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# 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.

If you are preparing for a tech interview at FAANG or any other Tier-1 tech company, register for Interview Kickstart's FREE webinar to understand the best way to prepare.

Interview Kickstart offers interview preparation courses taught by FAANG+ tech leads and seasoned hiring managers. Our programs include a comprehensive curriculum, unmatched teaching methods, and career coaching to help you nail your next tech interview.

We offer 18 interview preparation courses, each tailored to a specific engineering domain or role, including the most in-demand and highest-paying domains and roles, such as:

### Try yourself in the Editor

Note: Input and Output will already be taken care of.

# 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.

If you are preparing for a tech interview at FAANG or any other Tier-1 tech company, register for Interview Kickstart's FREE webinar to understand the best way to prepare.

Interview Kickstart offers interview preparation courses taught by FAANG+ tech leads and seasoned hiring managers. Our programs include a comprehensive curriculum, unmatched teaching methods, and career coaching to help you nail your next tech interview.

We offer 18 interview preparation courses, each tailored to a specific engineering domain or role, including the most in-demand and highest-paying domains and roles, such as: