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  2. Longest palindromic substring - Wikipedia

    en.wikipedia.org/wiki/Longest_palindromic_substring

    The loop at the center of the function only works for palindromes where the length is an odd number. The function works for even-length palindromes by modifying the input string. The character '|' is inserted between every character in the inputs string, and at both ends. So the input "book" becomes "|b|o|o|k|". The even-length palindrome "oo ...

  3. Maximum subarray problem - Wikipedia

    en.wikipedia.org/wiki/Maximum_subarray_problem

    For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.

  4. Longest increasing subsequence - Wikipedia

    en.wikipedia.org/wiki/Longest_increasing_subsequence

    This subsequence has length six; the input sequence has no seven-member increasing subsequences. The longest increasing subsequence in this example is not the only solution: for instance, 0, 4, 6, 9, 11, 15 0, 2, 6, 9, 13, 15 0, 4, 6, 9, 13, 15. are other increasing subsequences of equal length in the same input sequence.

  5. Heap's algorithm - Wikipedia

    en.wikipedia.org/wiki/Heap's_algorithm

    Induction: If the claim is true for arrays of length l ≥ 1, then we show that the claim is true for arrays of length l +1 (together with the base case this proves that the claim is true for arrays of all lengths). Since the claim depends on whether l is odd or even, we prove each case separately.

  6. Subset sum problem - Wikipedia

    en.wikipedia.org/wiki/Subset_sum_problem

    The problem is NP-hard even when all input integers are positive (and the target-sum T is a part of the input). This can be proved by a direct reduction from 3SAT. [2] It can also be proved by reduction from 3-dimensional matching (3DM): [3] We are given an instance of 3DM, where the vertex sets are W, X, Y.

  7. Skip list - Wikipedia

    en.wikipedia.org/wiki/Skip_list

    A schematic picture of the skip list data structure. Each box with an arrow represents a pointer and a row is a linked list giving a sparse subsequence; the numbered boxes (in yellow) at the bottom represent the ordered data sequence.

  8. Loop invariant - Wikipedia

    en.wikipedia.org/wiki/Loop_invariant

    The following C subroutine max() returns the maximum value in its argument array a[], provided its length n is at least 1. Comments are provided at lines 3, 6, 9, 11, and 13. Each comment makes an assertion about the values of one or more variables at that stage of the functio

  9. Bogosort - Wikipedia

    en.wikipedia.org/wiki/Bogosort

    import random # this function checks whether or not the array is sorted def is_sorted (random_array): for i in range (1, len (random_array)): if random_array [i] < random_array [i-1]: return False return True # this function repeatedly shuffles the elements of the array until they are sorted def bogo_sort (random_array): while not is_sorted (random_array): random. shuffle (random_array) return ...