Hyperoperation Golfing

Clash Royale CLAN TAG#URR8PPP

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Introduction

In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations) that starts with the unary operation of successor (n = 0), then continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3), after which the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity.

_(Source)

---

Challenge

Your challenge is code this sequence, given 3 inputs, n, a, and b, code a function such that $$displaystyle H_n(a,b)=begincasesb+1&textif n=0\a&textif n=1text and b=0\0&textif n=2text and b=0\1&textif ngeq 3text and b=0\H_n-1(a,H_n(a,b-1))&textotherwiseendcases$$
_{(Also from Wikipedia.)}

---

Input

3 positive decimal integers, n, a, and b, taken from STDIN, function or command line arguments, in any order. Make sure to specify this in your answer

---

Output

The result of applying $H_n(a,b)$ with the inputs

---

Example inputs and outputs

Input: 0, 6, 3
Output: 4

---

Input: 4 5 2
Output: 3125

---

Restrictions

• Your program/function should take input in base 10


• Don't use any built in function that already provides H(n, a, b)


• Standard loopholes apply

---

This is code-golf, so shortest code in bytes wins!

code-golf math sequence

share|improve this question

edited 33 mins ago

asked 59 mins ago

FireCubez

615

• 
  
  
  

  
  

  
  
  
  
  
  

  
  @JoKing Does it? I'll have a read
  – FireCubez
  54 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Arnauld will do.
  – FireCubez
  45 mins ago
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  <s>Possible duplicate of Evaluate the nth hyperoperation</s>
  – user202729
  43 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  (not really. That one "bans builtins" because it's from '13; plus, cumbersome input/output format)
  – user202729
  42 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dzaima fixed it.
  – FireCubez
  31 mins ago
  

  
  
  
  

add a comment | 

up vote
4
down vote

favorite

Introduction

In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations) that starts with the unary operation of successor (n = 0), then continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3), after which the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity.

_(Source)

---

Challenge

Your challenge is code this sequence, given 3 inputs, n, a, and b, code a function such that $$displaystyle H_n(a,b)=begincasesb+1&textif n=0\a&textif n=1text and b=0\0&textif n=2text and b=0\1&textif ngeq 3text and b=0\H_n-1(a,H_n(a,b-1))&textotherwiseendcases$$
_{(Also from Wikipedia.)}

---

Input

3 positive decimal integers, n, a, and b, taken from STDIN, function or command line arguments, in any order. Make sure to specify this in your answer

---

Output

The result of applying $H_n(a,b)$ with the inputs

---

Example inputs and outputs

Input: 0, 6, 3
Output: 4

---

Input: 4 5 2
Output: 3125

---

Restrictions

• Your program/function should take input in base 10


• Don't use any built in function that already provides H(n, a, b)


• Standard loopholes apply

---

This is code-golf, so shortest code in bytes wins!

code-golf math sequence

share|improve this question

edited 33 mins ago

asked 59 mins ago

FireCubez

615

• 
  
  
  

  
  

  
  
  
  
  
  

  
  @JoKing Does it? I'll have a read
  – FireCubez
  54 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Arnauld will do.
  – FireCubez
  45 mins ago
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  <s>Possible duplicate of Evaluate the nth hyperoperation</s>
  – user202729
  43 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  (not really. That one "bans builtins" because it's from '13; plus, cumbersome input/output format)
  – user202729
  42 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dzaima fixed it.
  – FireCubez
  31 mins ago
  

  
  
  
  

add a comment | 

up vote
4
down vote

favorite

up vote
4
down vote

favorite

Introduction

In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations) that starts with the unary operation of successor (n = 0), then continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3), after which the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity.

_(Source)

---

Challenge

Your challenge is code this sequence, given 3 inputs, n, a, and b, code a function such that $$displaystyle H_n(a,b)=begincasesb+1&textif n=0\a&textif n=1text and b=0\0&textif n=2text and b=0\1&textif ngeq 3text and b=0\H_n-1(a,H_n(a,b-1))&textotherwiseendcases$$
_{(Also from Wikipedia.)}

---

Input

3 positive decimal integers, n, a, and b, taken from STDIN, function or command line arguments, in any order. Make sure to specify this in your answer

---

Output

The result of applying $H_n(a,b)$ with the inputs

---

Example inputs and outputs

Input: 0, 6, 3
Output: 4

---

Input: 4 5 2
Output: 3125

---

Restrictions

• Your program/function should take input in base 10


• Don't use any built in function that already provides H(n, a, b)


• Standard loopholes apply

---

This is code-golf, so shortest code in bytes wins!

code-golf math sequence

share|improve this question

edited 33 mins ago

asked 59 mins ago

FireCubez

615

Introduction

In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations) that starts with the unary operation of successor (n = 0), then continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3), after which the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity.

