that layer as $ v = n(n-1) + 1 $. For even layers, the value at $ (x, y) $ is then $ v + x - y $, for odd layers $ v - x + y $.
X> % Get the maximum of the input coordinates, say n
ttq* % Duplicate that and multiply by n-1
Q % Add 1 to that. This is the diagonal value v at layer n
wo % Bring the original n on top and check if it's odd (1 or 0)
Eq % Change 1 or 0 to 1 or -1
Gd % Push input (x, y) again, get y - x
* % Multiply by 1 or -1
% For odd layers, no change. For even layers, y-x becomes x-y
+ % Add that to the diagonal value v
% Implicit output
Alternate 21 byte solution:
Pdt|Gs+ttqq*4/QJb^b*+
Try it online!
Collect and print as a matrix
From the above, we know that the function we want is
$$ f = m * (m - 1) + 1 + (-1)^m * (x - y) $$
where $ m = max(x, y) $.
Some basic calculation will show that one expression for max of two numbers is
$$ m = max(x, y) = fracx + y + abs(x - y)2 $$
Plugging one into another, we find that one alternate form for $ f $ is:
$$ f = (x-y)cdot i^k + frac14((k-2)cdot k) + 1 $$
where $ k = abs(x-y) + x + y $.
This is the function the solution implements.
answered Aug 17 at 21:07
sundar
4,656829
add a comment |Â
up vote
7
down vote
up vote
7
down vote
MATL, 15 bytes
X>ttq*QwoEqGd*+
Try it online!
Collect and print as a matrix
How?
Edit: Same technique as @Doorknob's answer, just arrived at differently.
The difference between the diagonal elements of the spiral is the arithmetic sequence $ 0, 2, 4, 6, 8, ldots $. Sum of $ n $ terms of this is $ n(n - 1) $ (by the usual AP formula). This sum, incremented by 1, gives the diagonal element at position $ (n, n) $.
Given $ (x, y) $, we find the maximum of these two, which is the "layer" of the spiral that this point belongs to. Then, we find the diagonal value of that layer as $ v = n(n-1) + 1 $. For even layers, the value at $ (x, y) $ is then $ v + x - y $, for odd layers $ v - x + y $.
X> % Get the maximum of the input coordinates, say n
ttq* % Duplicate that and multiply by n-1
Q % Add 1 to that. This is the diagonal value v at layer n
wo % Bring the original n on top and check if it's odd (1 or 0)
Eq % Change 1 or 0 to 1 or -1
Gd % Push input (x, y) again, get y - x
* % Multiply by 1 or -1
% For odd layers, no change. For even layers, y-x becomes x-y
+ % Add that to the diagonal value v
% Implicit output
Alternate 21 byte solution:
Pdt|Gs+ttqq*4/QJb^b*+
Try it online!
Collect and print as a matrix
From the above, we know that the function we want is
$$ f = m * (m - 1) + 1 + (-1)^m * (x - y) $$
where $ m = max(x, y) $.
Some basic calculation will show that one expression for max of two numbers is
$$ m = max(x, y) = fracx + y + abs(x - y)2 $$
Plugging one into another, we find that one alternate form for $ f $ is:
$$ f = (x-y)cdot i^k + frac14((k-2)cdot k) + 1 $$
where $ k = abs(x-y) + x + y $.
This is the function the solution implements.
answered Aug 17 at 21:07
sundar
4,656829
MATL, 15 bytes
X>ttq*QwoEqGd*+
Try it online!
Collect and print as a matrix
How?
Edit: Same technique as @Doorknob's answer, just arrived at differently.
The difference between the diagonal elements of the spiral is the arithmetic sequence $ 0, 2, 4, 6, 8, ldots $. Sum of $ n $ terms of this is $ n(n - 1) $ (by the usual AP formula). This sum, incremented by 1, gives the diagonal element at position $ (n, n) $.
Given $ (x, y) $, we find the maximum of these two, which is the "layer" of the spiral that this point belongs to. Then, we find the diagonal value of that layer as $ v = n(n-1) + 1 $. For even layers, the value at $ (x, y) $ is then $ v + x - y $, for odd layers $ v - x + y $.
