Medium
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
class Solution {
fun numberOfWays(n: Int, x: Int): Int {
val dp = IntArray(301)
val mod = 1000000007
var v: Int
dp[0] = 1
var a = 1
while ((Math.pow(a.toDouble(), x.toDouble())).also { v = it.toInt() } <= n) {
for (i in n downTo v) {
dp[i] = (dp[i] + dp[i - v]) % mod
}
a++
}
return dp[n]
}
}