Working with lists

For list operations, only the Head, Prepend and Tail functions, as well as the functions implemented in previous problems, are allowed, and no other functions are permitted.

Find the number of elements of a list

Example:

Eq[MyLength[{#a, #b, #c, #d}], 4];

Solution

Let[MyLength, Fun[{list},
  Block[
    Let[MyLength', Fun[{sub, n},
      If[Eq[Length[sub], 0], n,
        MyLength'[Tail[sub], Add[n, 1]]]]],
    MyLength'[list, 0]]]];

Find the last box of a list

Example:

Eq[MyLast[{#a, #b, #c, #d}], #d];

Solution

Let[MyLast, Fun[{list},
  If[Eq[MyLength[list], 0], {#err, "empty list"},
    If[Eq[MyLength[list], 1], Head[list], MyLast[Tail[list]]]]]];

Find the last but one box of a list

Example:

Eq[MyButLast[{#a, #b, #c, #d}], {#c, #d}];

Solution

Let[MyButLast, Fun[{list},
  If[Less[MyLength[list], 2], {#err, "short list"},
    If[Eq[MyLength[list], 2], list, MyButLast[Tail[list]]]]]];

Find the K’th element of a list

The first element in the list is number 1.

Example:

Eq[MyIndex[{#a, #b, #c, #d}, 3], #c];

Solution

Let[MyIndex, Fun[{list, n},
  If[Less[n, 1], {#err, "invalid index"},
    If[Eq[n, 1], Head[list], MyIndex[Tail[list], Sub[n, 1]]]]]];

Reverse a list

Example:

Eq[MyReverse[{#a, #b, #c, #d, #e}], {#e, #d, #c, #b, #a}];

Solution

Let[MyReverse, Fun[{list},
  Block[
    Let[MyReverse', Fun[{sub, acc},
      If[Eq[Length[sub], 0], acc,
        MyReverse'[Tail[sub], Prepend[acc, Head[sub]]]]]],
    MyReverse'[list, {}]]]];

Find out whether a list is a palindrome

Example:

IsPalindrome[{#a, #c, #b, #c, #a}];

Solution

Let[IsPalindrome, Fun[{list}, Eq[MyReverse[list], list]]];

Flatten a nested list structure

Example:

Eq[MyFlatten[{#a, {#b, {#c, #d}, #e}}], {#a, #b, #c, #d, #e}];

Solution

Let[MyListConcat, Fun[{list1, list2},
  Block[
    Let[MyListConcat', Fun[{list1, list2},
      If[Eq[MyLength[list2], 0], list1,
        MyListConcat'[Prepend[list1, Head[list2]], Tail[list2]]]]],
    MyReverse[MyListConcat'[MyReverse[list1], list2]]]]];

Let[MyFlatten, Fun[{list},
  Block[
    Let[MyFlatten', Fun[{sub, acc},
      If[Eq[Length[sub], 0], acc,
        MyFlatten'[Tail[sub],
          If[IsList[Head[sub]],
            MyListConcat[MyFlatten'[Head[sub], {}], acc],
            Prepend[acc, Head[sub]]]]]]],
    MyReverse[MyFlatten'[list, {}]]]]];

Eliminate consecutive duplicates of list elements

Example:

Eq[Compress[{#a, #a, #a, #a, #b, #c, #c, #a, #a, #d, #e, #e, #e, #e}],
  {#a, #b, #c, #a, #d, #e}];

Solution

Let[Compress, Fun[{list},
  Block[
    Let[Compress', Fun[{list, acc},
      If[Eq[Length[list], 0], acc,
        Compress'[Tail[list],
          If[Eq[Head[list], Head[acc]],
            acc, Prepend[acc, Head[list]]]]]]],
    MyReverse[Compress'[Tail[list], { Head[list] }]]]]];

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