X> % Get the maximum of the input coordinates, say n
ttq* % Duplicate that and multiply by n-1
Q % Add 1 to that. This is the diagonal value v at layer n
wo % Bring the original n on top and check if it's odd (1 or 0)
Eq % Change 1 or 0 to 1 or -1
Gd % Push input (x, y) again, get y - x
* % Multiply by 1 or -1
% For odd layers, no change. For even layers, y-x becomes x-y
+ % Add that to the diagonal value v
% Implicit output
Alternate 21 byte solution:
Pdt|Gs+ttqq*4/QJb^b*+
Try it online!
Collect and print as a matrix
From the above, we know that the function we want is
$$ f = m * (m - 1) + 1 + (-1)^m * (x - y) $$
where $ m = max(x, y) $.
Some basic calculation will show that one expression for max of two numbers is
$$ m = max(x, y) = fracx + y + abs(x - y)2 $$
Plugging one into another, we find that one alternate form for $ f $ is:
$$ f = (x-y)cdot i^k + frac14((k-2)cdot k) + 1 $$
where $ k = abs(x-y) + x + y $.
This is the function the solution implements.
answered Aug 17 at 21:07
sundar
4,656829
edited Aug 18 at 0:51
answered Aug 17 at 21:07
sundar
4,656829
answered Aug 17 at 21:07
sundar
4,656829
answered Aug 17 at 21:07
sundar
4,656829
4,656829
add a comment |Â
add a comment |Â
up vote
5
down vote
Japt, 16 bytes
Adapted from Doorknob's solution over a few beers.
wV
nU²ÒNr"n-"gUv
Try it
Explanation
:Implicit input of integers U=x and V=y
wV :Maximum of U & V
n :Reassign to U
U² :U squared
Ò :-~
"n-" :Literal string
Uv :Is U divisible by 2? Return 0 or 1
g :Get the character in the string at that index
Nr :Reduce the array of inputs by that, where n is inverse subtraction (XnY = Y-X)
n :Subtract U from the result of the above
answered Aug 17 at 22:26
Shaggy
16.2k21559
add a comment |Â
up vote
5
down vote
Japt, 16 bytes
Adapted from Doorknob's solution over a few beers.
wV
nU²ÒNr"n-"gUv
Try it
Explanation
:Implicit input of integers U=x and V=y
wV :Maximum of U & V
n :Reassign to U
U² :U squared
Ò :-~
"n-" :Literal string
Uv :Is U divisible by 2? Return 0 or 1
g :Get the character in the string at that index
Nr :Reduce the array of inputs by that, where n is inverse subtraction (XnY = Y-X)
n :Subtract U from the result of the above
answered Aug 17 at 22:26
Shaggy
16.2k21559
add a comment |Â
up vote
5
down vote
up vote
5
down vote
Japt, 16 bytes
Adapted from Doorknob's solution over a few beers.
wV
nU²ÒNr"n-"gUv
Try it
Explanation
:Implicit input of integers U=x and V=y
wV :Maximum of U & V
n :Reassign to U
U² :U squared
Ò :-~
"n-" :Literal string
Uv :Is U divisible by 2? Return 0 or 1
g :Get the character in the string at that index
Nr :Reduce the array of inputs by that, where n is inverse subtraction (XnY = Y-X)
n :Subtract U from the result of the above
answered Aug 17 at 22:26
Shaggy
16.2k21559
Japt, 16 bytes
Adapted from Doorknob's solution over a few beers.
wV
nU²ÒNr"n-"gUv
Try it
Explanation
:Implicit input of integers U=x and V=y
wV :Maximum of U & V
n :Reassign to U
U² :U squared
Ò :-~
"n-" :Literal string
Uv :Is U divisible by 2? Return 0 or 1
g :Get the character in the string at that index
Nr :Reduce the array of inputs by that, where n is inverse subtraction (XnY = Y-X)
n :Subtract U from the result of the above
answered Aug 17 at 22:26
Shaggy
16.2k21559
edited Aug 22 at 10:21
answered Aug 17 at 22:26
Shaggy
16.2k21559
answered Aug 17 at 22:26
Shaggy
16.2k21559
answered Aug 17 at 22:26
Shaggy
16.2k21559
16.2k21559
add a comment |Â
add a comment |Â
up vote
3
down vote
Pyth, 20 bytes
A~Qh.MZQh-+*-GH^_1Q*
Test suite
An almost literal translation of Rushabh Mehta's answer.
