2787. Ways to Express an Integer as Sum of Powers

Problem

Given two positive integers n and x.

Return **the number of ways *n* can be expressed as the sum of the xth power of unique positive integers, in other words, the number of sets of unique integers [n1, n2, ..., nk] where n = n1x + n2x + ... + nkx.**

Since the result can be very large, return it modulo 109 + 7.

For example, if n = 160 and x = 3, one way to express n is n = 23 + 33 + 53.

Example 1:

Input: n = 10, x = 2
Output: 1
Explanation: We can express n as the following: n = 32 + 12 = 10.
It can be shown that it is the only way to express 10 as the sum of the 2nd power of unique integers.

Example 2:

Input: n = 4, x = 1
Output: 2
Explanation: We can express n in the following ways:
- n = 41 = 4.
- n = 31 + 11 = 4.

Constraints:

• 1 <= n <= 300
• 1 <= x <= 5

Solution (Java)

class Solution {
    public int numberOfWays(int n, int x) {
        int dp[] = new int[301],  mod = 1000000007, v;
        dp[0] = 1;
        for (int a = 1; (v = (int)Math.pow(a, x)) <= n; a++)
            for (int i = n; i >= v; i--)
                dp[i] = (dp[i] + dp[i - v]) % mod;
        return dp[n];
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).