Package g2701_2800.s2787_ways_to_express_an_integer_as_sum_of_powers

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

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

    Medium

    Given two positive integers n and x.

    Return the number of ways n can be expressed as the sum of the <code>x<sup>th</sup></code> power of unique positive integers, in other words, the number of sets of unique integers <code>n<sub>1</sub>, n<sub>2</sub>, ..., n<sub>k</sub></code> where <code>n = n<sub>1</sub><sup>x</sup> + n<sub>2</sub><sup>x</sup> + ... + n<sub>k</sub><sup>x</sup></code>.

    Since the result can be very large, return it modulo <code>10<sup>9</sup> + 7</code>.

    For example, if n = 160 and x = 3, one way to express n is <code>n = 2<sup>3</sup> + 3<sup>3</sup> + 5<sup>3</sup></code>.

    Example 1:

    Input: n = 10, x = 2

    Output: 1

    Explanation:

    We can express n as the following: n = 3<sup>2</sup> + 1<sup>2</sup> = 10.

    It can be shown that it is the only way to express 10 as the sum of the 2<sup>nd</sup> power of unique integers.

    Example 2:

    Input: n = 4, x = 1

    Output: 2

    Explanation:

    We can express n in the following ways:

    • n = 4<sup>1</sup> = 4.

    • n = 3<sup>1</sup> + 1<sup>1</sup> = 4.

    Constraints:

    • 1 &lt;= n &lt;= 300

    • 1 &lt;= x &lt;= 5

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Integer numberOfWays(Integer n, Integer x)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait