Create TheCoinChangeProblem.cpp

Author: rachitiitr

Famous-Coding-Interview-Problems/TheCoinChangeProblem.cpp

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+//The Coin Change Problem
+//Given an Array of coins C, and money S, print number of ways to make a change for S
+//Eg: A=[1,2] S=4 answer is {1,1,1,1}, {2,2}, {2,1,1} i.e 3 ways
+#include <bits/stdc++.h>
+using namespace std;
+
+const int N = 1e3;
+int A[N], n;
+int vis[N][N], dp[N][N];
+
+int ways(int pos, int S) {
+	if(pos == n) return S == 0;
+	int &ans = dp[pos][S];
+  if(vis[pos][S]) return ans; vis[pos][S] = 1, ans = 0;
+	int times = 0;
+	while(times*A[pos] <= S) ans += ways(pos+1, S-times*A[pos]), times++;
+	return ans;
+}
+
+//Faster than ways function as it causes only two transitions
+int fasterWays(int pos, int S) {
+	if(pos == n) return S == 0;
+  if(S < 0) return 0;
+	int &ans = dp[pos][S];
+  if(vis[pos][S]) return ans; vis[pos][S] = 1, ans = 0;
+	ans = ways(pos, S-A[pos]) + ways(pos+1, S);
+	return ans;
+}
+
+int main() {
+	
+	int i, S;
+	cin >> n >> S;
+	for(i=0; i<n; i++) cin >> A[i];	
+	cout << fasterWays(0, S) << endl;
+	return 0;
+}