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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