Coin- Change Algorithm
The advent of paper money in the mid-17th century and the development of modern banking and floating exchange rates in the 20th century allowed a foreign exchange market to develop. This provided a manner for banks and other specialist fiscal company such as bureaux de change and forex brokers to easily change one state's money for another, and with the added confidence of transparency.
When outsiders, particularly traveling merchants, visited towns for a market fair, it became necessary to exchange foreign coins to local ones at local money changers. The merchant could then withdraw the money in local currency to conduct trade or, more likely, keep it deposited: the money changer would act as a clearing facility. In ancient times in Jerusalem, pilgrims visiting the Jewish Temple on Jewish Holy day would change some of their money from the standard Greek and Roman currency for Jewish and Tyrian money,
#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;
}
