CodeFights - Comfortable Numbers - Solution

Problem

Let's say that number a feels comfortable with number b if a ≠ b and b lies in the segment [a - s(a), a + s(a)], where s(x) is the sum of x's digits.

How many pairs (a, b) are there, such that a < b, both a and b lie on the segment [L, R], and each number feels comfortable with the other?

Example

For L = 10 and R = 12, the output should be
comfortableNumbers(L, R) = 2.

Here are all values of s(x) to consider:

• s(10) = 1, so 10 is comfortable with 9 and 11;
• s(11) = 2, so 11 is comfortable with 9, 10, 12 and 13;
• s(12) = 3, so 12 is comfortable with 9, 10, 11, 13, 14 and 15.

Thus, there are 2 pairs of numbers comfortable with each other within the segment [10; 12]: (10, 11) and (11, 12).

Input/Output

• [time limit] 500ms (cpp)

• [input] integer L
  Guaranteed constraints:
  1 ≤ L ≤ R ≤ 1000.
• [input] integer R
  Guaranteed constraints:
  1 ≤ L ≤ R ≤ 1000.
• [output] integer
  The number of pairs satisfying all the above conditions.

Solution

The problem is pretty straightforward due to constraints of the problem. We need to look at 1000C2 pairs in the worst case. We look at all the pairs in the range [L, R] and check if the pair of integers in a given pair are comfortable to each other.

Code

int digitSum(int n){
    int _sum = 0;
    
    while (n){
        _sum += (n%10);
        n = n/10;
    }
    
    return _sum;
}

int comfortableNumbers(int L, int R) {
    int total_pairs = 0;
    
    for(int i=L; i<=R; i++){
        for(int j=i+1; j<=R; j++){
            int s_a = digitSum(i);
            int s_b = digitSum(j);
            if (j>= (i-s_a) and j<= (i+s_a) and 
                  i>= (j-s_b) and i<= (j+s_b)
               ) {
                total_pairs++;
            }
        }
    }
    return total_pairs;
}