Explanation:
A~Qh.MZQh-+*-GH^_1Q* | Full code
A~Qh.MZQh-+*-GH^_1Q*QQQ | Code with implicit variables filled
| Assign Q as the evaluated input (implicit)
A | Assign [G,H] as
~Q | Q, then assign Q as
h.MZQ | Q's maximal value.
| Print (implicit)
h-+*-GH^_1Q*QQQ | (G-H)*(-1)^Q+Q*Q-Q+1
answered Aug 18 at 2:59
hakr14
1,03529
add a comment |Â
up vote
3
down vote
Pyth, 20 bytes
A~Qh.MZQh-+*-GH^_1Q*
Test suite
An almost literal translation of Rushabh Mehta's answer.
Explanation:
A~Qh.MZQh-+*-GH^_1Q* | Full code
A~Qh.MZQh-+*-GH^_1Q*QQQ | Code with implicit variables filled
| Assign Q as the evaluated input (implicit)
A | Assign [G,H] as
~Q | Q, then assign Q as
h.MZQ | Q's maximal value.
| Print (implicit)
h-+*-GH^_1Q*QQQ | (G-H)*(-1)^Q+Q*Q-Q+1
answered Aug 18 at 2:59
hakr14
1,03529
add a comment |Â
up vote
3
down vote
up vote
3
down vote
Pyth, 20 bytes
A~Qh.MZQh-+*-GH^_1Q*
Test suite
An almost literal translation of Rushabh Mehta's answer.
Explanation:
A~Qh.MZQh-+*-GH^_1Q* | Full code
A~Qh.MZQh-+*-GH^_1Q*QQQ | Code with implicit variables filled
| Assign Q as the evaluated input (implicit)
A | Assign [G,H] as
~Q | Q, then assign Q as
h.MZQ | Q's maximal value.
| Print (implicit)
h-+*-GH^_1Q*QQQ | (G-H)*(-1)^Q+Q*Q-Q+1
answered Aug 18 at 2:59
hakr14
1,03529
Pyth, 20 bytes
A~Qh.MZQh-+*-GH^_1Q*
Test suite
An almost literal translation of Rushabh Mehta's answer.
Explanation:
A~Qh.MZQh-+*-GH^_1Q* | Full code
A~Qh.MZQh-+*-GH^_1Q*QQQ | Code with implicit variables filled
| Assign Q as the evaluated input (implicit)
A | Assign [G,H] as
~Q | Q, then assign Q as
h.MZQ | Q's maximal value.
| Print (implicit)
h-+*-GH^_1Q*QQQ | (G-H)*(-1)^Q+Q*Q-Q+1
answered Aug 18 at 2:59
hakr14
1,03529
edited Aug 20 at 22:40
answered Aug 18 at 2:59
hakr14
1,03529
answered Aug 18 at 2:59
hakr14
1,03529
answered Aug 18 at 2:59
hakr14
1,03529
1,03529
add a comment |Â
add a comment |Â
up vote
2
down vote
Jelly, 13 bytes
»Ḃ-*×_‘+»×’$¥
Try it online!
Uses Doorknob's method. Way too long.
answered Aug 17 at 16:40
Mr. Xcoder
30.2k757193
Alternative:»á¸‚-*×_‘+»²_»Ê‹
– Mr. Xcoder
Aug 17 at 16:41
add a comment |Â
up vote
2
down vote
Jelly, 13 bytes
»Ḃ-*×_‘+»×’$¥
Try it online!
Uses Doorknob's method. Way too long.
answered Aug 17 at 16:40
Mr. Xcoder
30.2k757193
Alternative:»á¸‚-*×_‘+»²_»Ê‹
– Mr. Xcoder
Aug 17 at 16:41
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Jelly, 13 bytes
»Ḃ-*×_‘+»×’$¥
Try it online!
Uses Doorknob's method. Way too long.
answered Aug 17 at 16:40
Mr. Xcoder
30.2k757193
Jelly, 13 bytes
»Ḃ-*×_‘+»×’$¥
Try it online!