_(Source)

---

Challenge

Your challenge is code this sequence, given 3 inputs, n, a, and b, code a function such that $$displaystyle H_n(a,b)=begincasesb+1&textif n=0\a&textif n=1text and b=0\0&textif n=2text and b=0\1&textif ngeq 3text and b=0\H_n-1(a,H_n(a,b-1))&textotherwiseendcases$$
_{(Also from Wikipedia.)}

---

Input

3 positive decimal integers, n, a, and b, taken from STDIN, function or command line arguments, in any order. Make sure to specify this in your answer

---

Output

The result of applying $H_n(a,b)$ with the inputs

---

Example inputs and outputs

Input: 0, 6, 3
Output: 4

---

Input: 4 5 2
Output: 3125

---

Restrictions

• Your program/function should take input in base 10


• Don't use any built in function that already provides H(n, a, b)


• Standard loopholes apply

---

This is code-golf, so shortest code in bytes wins!

code-golf math sequence

code-golf math sequence

share|improve this question

edited 33 mins ago

asked 59 mins ago

FireCubez

615

share|improve this question

edited 33 mins ago

asked 59 mins ago

FireCubez

615

share|improve this question

share|improve this question

edited 33 mins ago

edited 33 mins ago

edited 33 mins ago

asked 59 mins ago

FireCubez

615

asked 59 mins ago

FireCubez

615

asked 59 mins ago

FireCubez

615

615

• 
  
  
  

  
  

  
  
  
  
  
  

  
  @JoKing Does it? I'll have a read
  – FireCubez
  54 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Arnauld will do.
  – FireCubez
  45 mins ago
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  <s>Possible duplicate of Evaluate the nth hyperoperation</s>
  – user202729
  43 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  (not really. That one "bans builtins" because it's from '13; plus, cumbersome input/output format)
  – user202729
  42 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dzaima fixed it.
  – FireCubez
  31 mins ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  @JoKing Does it? I'll have a read
  – FireCubez
  54 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Arnauld will do.
  – FireCubez
  45 mins ago
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  <s>Possible duplicate of Evaluate the nth hyperoperation</s>
  – user202729
  43 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  (not really. That one "bans builtins" because it's from '13; plus, cumbersome input/output format)
  – user202729
  42 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dzaima fixed it.
  – FireCubez
  31 mins ago
  

  
  
  
  

@JoKing Does it? I'll have a read
– FireCubez
54 mins ago

@JoKing Does it? I'll have a read
– FireCubez
54 mins ago

@Arnauld will do.
– FireCubez
45 mins ago

@Arnauld will do.
– FireCubez
45 mins ago

3

3

<s>Possible duplicate of Evaluate the nth hyperoperation</s>
– user202729
43 mins ago

<s>Possible duplicate of Evaluate the nth hyperoperation</s>
– user202729
43 mins ago

(not really. That one "bans builtins" because it's from '13; plus, cumbersome input/output format)
– user202729
42 mins ago

(not really. That one "bans builtins" because it's from '13; plus, cumbersome input/output format)
– user202729
42 mins ago

@dzaima fixed it.
– FireCubez
31 mins ago

@dzaima fixed it.
– FireCubez
31 mins ago

add a comment | 

3 Answers
3

active

oldest

votes

up vote
2
down vote

JavaScript (ES6),  49  47 bytes

Takes input as (a)(b,n).

a=>g=(b,n)=>n*b?g(g(b-1,n),n-1):-~[b,a-1,-1][n]

Try it online!

