Leetcode 2177: Find Three Consecutive Integers That Sum to a Given Number

Input: The input consists of a single integer `num`.

Example: 27

Constraints:

• 0 <= num <= 10^15

Output: The output is either an array containing the three consecutive integers that sum to `num` or an empty array if no such triplet exists.

Example: [8, 9, 10]

Constraints:

• The output must be a sorted array of three consecutive integers or an empty array.

Goal: The goal is to find if `num` can be written as the sum of three consecutive integers.

Steps:

• Check if `num` is divisible by 3.

• If `num` is divisible by 3, calculate the three consecutive integers using `num / 3 - 1`, `num / 3`, and `num / 3 + 1`.

• If not, return an empty array.

Goal: The input `num` should be within the given bounds.

Steps:

• 0 <= num <= 10^15

Assumptions:

• The integer `num` is non-negative.

• Input: 27

• Explanation: The number 27 can be expressed as 8 + 9 + 10. These are three consecutive integers that sum to 27.

Approach: The approach involves checking if the given number is divisible by 3, then finding the three consecutive integers that sum to the number.

Observations:

• The sum of three consecutive integers is always divisible by 3.

• Check if `num` is divisible by 3, then simply return the three integers. If not, return an empty array.

Steps:

• Check if `num` is divisible by 3.

• If it is, return `num / 3 - 1`, `num / 3`, `num / 3 + 1`.

• If it is not, return an empty array.

Empty Inputs:

• The input `num` is always non-negative and within the specified range.

Large Inputs:

• The solution should handle very large numbers, as `num` can be as large as 10^15.

Special Values:

• Consider the case when `num` is 0, as the sum of three consecutive integers can't result in 0.

Constraints:

• Ensure that the solution works within the input constraints.

vector<long long> sumOfThree(long long num) {
    vector<long long> ans;
    if(num %3 != 0) return ans;
    return {num / 3 - 1, num/ 3, num/3 + 1};
}

1 : Function Definition

vector<long long> sumOfThree(long long num) {

Define the function `sumOfThree` that takes a single long long integer `num` and returns a vector of long long integers.

2 : Variable Initialization

    vector<long long> ans;

Initialize an empty vector `ans` to store the result if `num` is divisible by 3.

3 : Condition Check

    if(num %3 != 0) return ans;

Check if `num` is divisible by 3. If not, return the empty vector `ans`.

4 : Return Result

    return {num / 3 - 1, num/ 3, num/3 + 1};

If `num` is divisible by 3, return a vector containing three integers: `num/3 - 1`, `num/3`, and `num/3 + 1`.

Best Case: O(1)

Average Case: O(1)

Worst Case: O(1)

Description: The time complexity is constant because the solution only requires a simple modulo check and arithmetic operations.

Best Case: O(1)

Worst Case: O(1)

Description: The space complexity is constant because we are only storing a fixed number of integers.

Leetcode 2177: Find Three Consecutive Integers That Sum to a Given Number

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