518. Coin Change 2.md

518. Coin Change 2

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You are given coins of different denominations and a total amount of money. Write a function to compute the number of combinations that make up that amount. You may assume that you have infinite number of each kind of coin.

Example 1:

Input: amount = 5, coins = [1, 2, 5]
Output: 4
Explanation: there are four ways to make up the amount:
5=5
5=2+2+1
5=2+1+1+1
5=1+1+1+1+1

Example 2:

Input: amount = 3, coins = [2]
Output: 0
Explanation: the amount of 3 cannot be made up just with coins of 2.

Example 3:

Input: amount = 10, coins = [10]
Output: 1

Note:

You can assume that

• 0 <= amount <= 5000
• 1 <= coin <= 5000
• the number of coins is less than 500
• the answer is guaranteed to fit into signed 32-bit integer

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Solution

• mine
  • Java

    • Dynamic Programming same as 70. Climbing Stairs.

      Runtime: 3 ms, faster than 61.40%, Memory Usage: 36.9 MB, less than 75.53% of Java online submissions

      // O(N*M)time O(N)space
      // N is amount,  M is coins.length
      public int change(int amount, int[] coins) {
          int[] dp = new int[amount + 1];
          dp[0] = 1;
          for(int coin : coins){
              for(int j = coin; j <= amount; j++){
                  dp[j] += dp[j - coin];
              }
          }
          return dp[amount];
      }
      

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