2177 - Find Three Consecutive Integers That Sum to a Given Number (Medium)

Problem Link

https://leetcode.com/problems/find-three-consecutive-integers-that-sum-to-a-given-number/

Problem Statement

Given an integer num, return three consecutive integers (as a sorted array) that sum to num. If num cannot be expressed as the sum of three consecutive integers, return an empty array.

Example 1:

Input: num = 33
Output: [10,11,12]
Explanation: 33 can be expressed as 10 + 11 + 12 = 33.
10, 11, 12 are 3 consecutive integers, so we return [10, 11, 12].

Example 2:

Input: num = 4
Output: []
Explanation: There is no way to express 4 as the sum of 3 consecutive integers.

Constraints:

• 0 <= num <= 10^15

Approach 1: Math

We can express it as $n + (n + 1) + (n + 2) = num$ and find what $n$ is.

$$n + (n + 1) + (n + 2) = num$$ $$3 * n + 3 = num$$ $$n = (num - 3) / 3$$

If $(num - 3)$ is not divisible by $3$, then return empty array. Otherwise, calculate $n$ and return $n$, $n + 1$, and $n + 2$.

class Solution {
public:
    vector<long long> sumOfThree(long long num) {
        num -= 3;
        if (num % 3 == 0) {
            long long n = num / 3;
            return {n, n + 1, n + 2};
        }
        return {};
    }
};

Alternatively, we can find the middle number and get the first and the third one.

class Solution {
public:
    vector<long long> sumOfThree(long long num) {
        if (num % 3 == 0) {
            long long x = num / 3;
            return {x - 1, x, x + 1};
        }
        return {};
    }
};