LeetCode 2787: Ways to Express an Integer as Sum of Powers Solution

Master LeetCode problem 2787 (Ways to Express an Integer as Sum of Powers), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

2787. Ways to Express an Integer as Sum of Powers

Medium

Dynamic Programming

Problem Explanation

Explanation:

To solve this problem, we can use dynamic programming. We will create a 2D array dp where dp[i][j] represents the number of ways to express i as the sum of the x-th power of unique positive integers up to j. We can iterate over each possible k from 1 to j and update dp[i][j] based on the conditions.

Initialize dp array with dimensions n+1 x x+1.
Base cases: Initialize dp[i][1] = 1 for all i from 1 to n.
For each i from 1 to n, calculate dp[i][j] using the formula dp[i][j] = dp[i][j] + dp[i - j^x][j - 1].
The final answer will be dp[n][x]. :

Solution Code

class Solution {
    public int waysToExpressInteger(int n, int x) {
        int mod = 1000000007;
        int[][] dp = new int[n + 1][x + 1];
        
        for (int i = 1; i <= n; i++) {
            dp[i][1] = 1;
        }
        
        for (int i = 1; i <= n; i++) {
            for (int j = 2; j <= x; j++) {
                for (int k = 1; k <= i; k++) {
                    if (i - k*k >= 0) {
                        dp[i][j] = (dp[i][j] + dp[i - k*k][j - 1]) % mod;
                    }
                }
            }
        }
        
        return dp[n][x];
    }
}

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