Let Y = (y1, Y2,..., Yn) and Z = (21, 2,..., Zk) be two different sequences. Write pseudocode for an algorithm that has complexity O(n) and checks whether Z is a subsequence of Y. If Z is a subsequence of Y, the algorithm should return an array I storing a subset of indices in Y that correspond to the subsequence Z (i.e., I = [i1, 12, .. algorithm should return false. Explain your algorithm and why it is correct, and prove that its runtime is O(n). ik] such that z4 = Yi, and i < iz < ...< ik). Otherwise, the

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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.