Determine the Widest Valley

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Imagine we get a slice of some mountainous region, this would result in a shape similar to this:



4 _
3 _ _ __/ 
2 / __/ _/ _ /
1 / / _/
0 /
 12322223210012233343221112


As we can see, we can represent this (to a certain degree) with a sequence of integers.



For the purpose of this challenge we define a valley as a contiguous subsequence where the values initially are decreasing and from some point on they are increasing. More formally for a sequence $(a_i)_i=1^n$ a valley will be indices $1 leq s < r < t leq n$ for which the following holds:



  • the valley's start and endpoint are the same: $a_s = a_t$

  • the valley starts and ends once the region gets lower: $a_s > a_s+1 land a_t-1 < a_t$

  • the valley is not flat: $a_s neq a_r land a_r neq a_t$

  • the valley initially decreases: $forall i in [s,r): a_i geq a_i+1$

  • the valley will at some point increase: $forall j in [r,t): a_j leq a_j+1$

Now we define the width of such a valley as the size of the indices $[s,t]$, ie. $t-s+1$.



Challenge



Given a height-profile (sequence of non-negative integers), your task is to determine the width of the widest valley.



Example



Given the height-profile [1,2,3,2,2,2,2,3,2,1,0,0,1,2,2,3,3,3,4,3,2,2,1,1,1,2], we can visualize it as before:



4 _
3 _ _ __/ 
2 / __/ _/ _ /
1 / / _/
0 /
 12322223210012233343221112
 aaaaaa ccccc
 bbbbbbbbb


Note how the second valley [3,2,1,0,0,1,2,2,3] does not extend further to the right because the left-most point is $3$ and not $4$. Furthermore we don't add the remaining two $3$s because we require that the endpoint is higher up than the second-last point.



Therefore the width of the widest valley is $9$.



Rules



  • Input will be a sequence of non-negative (sorry Dutch people) integers

    • you can assume that there is always at least one valley


  • Output will be the size of the widest valley as defined above

Testcases



[4,0,4] -> 3
[1,0,1,0,1] -> 3
[1,0,2,0,1,2] -> 4
[13,13,13,2,2,1,0,1,14,2,13,14] -> 4
[1,2,3,2,2,2,2,3,2,1,0,0,1,2,2,3,3,3,4,3,2,2,1,1,1,2] -> 9





code-golf array-manipulation







share|improve this question

























    up vote
    5
    down vote

    favorite
    1












    Imagine we get a slice of some mountainous region, this would result in a shape similar to this:



    4 _
    3 _ _ __/ 
    2 / __/ _/ _ /
    1 / / _/
    0 /
     12322223210012233343221112


    As we can see, we can represent this (to a certain degree) with a sequence of integers.



    For the purpose of this challenge we define a valley as a contiguous subsequence where the values initially are decreasing and from some point on they are increasing. More formally for a sequence $(a_i)_i=1^n$ a valley will be indices $1 leq s < r < t leq n$ for which the following holds:



    • the valley's start and endpoint are the same: $a_s = a_t$

    • the valley starts and ends once the region gets lower: $a_s > a_s+1 land a_t-1 < a_t$

    • the valley is not flat: $a_s neq a_r land a_r neq a_t$

    • the valley initially decreases: $forall i in [s,r): a_i geq a_i+1$

    • the valley will at some point increase: $forall j in [r,t): a_j leq a_j+1$

    Now we define the width of such a valley as the size of the indices $[s,t]$, ie. $t-s+1$.



    Challenge



    Given a height-profile (sequence of non-negative integers), your task is to determine the width of the widest valley.



    Example



    Given the height-profile [1,2,3,2,2,2,2,3,2,1,0,0,1,2,2,3,3,3,4,3,2,2,1,1,1,2], we can visualize it as before:



    4 _
    3 _ _ __/ 
    2 / __/ _/ _ /
    1 / / _/
    0 /
     12322223210012233343221112
     aaaaaa ccccc
     bbbbbbbbb


    Note how the second valley [3,2,1,0,0,1,2,2,3] does not extend further to the right because the left-most point is $3$ and not $4$. Furthermore we don't add the remaining two $3$s because we require that the endpoint is higher up than the second-last point.



