MediumLeetCode #322Dynamic Programming

Coin Change

You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money. Return the fewest number of coins that you need to make up that amount. If that amount of money cannot be made up by any combination of the coins, return -1.

Constraints

1 <= coins.length <= 12, 1 <= coins[i] <= 2^31 - 1, 0 <= amount <= 10^4

Examples

Input: coins = [1,2,5], amount = 11

Output: 3

11 = 5 + 5 + 1

Solution

Approach

DP where dp[i] = minimum coins to make amount i. For each amount, try each coin: dp[i] = min(dp[i], dp[i - coin] + 1).

def coinChange(coins, amount):
    dp = [float("inf")] * (amount + 1)
    dp[0] = 0
    for i in range(1, amount + 1):
        for coin in coins:
            if coin <= i:
                dp[i] = min(dp[i], dp[i - coin] + 1)
    return dp[amount] if dp[amount] != float("inf") else -1

Complexity

Time:O(amount * n)

Space:O(amount)

Hints

1.dp[i] = min coins for amount i
2.Try using each coin as the last coin
3.Initialize dp[0] = 0

Asked at

Google