Uses Doorknob's method. Way too long.
answered Aug 17 at 16:40
Mr. Xcoder
30.2k757193
edited Aug 18 at 0:00
answered Aug 17 at 16:40
Mr. Xcoder
30.2k757193
answered Aug 17 at 16:40
Mr. Xcoder
30.2k757193
answered Aug 17 at 16:40
Mr. Xcoder
30.2k757193
30.2k757193
Alternative:»á¸‚-*×_‘+»²_»Ê‹
– Mr. Xcoder
Aug 17 at 16:41
add a comment |Â
Alternative:»á¸‚-*×_‘+»²_»Ê‹
– Mr. Xcoder
Aug 17 at 16:41
Alternative:
»á¸‚-*×_‘+»²_»Ê‹– Mr. Xcoder
Aug 17 at 16:41
Alternative:
»á¸‚-*×_‘+»²_»Ê‹– Mr. Xcoder
Aug 17 at 16:41
add a comment |Â
up vote
2
down vote
Jelly, 13 12 bytes
ṀḂḤ’×I+²_’ṀƲ
Try it online!
Computes the diagonal term with ²_’Ṁ and adds/subtracts to the correct index value with ṀḂḤ’×I.
answered Aug 18 at 2:48
dylnan
3,4982526
add a comment |Â
up vote
2
down vote
Jelly, 13 12 bytes
ṀḂḤ’×I+²_’ṀƲ
Try it online!
Computes the diagonal term with ²_’Ṁ and adds/subtracts to the correct index value with ṀḂḤ’×I.
answered Aug 18 at 2:48
dylnan
3,4982526
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Jelly, 13 12 bytes
ṀḂḤ’×I+²_’ṀƲ
Try it online!
Computes the diagonal term with ²_’Ṁ and adds/subtracts to the correct index value with ṀḂḤ’×I.
answered Aug 18 at 2:48
dylnan
3,4982526
Jelly, 13 12 bytes
ṀḂḤ’×I+²_’ṀƲ
Try it online!
Computes the diagonal term with ²_’Ṁ and adds/subtracts to the correct index value with ṀḂḤ’×I.
answered Aug 18 at 2:48
dylnan
3,4982526
edited Aug 18 at 17:02
answered Aug 18 at 2:48
dylnan
3,4982526
answered Aug 18 at 2:48
dylnan
3,4982526
answered Aug 18 at 2:48
dylnan
3,4982526
3,4982526
add a comment |Â
add a comment |Â
up vote
2
down vote
Brain-Flak, 76 bytes
(((<>))<>[(())]<([()])<>>)<>(()([()])()<><([])><><><>)
Try it online!
answered Aug 18 at 17:08
Nitrodon
6,3011620
add a comment |Â
up vote
2
down vote
Brain-Flak, 76 bytes
(((<>))<>[(())]<([()])<>>)<>(()([()])()<><([])><><><>)
Try it online!
answered Aug 18 at 17:08
Nitrodon
6,3011620
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Brain-Flak, 76 bytes
(((<>))<>[(())]<([()])<>>)<>(()([()])()<><([])><><><>)
Try it online!
answered Aug 18 at 17:08
Nitrodon
6,3011620
Brain-Flak, 76 bytes
(((<>))<>[(())]<([()])<>>)<>(()([()])()<><([])><><><>)
Try it online!
answered Aug 18 at 17:08
Nitrodon
6,3011620
answered Aug 18 at 17:08
Nitrodon
6,3011620
answered Aug 18 at 17:08
Nitrodon
6,3011620
answered Aug 18 at 17:08
Nitrodon
6,3011620
6,3011620
add a comment |Â
add a comment |Â
up vote
2
down vote
05AB1E, 12 11 bytes
ZÃÂ<*>Ã…Â GR}Â¥+
-1 byte thanks to @Emigna changing Èi to G.
Port of @sundar's MATL answer, so make sure to upvote him!
Try it online or verify all test cases.
Explanation:
Z # Get the maximum of the (implicit) input-coordinate
# i.e. [4,5] → 5
à# Triplicate this maximum
< # Decrease it by 1
# i.e. 5 - 1 → 4
* # Multiply it
# i.e. 5 * 4 → 20
> # Increase it by 1
# i.e. 20 + 1 → 21
Ã…Â # Triple swap the top threes values on the stack (a,b,c to c,a,b)
# i.e. [4,5], 5, 21 → 21, [4,5], 5
G } # Loop n amount of times
R # Reverse the input-coordinate each iteration
# i.e. 5 and [4,5] → [5,4]→[4,5]→[5,4]→[4,5] → [5,4]
Â¥ # Calculate the delta of the coordinate
# [5,4] → [1]
+ # And add it to the earlier calculate value (output the result implicitly)
# 21 + [1] → [22]
answered Aug 20 at 8:37
Kevin Cruijssen
29.4k549162
1
Èicould beG.
