Please give detailed answers.

Determine the complexity of the addition, multiplication, and transposition of nxn matrices as follows: a. Addition: for(i = 0; i < n; i++) for(j = 0; j < n; j++) a[i][j] = b[i][j] + c[i][j]; b. Multiplication: for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { sum = 0; for(k = 0; k < n; k++) sum = sum + b[i][k] * c[k][j]; a[i][j] = sum; } } c. Transposition for(i = 0; i < n - 1; i++) for(j = i+1; j < n; j++) { tmp = a[i][j]; a[i][j] = a[j][i]; a[j][i] = tmp; } Problem 4. Find the complexity of the following function: int Min(int a[], int n) { int i, min; min = a[0]; for(i = 1; i < n; i++) if (a[i] < min) min = a[i]; return min; }

DATA STRUCTURE Assignment 2 - Algorithm analysis Problem 2. Compute the computational complexity of the following loops: a. for(cnt1 = 0, i = 1; i <= n; i++) for(j = 1; j <= n; j++) cnt1++; b. for(cnt2 = 0, 1 = 1; i <= n; i++) for(j = 1; j <= i; j++) cnt2++ c. for(cnt3 = 0, 1 = 1; i <= n; i *= 2) for(j = 1; } <= n; i++) cnt3++; for(cnt4 = 0, i = 1; i <= n; i for(j = 1; } <= 1; i++) cnt4++; Problem 3. Determine the complexity of the addition, multiplication, and transposition of nxn matrices as follows: sum = 0; for(k = 0; k