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2787. Ways to Express an Integer as Sum of Powers 👍

  • Time: $O(n\log n)$
  • Space: $O(n)$
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class Solution {
 public:
  int numberOfWays(int n, int x) {
    constexpr int kMod = 1'000'000'007;
    // dp[i] := the number of ways to express i
    vector<int> dp(n + 1);
    int ax;  // a^x

    dp[0] = 1;

    for (int a = 1; (ax = pow(a, x)) <= n; ++a)
      for (int i = n; i >= ax; --i) {
        dp[i] += dp[i - ax];
        dp[i] %= kMod;
      }

    return dp[n];
  }
};

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class Solution {
  public int numberOfWays(int n, int x) {
    final int kMod = 1_000_000_007;
    // dp[i] := the number of ways to express i
    int[] dp = new int[n + 1];
    int ax; // a^x

    dp[0] = 1;

    for (int a = 1; (ax = (int) Math.pow(a, x)) <= n; ++a)
      for (int i = n; i >= ax; --i) {
        dp[i] += dp[i - ax];
        dp[i] %= kMod;
      }

    return dp[n];
  }
}

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class Solution:
  def numberOfWays(self, n: int, x: int) -> int:
    kMod = 1_000_000_007
    # dp[i] := the number of ways to express i
    dp = [1] + [0] * n

    for a in range(1, n + 1):
      ax = a**x
      if ax > n:
        break
      for i in range(n, ax - 1, -1):
        dp[i] += dp[i - ax]
        dp[i] %= kMod

    return dp[n]