    Therefore the width of the widest valley is $9$.



    Rules



    • Input will be a sequence of non-negative (sorry Dutch people) integers

      • you can assume that there is always at least one valley


    • Output will be the size of the widest valley as defined above

    Testcases



    [4,0,4] -> 3
    [1,0,1,0,1] -> 3
    [1,0,2,0,1,2] -> 4
    [13,13,13,2,2,1,0,1,14,2,13,14] -> 4
    [1,2,3,2,2,2,2,3,2,1,0,0,1,2,2,3,3,3,4,3,2,2,1,1,1,2] -> 9





    code-golf array-manipulation







    share|improve this question























      up vote
      5
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      favorite
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      up vote
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      1





      Imagine we get a slice of some mountainous region, this would result in a shape similar to this:



      4 _
      3 _ _ __/ 
      2 / __/ _/ _ /
      1 / / _/
      0 /
       12322223210012233343221112


      As we can see, we can represent this (to a certain degree) with a sequence of integers.



      For the purpose of this challenge we define a valley as a contiguous subsequence where the values initially are decreasing and from some point on they are increasing. More formally for a sequence $(a_i)_i=1^n$ a valley will be indices $1 leq s < r < t leq n$ for which the following holds:



      • the valley's start and endpoint are the same: $a_s = a_t$

      • the valley starts and ends once the region gets lower: $a_s > a_s+1 land a_t-1 < a_t$

      • the valley is not flat: $a_s neq a_r land a_r neq a_t$

      • the valley initially decreases: $forall i in [s,r): a_i geq a_i+1$

      • the valley will at some point increase: $forall j in [r,t): a_j leq a_j+1$

      Now we define the width of such a valley as the size of the indices $[s,t]$, ie. $t-s+1$.



      Challenge



      Given a height-profile (sequence of non-negative integers), your task is to determine the width of the widest valley.



      Example



      Given the height-profile [1,2,3,2,2,2,2,3,2,1,0,0,1,2,2,3,3,3,4,3,2,2,1,1,1,2], we can visualize it as before:



      4 _
      3 _ _ __/ 
      2 / __/ _/ _ /
      1 / / _/
      0 /
       12322223210012233343221112
       aaaaaa ccccc
       bbbbbbbbb


      Note how the second valley [3,2,1,0,0,1,2,2,3] does not extend further to the right because the left-most point is $3$ and not $4$. Furthermore we don't add the remaining two $3$s because we require that the endpoint is higher up than the second-last point.



      Therefore the width of the widest valley is $9$.



      Rules



      • Input will be a sequence of non-negative (sorry Dutch people) integers

        • you can assume that there is always at least one valley


      • Output will be the size of the widest valley as defined above

      Testcases



      [4,0,4] -> 3
      [1,0,1,0,1] -> 3
      [1,0,2,0,1,2] -> 4
      [13,13,13,2,2,1,0,1,14,2,13,14] -> 4
      [1,2,3,2,2,2,2,3,2,1,0,0,1,2,2,3,3,3,4,3,2,2,1,1,1,2] -> 9





      code-golf array-manipulation







      share|improve this question













      Imagine we get a slice of some mountainous region, this would result in a shape similar to this:



      4 _
      3 _ _ __/ 
      2 / __/ _/ _ /
      1 / / _/
      0 /
       12322223210012233343221112


      As we can see, we can represent this (to a certain degree) with a sequence of integers.



      For the purpose of this challenge we define a valley as a contiguous subsequence where the values initially are decreasing and from some point on they are increasing. More formally for a sequence $(a_i)_i=1^n$ a valley will be indices $1 leq s < r < t leq n$ for which the following holds:



      • the valley's start and endpoint are the same: $a_s = a_t$

      • the valley starts and ends once the region gets lower: $a_s > a_s+1 land a_t-1 < a_t$

      • the valley is not flat: $a_s neq a_r land a_r neq a_t$

      • the valley initially decreases: $forall i in [s,r): a_i geq a_i+1$

      • the valley will at some point increase: $forall j in [r,t): a_j leq a_j+1$

      Now we define the width of such a valley as the size of the indices $[s,t]$, ie. $t-s+1$.