Commented

a => // main function taking a
 g = (b, n) => // g = recursive function taking b and n
 n * b ? // if neither n nor b is equal to 0:
 g( // go recursive:
 g(b - 1, n), // b = g(b - 1, n)
 n - 1 // decrement n
 ) // end of recursive call
 : // else:
 -~[ // this is a leaf node:
 b, // return b + 1 if n = 0
 a - 1, // return (a - 1) + 1 = a if n = 1
 -1 // return -1 + 1 = 0 if n = 2
 ][n] // return -~undefined = 1 if n > 2

share|improve this answer

edited 43 secs ago

answered 36 mins ago

Arnauld

64.1k580270

add a comment | 

up vote
1
down vote

Dyalog APL, 35 bytes

⍺=0:⍵+1⋄⍵=0:⍺⍺⍵1⊃⍨3⌊⍺⋄(⍺-1)∇⍺∇⍵-1

Try it online!

share

answered 9 mins ago

dzaima

13.1k21652

add a comment | 

up vote
0
down vote

Elixir, 86 bytes

(assumes functions can take a reference to itself as an argument)

fn 0,_,b,_->b+1
1,a,0,_->a
2,_,0,_->0
_,_,0,_->1
n,a,b,f->f.(n-1,a,f.(n,a,b-1,f),f)end

Try it online!

share|improve this answer

answered 33 mins ago

Okx

12k27100

add a comment | 

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3 Answers
3

active

oldest

votes

3 Answers
3

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote

JavaScript (ES6),  49  47 bytes

Takes input as (a)(b,n).

a=>g=(b,n)=>n*b?g(g(b-1,n),n-1):-~[b,a-1,-1][n]

Try it online!

Commented

a => // main function taking a
 g = (b, n) => // g = recursive function taking b and n
 n * b ? // if neither n nor b is equal to 0:
 g( // go recursive:
 g(b - 1, n), // b = g(b - 1, n)
 n - 1 // decrement n
 ) // end of recursive call
 : // else:
 -~[ // this is a leaf node:
 b, // return b + 1 if n = 0
 a - 1, // return (a - 1) + 1 = a if n = 1
 -1 // return -1 + 1 = 0 if n = 2
 ][n] // return -~undefined = 1 if n > 2

share|improve this answer

edited 43 secs ago

answered 36 mins ago

Arnauld

64.1k580270

add a comment | 

up vote
2
down vote

JavaScript (ES6),  49  47 bytes

Takes input as (a)(b,n).

a=>g=(b,n)=>n*b?g(g(b-1,n),n-1):-~[b,a-1,-1][n]

Try it online!

Commented

a => // main function taking a
 g = (b, n) => // g = recursive function taking b and n
 n * b ? // if neither n nor b is equal to 0:
 g( // go recursive:
 g(b - 1, n), // b = g(b - 1, n)
 n - 1 // decrement n
 ) // end of recursive call
 : // else:
 -~[ // this is a leaf node:
 b, // return b + 1 if n = 0
 a - 1, // return (a - 1) + 1 = a if n = 1
 -1 // return -1 + 1 = 0 if n = 2
 ][n] // return -~undefined = 1 if n > 2

share|improve this answer

edited 43 secs ago

answered 36 mins ago

Arnauld

64.1k580270

add a comment | 

up vote
2
down vote

up vote
2
down vote

JavaScript (ES6),  49  47 bytes

Takes input as (a)(b,n).

a=>g=(b,n)=>n*b?g(g(b-1,n),n-1):-~[b,a-1,-1][n]

Try it online!

Commented

a => // main function taking a
 g = (b, n) => // g = recursive function taking b and n
 n * b ? // if neither n nor b is equal to 0:
 g( // go recursive:
 g(b - 1, n), // b = g(b - 1, n)
 n - 1 // decrement n
 ) // end of recursive call
 : // else:
 -~[ // this is a leaf node:
 b, // return b + 1 if n = 0
 a - 1, // return (a - 1) + 1 = a if n = 1
 -1 // return -1 + 1 = 0 if n = 2
 ][n] // return -~undefined = 1 if n > 2

share|improve this answer

edited 43 secs ago

answered 36 mins ago

Arnauld

64.1k580270

JavaScript (ES6),  49  47 bytes

Takes input as (a)(b,n).

a=>g=(b,n)=>n*b?g(g(b-1,n),n-1):-~[b,a-1,-1][n]

Try it online!

