Algorithm 5.7 The Backtracking Algorithm for the 0-1 Knapsack Problem Problem: Let n items be given, where each item has a weight and a profit. The weights and profits are positive integers. Furthermore, let a positive integer W be given. Determine a set of items with maximum total profit, under the constraint that the sum of their weights cannot exceed W. Inputs: Positive integers n and W; arrays w and p, each indexed from 1 to n, and each containing positive integers sorted in nonincreasing order according to the values of p[i]/w[i]. Outputs: an array bestset indexed from 1 to n, where the values of bestset[i] is "yes" if the ith item is included in the optimal set and is "no" otherwise; an integer maxprofit that is the maximum profit. BACKTRACKING void knapsack (index i, 1 int profit, int weight) if (weight W && profit > maxprofit){\ } maxprofit numbest = i; profit; bestset include; if (promising (i)){ include [i+1] = "yes"; This set is best // so far. // Set numbest to // number of items considered. Set //bestset to this // solution. // Include w[i+1]. knapsack (i+1, profit + p[i+1], weight + w[i + 1]); include [i+1] = "no"; knapsack (i+1, profit, weight); // Do not include // w[i + 1]. } } bool promising (index i) { index j, k; int totweight; float bound; if (weight > W) return false; else{ j = i + 1; bound profit; totweight weight; // Node is promising only if we should expand to its children. There must be some capacity left for // the children. while (j <=n&& totweight + w[j] < = W){\ totweight totweight + w[j]; bound bound + p[j]; Grab as many items as possible. j++; } k = j; if (k <=n) bound = bound (Wtotweight) p[k]/w[k]; Use k for consistency // with formula in text. * return bound > maxprofit; // Grab fraction of kth // item. } } 33. Use the Backtracking algorithm for the 0-1 Knapsack problem (Algorithm 5.7) to maximize the profit for the following problem instance. Show the actions step by step. Pi i Pi Wi Wi 1 $20 2 10 2 $30 3 $35 7 5 W = 9 4 $12 3 4 5 $3 1 3