Coin Change With Infinite Coins Problem Statement

Given a variety of coin denominations defining a currency system, find the number of combinations that make up the given amount.

Example One

{
"amount": 5,
"coins": [1, 2, 3]
}

Output:

5

There are five ways to make up the amount:
1 + 1 + 1 + 1 + 1
1 + 1 + 1 + 2
1 + 2 + 2
1 + 1 + 3
2 + 3

Example Two

{
"amount": 3,
"coins": [4, 5, 6]
}

Output:

0

Notes

• You may assume that you have an infinite number of coins of each kind.
• Since the number of combinations can be very large, return it modulo 10⁹+7.

Constraints:

• 1 <= type of coins <= 300
• 1 <= value of any coin <= 5000
• 1 <= amount to be made <= 5000
• Every element in the input list is distinct

Code For Coin Change With Infinite Coins Solution: Dynamic Programming

/*
Asymptotic complexity in terms of amount `n` and number of different coins `m`:
* Time: O(n * m).
* Auxiliary space: O(n).
* Total space: O(n + m).
*/
int coin_change(int amount, vector<int> &coins) {
    const int mod = 1e9 + 7;
    vector<int> dp(amount + 1); // dp[i] = ways to make the amount i using given coins.
    dp[0] = 1;
    for(int coin: coins) {
        for(int current_amount = coin; current_amount <= amount; current_amount++) {
            dp[current_amount] = (dp[current_amount] + dp[current_amount - coin]) % mod;
        }
    }
    return dp[amount];
}

We hope that these solutions to coin change problem have helped you level up your coding skills. You can expect problems like these at top tech companies like Amazon and Google.

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