0/1 Knapsack problem (Dynamic Programming) in C++

Author: ErR0rpj

classical_algorithms/c++/01_knapsack_problem.cpp

@@ -0,0 +1,52 @@
+//This is a code for 01 Knapsack problem.
+//input for number of items, capacity of the bag (total weight the bag can take).
+//Input for values of each items and their weights.
+//Output is maximum possible value the bag can take.
+#include <bits/stdc++.h>
+using namespace std;
+
+int main() {
+
+    int Number_of_items, Capacity;
+    cout<<"Enter total number of items and capacity:\n";
+	cin>>Number_of_items>>Capacity;
+	    
+    vector<int> values (Number_of_items+1);
+	vector<int> weights (Number_of_items+1);
+    values[0] = 0;
+	weights[0] = 0;
+
+    //DP array.
+	vector<vector<int>> dp (Number_of_items+1, vector<int>(Capacity+1, 0));
+
+    //Input for values
+    cout<<"Enter the values of each items:\n";
+	for(int i=1; i<Number_of_items+1; i++){
+	    cin>>values[i];
+	}
+
+    //Input for weights of the items with respect to values.
+    cout<<"Enter the values of each weights:\n";
+	for(int i=1; i<Number_of_items+1; i++){
+        cin>>weights[i];
+    }
+	    
+    //Main algo for 0/1 Knapsack.
+	for(int i=1; i<Number_of_items+1; i++){
+	    int wnow = weights[i];
+	    int vnow = values[i];
+	    for(int j=1; j<Capacity+1; j++){
+	        if(j < wnow){
+	            dp[i][j] = dp[i-1][j];
+            }
+	        else{
+	            dp[i][j] = max(dp[i-1][j], values[i] + dp[i-1][j - weights[i]]);
+            }	            
+	    }
+	}
+
+    cout<<"The maximum value the bag can store with the given capacity is: ";
+    cout<<dp[Number_of_items][Capacity]<<"\n";
+
+	return 0;
+}