Create Unbounded_knapsack.cpp

dynamic_programming/Unbounded_knapsack.cpp

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+/* 
+The Unbounded Knapsack problem allows you to take unlimited quantities of each item. The goal is to maximize the total value 
+without exceeding the given knapsack capacity. Unlike the 0/1 knapsack, where each item can be taken only once, in this 
+variation, you can pick any item as many times as needed, as long as the total weight stays within the knapsack's capacity. 
+The problem is commonly solved using dynamic programming.
+
+TASK - Given a set of N items, each with a weight and a value, represented by the array wt and val respectively. Also, a knapsack with weight limit W.
+The task is to fill the knapsack in such a way that we can get the maximum profit. Return the maximum profit.
+Note: Each item can be taken any number of times.
+
+Test Cases -
+Input: 
+N = 4, W = 8, val[] = {6, 1, 7, 7}, wt[] = {1, 3, 4, 5}
+Output:
+48
+*/
+
+// Code
+#include <bits/stdc++.h>
+using namespace std;
+
+int KnapSackFilling(int i,int W, vector<int> val,vector<int> wt, vector<vector<int>> &dp){
+    if(i==0){
+        if(wt[0]<=W){
+            return (W/wt[0])*val[0];
+        }else{
+            return 0;
+        }
+     }
+     if(dp[i][W]!=-1)return dp[i][W];
+     int nottake=KnapSackFilling(i-1,W,val,wt,dp);
+     int take=0;
+     if(W>=wt[i]){
+         take=val[i]+KnapSackFilling(i,W-wt[i],val,wt,dp);
+     }
+     return dp[i][W]=max(take,nottake);
+}
+int unboundedKnapsack(int N, int W, vector<int> val, vector<int> wt)
+{
+    vector<vector<int>> dp(N,vector<int>(W+1,-1));
+    return KnapSackFilling(N-1,W,val,wt,dp);
+}
+int main() {
+    int N;
+    N=4;
+    vector<int> wt= {1, 3, 4, 5};
+    vector<int> val= {6, 1, 7, 7}; 
+    int W = 8;
+
+    cout << "The Maximum value of items is " << unboundedKnapsack(N, W, val, wt) << endl;
+
+    return 0; 
+}
+