Solution.cpp

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

int coinChange(vector<int>& coins, int amount) {
    vector<int> dp(amount + 1, INT_MAX);
    dp[0] = 0;

    for (int i = 1; i <= amount; i++) {
        for (int coin : coins) {
            if (i >= coin && dp[i - coin] != INT_MAX) {
                dp[i] = min(dp[i], dp[i - coin] + 1);
            }
        }
    }

    return dp[amount] == INT_MAX ? -1 : dp[amount];
}

int main() {
    int n, amount;
    cout << "Enter the number of coin types: ";
    cin >> n;

    vector<int> coins(n);
    cout << "Enter the coin denominations:\n";
    for (int i = 0; i < n; i++)
        cin >> coins[i];

    cout << "Enter the amount: ";
    cin >> amount;

    int result = coinChange(coins, amount);
    if (result == -1)
        cout << "No solution exists.\n";
    else
        cout << "Minimum coins needed: " << result << endl;

    return 0;
}