2787. Ways to Express an Integer as Sum of Powers
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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 <= 3001 <= x <= 5
Hints
Hint 1
You can use dynamic programming, where dp[k][j] represents the number of ways to express k as the sum of the x-th power of unique positive integers such that the biggest possible number we use is j.
Hint 2
To calculate dp[k][j], you can iterate over the numbers smaller than j and try to use each one as a power of x to make our sum k.