      Challenge



      Given a height-profile (sequence of non-negative integers), your task is to determine the width of the widest valley.



      Example



      Given the height-profile [1,2,3,2,2,2,2,3,2,1,0,0,1,2,2,3,3,3,4,3,2,2,1,1,1,2], we can visualize it as before:



      4 _
      3 _ _ __/ 
      2 / __/ _/ _ /
      1 / / _/
      0 /
       12322223210012233343221112
       aaaaaa ccccc
       bbbbbbbbb


      Note how the second valley [3,2,1,0,0,1,2,2,3] does not extend further to the right because the left-most point is $3$ and not $4$. Furthermore we don't add the remaining two $3$s because we require that the endpoint is higher up than the second-last point.



      Therefore the width of the widest valley is $9$.



      Rules



      • Input will be a sequence of non-negative (sorry Dutch people) integers

        • you can assume that there is always at least one valley


      • Output will be the size of the widest valley as defined above

      Testcases



      [4,0,4] -> 3
      [1,0,1,0,1] -> 3
      [1,0,2,0,1,2] -> 4
      [13,13,13,2,2,1,0,1,14,2,13,14] -> 4
      [1,2,3,2,2,2,2,3,2,1,0,0,1,2,2,3,3,3,4,3,2,2,1,1,1,2] -> 9





      code-golf array-manipulation




      code-golf array-manipulation






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      asked 1 hour ago









      BMO

      10.4k21879




      10.4k21879




















          3 Answers
          3






          active

          oldest

          votes

















          up vote
          1
          down vote














          Python 2, 120 115 89 87 86 bytes





          lambda a:max(r-l+1for l,v in e(a)for r,w in e(a)if v==w>max(a[l+1:r]+[0]))
          e=enumerate


          Try it online!



          -1 byte, thanks to BMO






          share|improve this answer






















          • Does replacing [-1] with [0] work?
            – BMO
            1 hour ago










          • @BMO Yeah, I guess it does. A valley must always start with n>0 right?
            – TFeld
            1 hour ago










          • Yes, there can only be non-negative integers and as such a valley has to start with n>0.
            – BMO
            1 hour ago

















          up vote
          1
          down vote













          Haskell, 66 bytes



          f(a:b)|(_:h,i:_)<-span(<a)b,i==a=max(length h+3)$f b|1<2=f b
          f _=0


          Try it online!






          share|improve this answer



























            up vote
            1
            down vote














            Jelly, 17 16 bytes



            Ẇ>þị@€.¬Ø.¦ȦƲƇẈṀ


            Try it online!



             ẈṀ Maximum of lengths of…
            Ẇ Ƈ All sublists satisfying:
             Ʋ This funky 4-link monad:
             >þ ị@€. ¬Ø.¦ Ȧ Is a valley.


            First, >þ makes a table of $a[x]>a[y]$ for our valley candidate. For $[6, 2, 3, 1, 4, 6]$ it's:



            beginbmatrix
            color#0000&0&0&0&0&colorred0\
            colorblue1&color#0000&1&0&1&colorblue1\
            colorblue1&0&color#0000&0&1&colorblue1\
            colorblue1&1&1&color#0000&1&colorblue1\
            colorblue1&0&0&0&color#0000&colorblue1\
            colorred0&0&0&0&0&color#0000
            endbmatrix



            We want the $colorredtextred$ elements to be both zero, representing that the start and end are equal.



            We want the $colorbluetextblue$ elements to be all ones, representing that the endpoints are > everything in the middle.



            We apply ị@€.: index each by 0.5, i.e. get the start and end of every row. This gets us



            beginbmatrix
            color#0000&colorred0\
            colorblue1&colorblue1\
            colorblue1&colorblue1\
            colorblue1&colorblue1\
            colorblue1&colorblue1\
            colorred0&color#0000
            endbmatrix



            Then ¬Ø.¦ negates the first and last rows, and Ȧ checks that the matrix is all ones.



