Q1: MCM Algorithm Implementation Implement Matrix Chain Multiplication (MCM) algorithm using the following pseudocode as instructed in the Class Lecture. MATRIX-CHAIN-ORDER (p) 1 ne length[p] - 1 2 for i +1 ton 3 do m[i, i] +0 4 for / +2 to n 5 Dl is the chain length. do for i +1 to n-1+1 do jei+l-1 mli, j] + 0 for k +i to j - 1 7 8 9. do q + m[i, k] + m[k + 1, j]+ Pi–1 PkPj if q < m[i, j] then m[i, j] + q s[i, j] +k 10 11 12 13 return m and s

Merge sort is an efficient sorting algorithm with a time complexity of O(n log n). This means that as the number of elements (chocolates or students) increases significantly, the efficiency of merge sort remains relatively stable compared to other sorting algorithms. Merge sort achieves this efficiency by recursively dividing the input array into smaller sub-arrays, sorting them individually, and then merging them back together. The efficiency of merge sort is primarily determined by its time complexity, which is , where n is the number of elements in the array. This time complexity indicates that the time taken by merge sort grows logarithmically with the size of the input array. Therefore, even as the number of chocolates or students increases significantly, merge sort maintains its relatively efficient performance. Regarding the distribution of a given set of x to y using iterative and recursive functions, the complexity analysis depends on the specific implementation of each…

The n-th harmonic is the sum of the reciprocals of the first n natural numbers given by: 17 1.1 1 1 H₁ =Σ =1+=+=+ - 2 3 4 k=1 k +. + n (i) Write a recursive algorithm of this function returning, H, with nε N. (ii) Give a recurrence relation for the number of divisions the recursive algorithm calculates for an input n & N. iii) Solve the recurrence relation and give the O(n) of the algorithm.

Use matlab