– Emigna
Aug 20 at 10:39
@Emigna Oh smart, thanks! :D
– Kevin Cruijssen
Aug 20 at 11:01
add a comment |Â
up vote
2
down vote
05AB1E, 12 11 bytes
ZÃÂ<*>Ã…Â GR}Â¥+
-1 byte thanks to @Emigna changing Èi to G.
Port of @sundar's MATL answer, so make sure to upvote him!
Try it online or verify all test cases.
Explanation:
Z # Get the maximum of the (implicit) input-coordinate
# i.e. [4,5] → 5
à# Triplicate this maximum
< # Decrease it by 1
# i.e. 5 - 1 → 4
* # Multiply it
# i.e. 5 * 4 → 20
> # Increase it by 1
# i.e. 20 + 1 → 21
Ã…Â # Triple swap the top threes values on the stack (a,b,c to c,a,b)
# i.e. [4,5], 5, 21 → 21, [4,5], 5
G } # Loop n amount of times
R # Reverse the input-coordinate each iteration
# i.e. 5 and [4,5] → [5,4]→[4,5]→[5,4]→[4,5] → [5,4]
Â¥ # Calculate the delta of the coordinate
# [5,4] → [1]
+ # And add it to the earlier calculate value (output the result implicitly)
# 21 + [1] → [22]
answered Aug 20 at 8:37
Kevin Cruijssen
29.4k549162
1
Èicould beG.
– Emigna
Aug 20 at 10:39
@Emigna Oh smart, thanks! :D
– Kevin Cruijssen
Aug 20 at 11:01
add a comment |Â
up vote
2
down vote
up vote
2
down vote
05AB1E, 12 11 bytes
ZÃÂ<*>Ã…Â GR}Â¥+
-1 byte thanks to @Emigna changing Èi to G.
Port of @sundar's MATL answer, so make sure to upvote him!
Try it online or verify all test cases.
Explanation:
Z # Get the maximum of the (implicit) input-coordinate
# i.e. [4,5] → 5
à# Triplicate this maximum
< # Decrease it by 1
# i.e. 5 - 1 → 4
* # Multiply it
# i.e. 5 * 4 → 20
> # Increase it by 1
# i.e. 20 + 1 → 21
Ã…Â # Triple swap the top threes values on the stack (a,b,c to c,a,b)
# i.e. [4,5], 5, 21 → 21, [4,5], 5
G } # Loop n amount of times
R # Reverse the input-coordinate each iteration
# i.e. 5 and [4,5] → [5,4]→[4,5]→[5,4]→[4,5] → [5,4]
Â¥ # Calculate the delta of the coordinate
# [5,4] → [1]
+ # And add it to the earlier calculate value (output the result implicitly)
# 21 + [1] → [22]
answered Aug 20 at 8:37
Kevin Cruijssen
29.4k549162
05AB1E, 12 11 bytes
ZÃÂ<*>Ã…Â GR}Â¥+
-1 byte thanks to @Emigna changing Èi to G.
Port of @sundar's MATL answer, so make sure to upvote him!
Try it online or verify all test cases.
Explanation:
Z # Get the maximum of the (implicit) input-coordinate
# i.e. [4,5] → 5
à# Triplicate this maximum
< # Decrease it by 1
# i.e. 5 - 1 → 4
* # Multiply it
# i.e. 5 * 4 → 20
> # Increase it by 1
# i.e. 20 + 1 → 21
Ã…Â # Triple swap the top threes values on the stack (a,b,c to c,a,b)
# i.e. [4,5], 5, 21 → 21, [4,5], 5
G } # Loop n amount of times
R # Reverse the input-coordinate each iteration
# i.e. 5 and [4,5] → [5,4]→[4,5]→[5,4]→[4,5] → [5,4]
Â¥ # Calculate the delta of the coordinate
# [5,4] → [1]
+ # And add it to the earlier calculate value (output the result implicitly)
# 21 + [1] → [22]
answered Aug 20 at 8:37
Kevin Cruijssen
29.4k549162
edited Aug 20 at 16:34
answered Aug 20 at 8:37
Kevin Cruijssen
29.4k549162
answered Aug 20 at 8:37
Kevin Cruijssen
29.4k549162
answered Aug 20 at 8:37
Kevin Cruijssen
29.4k549162
29.4k549162
1
Èicould beG.