            (The top-left and bottom-right corners are guaranteed to be 0s in the table we started from, as they're on the diagonal, and $ x not> x $. So we don't need to check them at all.)






            share|improve this answer






















            • Also, L€ → Ẉ.
              – Erik the Outgolfer
              7 mins ago










            Your Answer





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            3 Answers
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            active

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            3 Answers
            3






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            1
            down vote














            Python 2, 120 115 89 87 86 bytes





            lambda a:max(r-l+1for l,v in e(a)for r,w in e(a)if v==w>max(a[l+1:r]+[0]))
            e=enumerate


            Try it online!



            -1 byte, thanks to BMO






            share|improve this answer






















            • Does replacing [-1] with [0] work?
              – BMO
              1 hour ago










            • @BMO Yeah, I guess it does. A valley must always start with n>0 right?
              – TFeld
              1 hour ago










            • Yes, there can only be non-negative integers and as such a valley has to start with n>0.
              – BMO
              1 hour ago














            up vote
            1
            down vote














            Python 2, 120 115 89 87 86 bytes





            lambda a:max(r-l+1for l,v in e(a)for r,w in e(a)if v==w>max(a[l+1:r]+[0]))
            e=enumerate


            Try it online!



            -1 byte, thanks to BMO






            share|improve this answer






















            • Does replacing [-1] with [0] work?
              – BMO
              1 hour ago










            • @BMO Yeah, I guess it does. A valley must always start with n>0 right?
              – TFeld
              1 hour ago










            • Yes, there can only be non-negative integers and as such a valley has to start with n>0.
              – BMO
              1 hour ago












            up vote
            1
            down vote










            up vote
            1
            down vote










            Python 2, 120 115 89 87 86 bytes





            lambda a:max(r-l+1for l,v in e(a)for r,w in e(a)if v==w>max(a[l+1:r]+[0]))
            e=enumerate


            Try it online!



            -1 byte, thanks to BMO






            share|improve this answer















            Python 2, 120 115 89 87 86 bytes





            lambda a:max(r-l+1for l,v in e(a)for r,w in e(a)if v==w>max(a[l+1:r]+[0]))
            e=enumerate


            Try it online!



            -1 byte, thanks to BMO







            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited 1 hour ago

























            answered 1 hour ago









            TFeld

            12.9k2836




            12.9k2836











            • Does replacing [-1] with [0] work?
              – BMO
              1 hour ago










            • @BMO Yeah, I guess it does. A valley must always start with n>0 right?
              – TFeld
              1 hour ago










            • Yes, there can only be non-negative integers and as such a valley has to start with n>0.
              – BMO
              1 hour ago
















            • Does replacing [-1] with [0] work?
              – BMO
              1 hour ago










            • @BMO Yeah, I guess it does. A valley must always start with n>0 right?
              – TFeld
              1 hour ago










            • Yes, there can only be non-negative integers and as such a valley has to start with n>0.
              – BMO
              1 hour ago















            Does replacing [-1] with [0] work?
            – BMO
            1 hour ago




            Does replacing [-1] with [0] work?
            – BMO
            1 hour ago












            @BMO Yeah, I guess it does. A valley must always start with n>0 right?
            – TFeld
            1 hour ago




            @BMO Yeah, I guess it does. A valley must always start with n>0 right?
            – TFeld
            1 hour ago












            Yes, there can only be non-negative integers and as such a valley has to start with n>0.
            – BMO
            1 hour ago




            Yes, there can only be non-negative integers and as such a valley has to start with n>0.
            – BMO
            1 hour ago










            up vote
            1
            down vote













            Haskell, 66 bytes



            f(a:b)|(_:h,i:_)<-span(<a)b,i==a=max(length h+3)$f b|1<2=f b
            f _=0


            Try it online!






            share|improve this answer
























              up vote
              1
              down vote













              Haskell, 66 bytes



              f(a:b)|(_:h,i:_)<-span(<a)b,i==a=max(length h+3)$f b|1<2=f b
              f _=0


              Try it online!






              share|improve this answer






















                up vote
                1
                down vote










                up vote
                1
                down vote









                Haskell, 66 bytes



                f(a:b)|(_:h,i:_)<-span(<a)b,i==a=max(length h+3)$f b|1<2=f b
                f _=0


                Try it online!






                share|improve this answer












                Haskell, 66 bytes



                f(a:b)|(_:h,i:_)<-span(<a)b,i==a=max(length h+3)$f b|1<2=f b
                f _=0


                Try it online!







