Using for loop to find minimal sum of digits in given number interval

So, I am doing a task that asks to find the amount of positive integers from interval [m, n] with minimum sum of digits.

I declared a function that computes the sum of digits, however I am having problems finding the amount of numbers. Below is the code I wrote for finding the minimum sum of digits and counting. I hope I made myself clear. I would appreciate if you could help me fix this code.

Input: 1 100
Output: 3

int minSum(int m, int n){
  
    for (int i=m; i<=n; i++){
        int sm=sum(i);
        if (sm<min) min=sm;
        if (min==sm)  cnt++;
    }
    return cnt;
}

For starters the variables min and cnt are not declared within the function. If they are a file scope variables then using file scope variables in the function is a bad idea.

The function can look the following way. I assume that sum of digits can not be a negative number.

unsigned int minSum( int m, int n )
{
    unsigned int cnt = 0; 
    int min = 0;

    if ( !( n < m ) )
    {
        do
        {
            int sm = sum( m );
            if ( sm < min ) 
            {
                min = sm;
                cnt = 1;
            }
            else if ( !( min < sm ) )
            {
                ++cnt;
            }
        } while ( m++ != n ); 
    }

    return cnt;
}

Pay attention to that the for loop in your original code

for (int i=m; i<=n; i++){

can invoke undefined behavior for example when n is equal to INT_MAX.

int sum(int x)
{
    int result = 0;
    while(x) 
    {
        result += abs(x % 10);
        x /= 10;
    }
    return result;
}

size_t minSum(int m, int n){
    int min = sum(m);
    int sm;
    size_t cnt = 0;

    for (int i = m + 1; i <= n; i++)
        if ((sm = sum(i)) < min) min = sm;

    for (int i = m; i <= n; i++)
        if (sum(i) == min) cnt++;

    return cnt;
}

Or less brute force:

size_t minsum(int m, int n){
    int min = sum(m);
    int sm;
    size_t cnt = 1;

    for (int i = m + 1; i <= n; i++)
    {
        sm = sum(i);
        if (sm < min) 
        {
            min = sm; 
            cnt = 1;
        }
        else if(sm == min) cnt++;
    }

    return cnt;
}

Problems:

1. cnt and min not initialized in the function (nor defined)

2. cnt is not reset when a new minimum value is found.

Your code is easy to fix. Like:

int minSum(int m, int n){
    int cnt = 0;        // Initialize cnt
    int min = INT_MAX;  // Initialize min to a high value

    for (int i=m; i<=n; i++){
        int sm=sum(i);
        if (sm<min)
        {
            cnt = 0;   // Reset cnt
            min=sm;
        }
        if (min==sm)  cnt++;
    }
    return cnt;
}