Coin Change 2 LeetCode solution in C++

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class Solution {
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 public:
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  int change(int amount, vector<int> &coins) {
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    if (amount == 0) return 1;
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    int dp[coins.size() + 1][amount + 1];
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    memset(dp, 0, sizeof(dp));
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    for (int i = 0; i <= coins.size(); i++) dp[i][0] = 1;
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    for (int i = 1; i <= coins.size(); i++) {
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      for (int j = 1; j <= amount; j++) {
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        if (j < coins[i - 1])
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          dp[i][j] = dp[i - 1][j];
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        else
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          dp[i][j] = dp[i - 1][j] + dp[i][j - coins[i - 1]];
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      }
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    }
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    return dp[coins.size()][amount];
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  }
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};