my function is skipping

Question

I wrote a function in C code that calculates a polynomial value from a given array arr[] of arrsize size, where the elements are the coeffiecients.

the polynomial formula is:

$$p(x) = \sum_{i = 0}^{arrsize - 1} a_ix^i$$

With $a_i$ the polynomial coefficients. The function needs to calculate the sum $s$:

$$s = \sum_{i = 0}^{arrsize - 1} p(a_i)$$

    int helper(int arr[], int arrsize, int x, int i)  /*helper function that calculates the value of the polynomial*/
    {    
        if (i==arrsize) 
    
        {return 0;}    
        else        
    {    
            printf("arr[%d] * %d^%d = %d\n", i, x, i, arr[i] * power_(x,i));    
            return arr[i]*power_(x,i) + helper(arr, arrsize, x,i+1);   
        }   
    }
    int sumOfEvaluations(int arr[], int arrsize) {
    
        if (arrsize == 0)     
        {return 0;}
        else {    
            return helper(arr, arrsize, arr[arrsize-1],0) + sumOfEvaluations(arr, arrsize-1);   
        }
    }

my problem is whenever i input an array, i don't get the result i want, for example for the array {1,2,3,4) the result should be 514, but the helper function skips part of the calculations.

i tried adding a print function before the recursive part of the function to see where it goes wrong, this is what it prints

    arr[0] * 4^0 = 1    
    arr[1] * 4^1 = 8    
    arr[2] * 4^2 = 48    
    arr[3] * 4^3 = 256    
    arr[0] * 3^0 = 1    
    arr[1] * 3^1 = 6    
    arr[2] * 3^2 = 27

it starts skipping here

    arr[0] * 2^0 = 1    
    arr[1] * 2^1 = 4    
    arr[0] * 1^0 = 1

Answer 1

From the code it seems you are trying to recursively compute the value of a polynomial:

$$p(x) = \sum_{i = 0}^{n - 1} a_i \cdot x^i$$

If this is the case then your helper function will compute this value. Then you simply remove the recursive call in sumOfEvaluations giving:

int sumOfEvaluations(int arr[], int arrsize, int x) {

    if (arrsize == 0)
        return 0;
    else
        return helper(arr, arrsize, x, 0);
}

Now sumOfEvaluations computes the desired value.

Edit: It seems I initially misunderstood the problem. You do indeed want to evaluate the polynomials with the polynomial coefficients as input. In this case the following implementation will compute the desired value:

int func1(int arr[], int k, int i) {
    
    int res = 0;
    
    if(i < 0)
        return 0;
    
    res = arr[k] * pow(arr[i], k) + func1(arr, k, i - 1);
    
    return res;
}

int func2(int arr[], int k, int i) {
    
    int res = 0;
    
    if(k < 0)
        return 0;
    
    res = arr[k] * pow(arr[i], k) + func2(arr, k - 1, i);
    
    return res;
}

int sumOfEvaluations(int arr[], int arrsize) {
    
    int res = 0;
    
    if(arrsize < 0)
        return 0;
    
    res = res + func1(arr, arrsize - 1, arrsize - 1);
    res = res + func2(arr, arrsize - 2, arrsize - 1);
    
    res = res + sumOfEvaluations(arr, arrsize - 1);
    
    return res;
}

In the case you provided the above gives $514$ as output.