Complexity Analysis: a. Write a short Java program that takes an array of int values as input and find if there is a pair of numbers with a given sum. What is the total number of operations that occur in terms of input size n in closed form for worst case scenario. What is the time complexity in Big O-notation? Example: Input: arr[] = {11, 15, 6, 8, 9, 10}, x = 16 Output: 6 + 10 = 16 , true Input: arr[] = {11, 15, 6, 8, 9, 10}, x = 27 Output: false

b. Write a short Java program that takes an array of int values as input and find if there is a triplet of numbers with a given sum. What is the total number of operations that occur in terms of input size n in closed form for worst case scenario. What is the time complexity in Big O-notation? Example: Input: arr[] = {11, 15, 6, 8, 9, 10}, x = 25 Output: 11 + 6 + 8 = 25 , true Input: arr[] = {11, 15, 6, 8, 9, 10}, x = 39 Output: false c. Given the following matrix multiplication code. What is the total number of operations that occur in terms of input size n in closed form. What is the time complexity in Big O-notation? What is the space complexity of this code? for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { double sum = 0; for (int k = 0; k < n; k++) { sum += a[i][k] * b[k][j]; } c[i][j] = sum; } }