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 35 mins ago









                nimi

                30.5k31985




                30.5k31985




















                    up vote
                    1
                    down vote














                    Jelly, 17 16 bytes



                    Ẇ>þị@€.¬Ø.¦ȦƲƇẈṀ


                    Try it online!



                     ẈṀ Maximum of lengths of…
                    Ẇ Ƈ All sublists satisfying:
                     Ʋ This funky 4-link monad:
                     >þ ị@€. ¬Ø.¦ Ȧ Is a valley.


                    First, >þ makes a table of $a[x]>a[y]$ for our valley candidate. For $[6, 2, 3, 1, 4, 6]$ it's:



                    beginbmatrix
                    color#0000&0&0&0&0&colorred0\
                    colorblue1&color#0000&1&0&1&colorblue1\
                    colorblue1&0&color#0000&0&1&colorblue1\
                    colorblue1&1&1&color#0000&1&colorblue1\
                    colorblue1&0&0&0&color#0000&colorblue1\
                    colorred0&0&0&0&0&color#0000
                    endbmatrix



                    We want the $colorredtextred$ elements to be both zero, representing that the start and end are equal.



                    We want the $colorbluetextblue$ elements to be all ones, representing that the endpoints are > everything in the middle.



                    We apply ị@€.: index each by 0.5, i.e. get the start and end of every row. This gets us



                    beginbmatrix
                    color#0000&colorred0\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorred0&color#0000
                    endbmatrix



                    Then ¬Ø.¦ negates the first and last rows, and Ȧ checks that the matrix is all ones.



                    (The top-left and bottom-right corners are guaranteed to be 0s in the table we started from, as they're on the diagonal, and $ x not> x $. So we don't need to check them at all.)






                    share|improve this answer






















                    • Also, L€ → Ẉ.
                      – Erik the Outgolfer
                      7 mins ago














                    up vote
                    1
                    down vote














                    Jelly, 17 16 bytes



                    Ẇ>þị@€.¬Ø.¦ȦƲƇẈṀ


                    Try it online!



                     ẈṀ Maximum of lengths of…
                    Ẇ Ƈ All sublists satisfying:
                     Ʋ This funky 4-link monad:
                     >þ ị@€. ¬Ø.¦ Ȧ Is a valley.


                    First, >þ makes a table of $a[x]>a[y]$ for our valley candidate. For $[6, 2, 3, 1, 4, 6]$ it's:



                    beginbmatrix
                    color#0000&0&0&0&0&colorred0\
                    colorblue1&color#0000&1&0&1&colorblue1\
                    colorblue1&0&color#0000&0&1&colorblue1\
                    colorblue1&1&1&color#0000&1&colorblue1\
                    colorblue1&0&0&0&color#0000&colorblue1\
                    colorred0&0&0&0&0&color#0000
                    endbmatrix



                    We want the $colorredtextred$ elements to be both zero, representing that the start and end are equal.



                    We want the $colorbluetextblue$ elements to be all ones, representing that the endpoints are > everything in the middle.



                    We apply ị@€.: index each by 0.5, i.e. get the start and end of every row. This gets us



                    beginbmatrix
                    color#0000&colorred0\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorred0&color#0000
                    endbmatrix



                    Then ¬Ø.¦ negates the first and last rows, and Ȧ checks that the matrix is all ones.



