Find ways an Integer can be expressed as sum of n-th power of unique natural numbers - GeeksforGeeks


Find ways an Integer can be expressed as sum of n-th power of unique natural numbers - GeeksforGeeks
Given two numbers x and n, find number of ways x can be expressed as sum of n-th power of unique natural numbers.
int power(int num, unsigned int n)
{
    if (n == 0)
        return 1;
    else if (n%2 == 0)
        return power(num, n/2)*power(num, n/2);
    else
        return num*power(num, n/2)*power(num, n/2);
}
 
// Function to check power representations recursively
int checkRecursive(int x, int n, int curr_num = 1,
                   int curr_sum = 0)
{
    // Initialize number of ways to express
    // x as n-th powers of different natural
    // numbers
    int results = 0;
 
    // Calling power of 'i' raised to 'n'
    int p = power(curr_num, n);
    while (p + curr_sum < x)
    {
        // Recursively check all greater values of i
        results += checkRecursive(x, n, curr_num+1,
                                        p+curr_sum);
        curr_num++;
        p = power(curr_num, n);
    }
 
    // If sum of powers is equal to x
    // then increase the value of result.
    if (p + curr_sum == x)
        results++;
 
    // Return the final result
    return results;
}
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