TheAlgorithms-C-Plus-Plus/dynamic_programming/Coin-Change.cpp

#include <iostream>
#include <climits>
using namespace std;

// Function to find the Minimum number of coins required to get Sum S
int findMinCoins(int arr[], int n, int N)
{
	// dp[i] = no of coins required to get a total of i
	int dp[N + 1];

	// 0 coins are needed for 0 sum

	dp[0] = 0;

	for (int i = 1; i <= N; i++)
	{
		// initialize minimum number of coins needed to infinity
		dp[i] = INT_MAX;
		int res = INT_MAX;

		// do for each coin
		for (int c = 0; c < n; c++)
		{
			if (i - arr[c] >= 0) // check if coins doesn't become negative by including it
				res = dp[i - arr[c]];

			// if total can be reached by including current coin c,
			// update minimum number of coins needed dp[i]
			if (res != INT_MAX)
				dp[i] = min(dp[i], res + 1);
		}
	}

	// The Minimum No of Coins Required for N = dp[N]
	return dp[N];
}

int main()
{
	// No of Coins We Have
	int arr[] = {1, 2, 3, 4};
	int n = sizeof(arr) / sizeof(arr[0]);

	// Total Change Required
	int N = 15;

	cout << "Minimum Number of Coins Required " << findMinCoins(arr, n, N) << "\n";

	return 0;
}