                    (The top-left and bottom-right corners are guaranteed to be 0s in the table we started from, as they're on the diagonal, and $ x not> x $. So we don't need to check them at all.)






                    share|improve this answer






















                    • Also, L€ → Ẉ.
                      – Erik the Outgolfer
                      7 mins ago












                    up vote
                    1
                    down vote










                    up vote
                    1
                    down vote










                    Jelly, 17 16 bytes



                    Ẇ>þị@€.¬Ø.¦ȦƲƇẈṀ


                    Try it online!



                     ẈṀ Maximum of lengths of…
                    Ẇ Ƈ All sublists satisfying:
                     Ʋ This funky 4-link monad:
                     >þ ị@€. ¬Ø.¦ Ȧ Is a valley.


                    First, >þ makes a table of $a[x]>a[y]$ for our valley candidate. For $[6, 2, 3, 1, 4, 6]$ it's:



                    beginbmatrix
                    color#0000&0&0&0&0&colorred0\
                    colorblue1&color#0000&1&0&1&colorblue1\
                    colorblue1&0&color#0000&0&1&colorblue1\
                    colorblue1&1&1&color#0000&1&colorblue1\
                    colorblue1&0&0&0&color#0000&colorblue1\
                    colorred0&0&0&0&0&color#0000
                    endbmatrix



                    We want the $colorredtextred$ elements to be both zero, representing that the start and end are equal.



                    We want the $colorbluetextblue$ elements to be all ones, representing that the endpoints are > everything in the middle.



                    We apply ị@€.: index each by 0.5, i.e. get the start and end of every row. This gets us



                    beginbmatrix
                    color#0000&colorred0\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorred0&color#0000
                    endbmatrix



                    Then ¬Ø.¦ negates the first and last rows, and Ȧ checks that the matrix is all ones.



                    (The top-left and bottom-right corners are guaranteed to be 0s in the table we started from, as they're on the diagonal, and $ x not> x $. So we don't need to check them at all.)






                    share|improve this answer















                    Jelly, 17 16 bytes



                    Ẇ>þị@€.¬Ø.¦ȦƲƇẈṀ


                    Try it online!



                     ẈṀ Maximum of lengths of…
                    Ẇ Ƈ All sublists satisfying:
                     Ʋ This funky 4-link monad:
                     >þ ị@€. ¬Ø.¦ Ȧ Is a valley.


                    First, >þ makes a table of $a[x]>a[y]$ for our valley candidate. For $[6, 2, 3, 1, 4, 6]$ it's:



                    beginbmatrix
                    color#0000&0&0&0&0&colorred0\
                    colorblue1&color#0000&1&0&1&colorblue1\
                    colorblue1&0&color#0000&0&1&colorblue1\
                    colorblue1&1&1&color#0000&1&colorblue1\
                    colorblue1&0&0&0&color#0000&colorblue1\
                    colorred0&0&0&0&0&color#0000
                    endbmatrix



                    We want the $colorredtextred$ elements to be both zero, representing that the start and end are equal.



                    We want the $colorbluetextblue$ elements to be all ones, representing that the endpoints are > everything in the middle.



                    We apply ị@€.: index each by 0.5, i.e. get the start and end of every row. This gets us



                    beginbmatrix
                    color#0000&colorred0\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorblue1&colorblue1\
                    colorred0&color#0000
                    endbmatrix



                    Then ¬Ø.¦ negates the first and last rows, and Ȧ checks that the matrix is all ones.



                    (The top-left and bottom-right corners are guaranteed to be 0s in the table we started from, as they're on the diagonal, and $ x not> x $. So we don't need to check them at all.)







                    share|improve this answer














                    share|improve this answer



                    share|improve this answer








                    edited 3 mins ago

























                    answered 12 mins ago









                    Lynn

                    49k694223




                    49k694223











                    • Also, L€ → Ẉ.
                      – Erik the Outgolfer
                      7 mins ago
















                    • Also, L€ → Ẉ.
                      – Erik the Outgolfer
                      7 mins ago















                    Also, L€ → Ẉ.
                    – Erik the Outgolfer
                    7 mins ago




                    Also, L€ → Ẉ.
                    – Erik the Outgolfer
                    7 mins ago

















                     

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