Find Three Consecutive Integers That Sum to a Given Number - Problem
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.
Note: Consecutive integers are integers that follow each other in order without gaps. For example: 1, 2, 3 or -2, -1, 0.
Input & Output
Example 1 — Basic Case
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Input:
num = 33
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Output:
[10,11,12]
💡 Note:
Three consecutive integers 10, 11, 12 sum to 33: 10 + 11 + 12 = 33
Example 2 — Small Number
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Input:
num = 4
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Output:
[]
💡 Note:
No three consecutive integers can sum to 4. The minimum sum is 0+1+2=3, next is 1+2+3=6
Example 3 — Negative Numbers
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Input:
num = 0
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Output:
[-1,0,1]
💡 Note:
Three consecutive integers -1, 0, 1 sum to 0: -1 + 0 + 1 = 0
Constraints
- -1015 ≤ num ≤ 1015
Visualization
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Understanding the Visualization
1
Input
Given target sum num = 33
2
Process
Find x, x+1, x+2 where sum equals target
3
Output
Return [10, 11, 12] or empty array if impossible
Key Takeaway
🎯 Key Insight: Three consecutive integers x, x+1, x+2 sum to 3x+3, so check if (num-3) is divisible by 3
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Explanation
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