2843. Count Symmetric Integers

Description

You are given two positive integers low and high.

An integer x consisting of 2 * n digits is symmetric if the sum of the first n digits of x is equal to the sum of the last n digits of x. Numbers with an odd number of digits are never symmetric.

Return the number of symmetric integers in the range [low, high].

 

Example 1:

Input: low = 1, high = 100
Output: 9
Explanation: There are 9 symmetric integers between 1 and 100: 11, 22, 33, 44, 55, 66, 77, 88, and 99.

Example 2:

Input: low = 1200, high = 1230
Output: 4
Explanation: There are 4 symmetric integers between 1200 and 1230: 1203, 1212, 1221, and 1230.

 

Constraints:

• 1 <= low <= high <= 104

 

Solutions

Solution: Math

• Time complexity: O(high-low)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {number} low
 * @param {number} high
 * @return {number}
 */
const countSymmetricIntegers = function (low, high) {
  let result = 0;

  const isSymmetric = num => {
    if (num < 10) return false;
    if (num < 100) return num % 10 === Math.floor(num / 10);
    if (num < 1000) return false;
    const left = Math.floor(num / 100);
    const right = num % 100;
    const leftSum = (left % 10) + Math.floor(left / 10);
    const rightSum = (right % 10) + Math.floor(right / 10);

    return leftSum === rightSum;
  };

  for (let num = low; num <= high; num++) {
    if (!isSymmetric(num)) continue;

    result += 1;
  }

  return result;
};