How do you solve Reach a Number on LeetCode?

Reach a Number (LeetCode #754) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The target can be negative, but the approach remains the same by taking the absolute value.

What is the brute force solution for Reach a Number?

The brute force approach for Reach a Number is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we explore all possible combinations of moves to see if we can reach the target. This involves simulating every possible path we could take, which can be inefficient but helps us understand the problem. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Reach a Number?

Reach a Number uses the following concepts: Math, Binary Search. The recommended patterns to study are: Mathematical reasoning, Greedy algorithms.

What are the interview tips for Reach a Number?

Always clarify the problem statement and constraints. Think about edge cases, like negative targets. Explain your thought process clearly while coding.

What are common mistakes when solving Reach a Number?

Not considering the absolute value of the target. Failing to check the condition for even difference between sum and target.

#754

Reach a Number

Medium

MathBinary SearchMathematical reasoningGreedy algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(1)

The optimal approach uses mathematical reasoning to find the minimum number of moves required to reach the target. By calculating the sum of moves and using properties of arithmetic sequences, we can determine the minimum moves without simulating each path.

⚙️

Algorithm

3 steps

1Step 1: Calculate the absolute value of the target since the number line is symmetric.
2Step 2: Initialize a move counter and a sum variable to keep track of the total steps taken.
3Step 3: Increment the move counter and add the current move count to the sum until the sum is greater than or equal to the target and the difference between the sum and target is even.

solution.py15 lines

1# Full working Python code
2
3def reach_number(target):
4    target = abs(target)
5    move_count = 0
6    sum_moves = 0
7    while True:
8        move_count += 1
9        sum_moves += move_count
10        if sum_moves >= target and (sum_moves - target) % 2 == 0:
11            return move_count
12
13# Example usage
14print(reach_number(2))  # Output: 3
15print(reach_number(3))  # Output: 2

ℹ

Complexity note: The time complexity is O(n) because we incrementally check each move until we find the minimum moves required to reach the target.

1The target can be negative, but the approach remains the same by taking the absolute value.
2The sum of the first n natural numbers is n(n+1)/2, which helps in determining the minimum moves.

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