What is the time complexity of Find Three Consecutive Integers That Sum to a Given Number?

The optimal solution for Find Three Consecutive Integers That Sum to a Given Number runs in O(1) time and uses O(1) space. The time complexity is O(1) because we are performing a constant number of operations regardless of the input size.

What is the brute force solution for Find Three Consecutive Integers That Sum to a Given Number?

The brute force approach for Find Three Consecutive Integers That Sum to a Given Number is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible triplet of consecutive integers to see if their sum equals the given number. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Find Three Consecutive Integers That Sum to a Given Number?

Find Three Consecutive Integers That Sum to a Given Number uses the following concepts: Math, Simulation. The recommended patterns to study are: Mathematical properties, Array manipulation.

What are the interview tips for Find Three Consecutive Integers That Sum to a Given Number?

Always consider edge cases, such as small values of num. Think about mathematical properties of the problem before jumping into coding. Explain your thought process clearly while coding to demonstrate your understanding.

What are common mistakes when solving Find Three Consecutive Integers That Sum to a Given Number?

Failing to check if num is divisible by 3 before calculating x. Returning an empty array without considering the divisibility condition.

#2177

Find Three Consecutive Integers That Sum to a Given Number

Medium

MathSimulationMathematical propertiesArray manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(1)
Space	O(1)	O(1)

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Intuition

Time O(1)Space O(1)

The optimal approach recognizes that if three consecutive integers can sum to a number, they can be represented as x-1, x, and x+1. This leads us to derive a formula for x directly from num.

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Algorithm

4 steps

1Step 1: Check if num is divisible by 3.
2Step 2: If not divisible, return an empty array since three consecutive integers cannot sum to num.
3Step 3: Calculate x as num / 3.
4Step 4: Return the array [x-1, x, x+1].

solution.py7 lines

1# Full working Python code
2
3def find_consecutive_integers(num):
4    if num % 3 != 0:
5        return []
6    x = num // 3
7    return [x - 1, x, x + 1]

ℹ

Complexity note: The time complexity is O(1) because we are performing a constant number of operations regardless of the input size.

1Three consecutive integers can be expressed in terms of their average.
2If the sum is not divisible by 3, it's impossible to find three consecutive integers that sum to it.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.