– Emigna
Aug 20 at 10:39
@Emigna Oh smart, thanks! :D
– Kevin Cruijssen
Aug 20 at 11:01
add a comment |Â
1
Èicould beG.
– Emigna
Aug 20 at 10:39
@Emigna Oh smart, thanks! :D
– Kevin Cruijssen
Aug 20 at 11:01
1
1
Èi could be G.– Emigna
Aug 20 at 10:39
Èi could be G.– Emigna
Aug 20 at 10:39
@Emigna Oh smart, thanks! :D
– Kevin Cruijssen
Aug 20 at 11:01
@Emigna Oh smart, thanks! :D
– Kevin Cruijssen
Aug 20 at 11:01
add a comment |Â
up vote
0
down vote
Pascal (FPC), 90 bytes
uses math;var x,y,z:word;begin read(x,y);z:=max(x,y);write(z*z-z+1+(1and z*2-1)*(y-x))end.
Try it online!
Port of Doorknob's answer, but sundar's answer gave me idea for z mod 2*2-1 which I transformed into 1and z*2-1 to remove space.
answered Aug 17 at 22:38
AlexRacer
57928
add a comment |Â
up vote
0
down vote
Pascal (FPC), 90 bytes
uses math;var x,y,z:word;begin read(x,y);z:=max(x,y);write(z*z-z+1+(1and z*2-1)*(y-x))end.
Try it online!
Port of Doorknob's answer, but sundar's answer gave me idea for z mod 2*2-1 which I transformed into 1and z*2-1 to remove space.
answered Aug 17 at 22:38
AlexRacer
57928
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Pascal (FPC), 90 bytes
uses math;var x,y,z:word;begin read(x,y);z:=max(x,y);write(z*z-z+1+(1and z*2-1)*(y-x))end.
Try it online!
Port of Doorknob's answer, but sundar's answer gave me idea for z mod 2*2-1 which I transformed into 1and z*2-1 to remove space.
answered Aug 17 at 22:38
AlexRacer
57928
Pascal (FPC), 90 bytes
uses math;var x,y,z:word;begin read(x,y);z:=max(x,y);write(z*z-z+1+(1and z*2-1)*(y-x))end.
Try it online!
Port of Doorknob's answer, but sundar's answer gave me idea for z mod 2*2-1 which I transformed into 1and z*2-1 to remove space.
answered Aug 17 at 22:38
AlexRacer
57928
edited Aug 17 at 23:42
answered Aug 17 at 22:38
AlexRacer
57928
answered Aug 17 at 22:38
AlexRacer
57928
answered Aug 17 at 22:38
AlexRacer
57928
57928
add a comment |Â
add a comment |Â
up vote
0
down vote
Mathematica 34 bytes
x = 5, 8;
so:
m = Max[x];
Subtract @@ x (-1)^m + m^2 - m + 1
(*
54
*)
answered Aug 18 at 0:31
David G. Stork
1637
add a comment |Â
up vote
0
down vote
Mathematica 34 bytes
x = 5, 8;
so:
m = Max[x];
Subtract @@ x (-1)^m + m^2 - m + 1
(*
54
*)
answered Aug 18 at 0:31
David G. Stork
1637
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Mathematica 34 bytes
x = 5, 8;
so:
m = Max[x];
Subtract @@ x (-1)^m + m^2 - m + 1
(*
54
*)
answered Aug 18 at 0:31
David G. Stork
1637
Mathematica 34 bytes
x = 5, 8;
so:
m = Max[x];
Subtract @@ x (-1)^m + m^2 - m + 1
(*
54
*)
answered Aug 18 at 0:31
David G. Stork
1637
answered Aug 18 at 0:31
David G. Stork
1637
answered Aug 18 at 0:31
David G. Stork
1637
answered Aug 18 at 0:31
David G. Stork
1637
1637
add a comment |Â
add a comment |Â
up vote
0
down vote
Julia 1.0, 35 bytes
xy=(m=max(x,y))*~-m+1+(-1)^m*(x-y)
Try it online!
answered Aug 18 at 8:12
sundar
4,656829
add a comment |Â
up vote
0
down vote
Julia 1.0, 35 bytes
xy=(m=max(x,y))*~-m+1+(-1)^m*(x-y)
Try it online!
answered Aug 18 at 8:12
sundar
4,656829
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Julia 1.0, 35 bytes
xy=(m=max(x,y))*~-m+1+(-1)^m*(x-y)
Try it online!
answered Aug 18 at 8:12
sundar
4,656829
Julia 1.0, 35 bytes
xy=(m=max(x,y))*~-m+1+(-1)^m*(x-y)
Try it online!
answered Aug 18 at 8:12
sundar
4,656829
answered Aug 18 at 8:12
sundar
4,656829
answered Aug 18 at 8:12
sundar
4,656829
answered Aug 18 at 8:12
sundar
4,656829
4,656829
add a comment |Â
add a comment |Â
up vote
0
down vote
JavaScript (ES6), 46 bytes
f=(r,c,x)=>r<c?f(c,r,1):r%2-!x?r*r-c+1:--r*r+c
answered Aug 19 at 11:36
James
1313
add a comment |Â
up vote
0
down vote
JavaScript (ES6), 46 bytes
f=(r,c,x)=>r<c?f(c,r,1):r%2-!x?r*r-c+1:--r*r+c
answered Aug 19 at 11:36
James
1313
add a comment |Â
up vote
0
down vote
up vote
0
down vote
JavaScript (ES6), 46 bytes
f=(r,c,x)=>r<c?f(c,r,1):r%2-!x?r*r-c+1:--r*r+c
answered Aug 19 at 11:36
James
1313
JavaScript (ES6), 46 bytes
f=(r,c,x)=>r<c?f(c,r,1):r%2-!x?r*r-c+1:--r*r+c
answered Aug 19 at 11:36
James
1313
answered Aug 19 at 11:36
James
1313
answered Aug 19 at 11:36
James
1313
answered Aug 19 at 11:36
James
1313
1313
add a comment |Â
add a comment |Â
up vote
0
down vote
Java (JDK 10), 39 bytes
x->y->(y-x)*((y=x>y?x:y)%2*2-1)+y*y-y+1
Try it online!
Credits
- Port of Doorknob's answer.
answered Aug 20 at 11:09
Olivier Grégoire
7,48311739
add a comment |Â
up vote
0
down vote
Java (JDK 10), 39 bytes
x->y->(y-x)*((y=x>y?x:y)%2*2-1)+y*y-y+1
Try it online!
Credits
- Port of Doorknob's answer.
answered Aug 20 at 11:09
Olivier Grégoire
7,48311739
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Java (JDK 10), 39 bytes
x->y->(y-x)*((y=x>y?x:y)%2*2-1)+y*y-y+1
Try it online!
Credits
- Port of Doorknob's answer.
answered Aug 20 at 11:09
Olivier Grégoire
7,48311739
Java (JDK 10), 39 bytes
x->y->(y-x)*((y=x>y?x:y)%2*2-1)+y*y-y+1
Try it online!
Credits
- Port of Doorknob's answer.
answered Aug 20 at 11:09
Olivier Grégoire
7,48311739
answered Aug 20 at 11:09
Olivier Grégoire
7,48311739
answered Aug 20 at 11:09
Olivier Grégoire
7,48311739
answered Aug 20 at 11:09
Olivier Grégoire
7,48311739
7,48311739
add a comment |Â
add a comment |Â
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1
It looks like your inputs are 1 indexed (coordinates start at 1,1) (although this has to be intuited from the test cases) can we use 0 indexing (coordinates start at 0,0)?
– W W
Aug 17 at 16:26
4
What is the reasoning for this?
– W W
Aug 17 at 16:30
3
Nice challenge, but I don't really like that you force it to be 1-indexed... +1 anyway...
– Stewie Griffin
Aug 18 at 8:30
7
I think it's absolutely fine for the coordinates to start at (1, 1), especially if the program is posted that way on CSES, and the OP doesn't need to justify this. I think golfers here are getting a little too used to somewhat arbitrary freedoms.
– Lynn
Aug 18 at 12:57
2
@Lynn I second that
– Agile_Eagle
Aug 18 at 12:58