Given a string S[1, . . . , n] and a dictionary of strings S, return true if S[1, . . . , n] can be segmented into a space-separated sequence of one or more dictionary words. Note that the same word in the dictionary may be reused multiple times in the segmentation. Precisely define the subproblem. Provide the recurrence equation. Describe the algorithm in pseudocode to compute the optimal value. Describe the algorithm in pseudocode to print out an optimal solution.

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Counting sort

The counting sort algorithm sorts an array’s contents by counting the repetition of each element that occurs in the array. A counting sort algorithm is a stable algorithm that works the best when the range of elements in the array is small, say for example from 0 to 9. The count which is the number of repetitions of an element in the array is mapped to an index of an auxiliary array, which is then saved in an auxiliary array. The counting sort algorithm has a stable time complexity of the order of O(size of array + size of auxiliary array). Let’s discuss the algorithm in detail as follows.