Commented

a => // main function taking a
 g = (b, n) => // g = recursive function taking b and n
 n * b ? // if neither n nor b is equal to 0:
 g( // go recursive:
 g(b - 1, n), // b = g(b - 1, n)
 n - 1 // decrement n
 ) // end of recursive call
 : // else:
 -~[ // this is a leaf node:
 b, // return b + 1 if n = 0
 a - 1, // return (a - 1) + 1 = a if n = 1
 -1 // return -1 + 1 = 0 if n = 2
 ][n] // return -~undefined = 1 if n > 2

share|improve this answer

edited 43 secs ago

answered 36 mins ago

Arnauld

64.1k580270

share|improve this answer

share|improve this answer

edited 43 secs ago

edited 43 secs ago

edited 43 secs ago

answered 36 mins ago

Arnauld

64.1k580270

answered 36 mins ago

Arnauld

64.1k580270

answered 36 mins ago

Arnauld

64.1k580270

64.1k580270

add a comment | 

add a comment | 

up vote
1
down vote

Dyalog APL, 35 bytes

⍺=0:⍵+1⋄⍵=0:⍺⍺⍵1⊃⍨3⌊⍺⋄(⍺-1)∇⍺∇⍵-1

Try it online!

share

answered 9 mins ago

dzaima

13.1k21652

add a comment | 

up vote
1
down vote

Dyalog APL, 35 bytes

⍺=0:⍵+1⋄⍵=0:⍺⍺⍵1⊃⍨3⌊⍺⋄(⍺-1)∇⍺∇⍵-1

Try it online!

share

answered 9 mins ago

dzaima

13.1k21652

add a comment | 

up vote
1
down vote

up vote
1
down vote

Dyalog APL, 35 bytes

⍺=0:⍵+1⋄⍵=0:⍺⍺⍵1⊃⍨3⌊⍺⋄(⍺-1)∇⍺∇⍵-1

Try it online!

share

answered 9 mins ago

dzaima

13.1k21652

Dyalog APL, 35 bytes

⍺=0:⍵+1⋄⍵=0:⍺⍺⍵1⊃⍨3⌊⍺⋄(⍺-1)∇⍺∇⍵-1

Try it online!

share

answered 9 mins ago

dzaima

13.1k21652

share

share

answered 9 mins ago

dzaima

13.1k21652

answered 9 mins ago

dzaima

13.1k21652

answered 9 mins ago

dzaima

13.1k21652

13.1k21652

add a comment | 

add a comment | 

up vote
0
down vote

Elixir, 86 bytes

(assumes functions can take a reference to itself as an argument)

fn 0,_,b,_->b+1
1,a,0,_->a
2,_,0,_->0
_,_,0,_->1
n,a,b,f->f.(n-1,a,f.(n,a,b-1,f),f)end

Try it online!

share|improve this answer

answered 33 mins ago

Okx

12k27100

add a comment | 

up vote
0
down vote

Elixir, 86 bytes

(assumes functions can take a reference to itself as an argument)

fn 0,_,b,_->b+1
1,a,0,_->a
2,_,0,_->0
_,_,0,_->1
n,a,b,f->f.(n-1,a,f.(n,a,b-1,f),f)end

Try it online!

share|improve this answer

answered 33 mins ago

Okx

12k27100

add a comment | 

up vote
0
down vote

up vote
0
down vote

Elixir, 86 bytes

(assumes functions can take a reference to itself as an argument)

fn 0,_,b,_->b+1
1,a,0,_->a
2,_,0,_->0
_,_,0,_->1
n,a,b,f->f.(n-1,a,f.(n,a,b-1,f),f)end

Try it online!

share|improve this answer

answered 33 mins ago

Okx

12k27100

Elixir, 86 bytes

(assumes functions can take a reference to itself as an argument)

fn 0,_,b,_->b+1
1,a,0,_->a
2,_,0,_->0
_,_,0,_->1
n,a,b,f->f.(n-1,a,f.(n,a,b-1,f),f)end

Try it online!

share|improve this answer

answered 33 mins ago

Okx

12k27100

share|improve this answer

share|improve this answer

answered 33 mins ago

Okx

12k27100

answered 33 mins ago

Okx

12k27100

answered 33 mins ago

Okx

12k27100

12k27100

add a comment | 

add a comment | 

 

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