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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