added Coin Change 2

Author: sourav-naskar

Dynamic Programming/Coin_Change.cpp

@@ -0,0 +1,55 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+long countWaysToMakeChangeUtil(vector<int>& arr,int ind, int T, vector<vector<long
+>>& dp){
+
+    if(ind == 0){
+        return (T%arr[0]==0);
+    }
+    
+    if(dp[ind][T]!=-1)
+        return dp[ind][T];
+        
+    long notTaken = countWaysToMakeChangeUtil(arr,ind-1,T,dp);
+    
+    long taken = 0;
+    if(arr[ind] <= T)
+        taken = countWaysToMakeChangeUtil(arr,ind,T-arr[ind],dp);
+        
+    return dp[ind][T] = notTaken + taken;
+}
+
+
+long countWaysToMakeChange(vector<int>& arr, int n, int T){
+    
+    vector<vector<long>> dp(n,vector<long>(T+1,-1));
+    return countWaysToMakeChangeUtil(arr,n-1, T, dp);
+}
+
+int main() {
+
+  vector<int> arr ={1,2,3};
+  int target=4;
+  
+  int n =arr.size();
+                                 
+  cout<<"The total number of ways is " <<countWaysToMakeChange(arr,n,target);
+}
+
+/*
+Output:
+
+The total number of ways is 4
+
+Time Complexity: O(N*T)
+
+Reason: There are N*W states therefore at max ‘N*T’ new problems will be solved.
+
+Space Complexity: O(N*T) + O(N)
+
+Reason: We are using a recursion stack space(O(N)) and a 2D array ( O(N*T)).
+*/
+
+//contributed by Sourav Naskar