How do you solve Minimum Time Visiting All Points on LeetCode?

Minimum Time Visiting All Points (LeetCode #1266) 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 fastest way to move between two points is to maximize diagonal movement first.

What is the brute force solution for Minimum Time Visiting All Points?

The brute force approach for Minimum Time Visiting All Points is Brute Force, with O(n) time complexity and O(1) space complexity. The brute force approach involves calculating the distance between each pair of consecutive points using the maximum of the absolute differences in their x and y coordinates. This method is straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Time Visiting All Points?

Minimum Time Visiting All Points uses the following concepts: Array, Math, Geometry. The recommended patterns to study are: Greedy Algorithms, Distance Calculation.

What are the interview tips for Minimum Time Visiting All Points?

Always clarify the movement rules before starting to solve the problem. Consider edge cases and how they might affect your logic. Practice explaining your thought process as you code, as communication is key in interviews.

What are common mistakes when solving Minimum Time Visiting All Points?

Confusing the distance calculation by using Euclidean distance instead of the correct max-based calculation. Neglecting to handle edge cases, such as points being the same.

#1266

Minimum Time Visiting All Points

Easy

ArrayMathGeometryGreedy AlgorithmsDistance Calculation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(1)

The optimal solution is actually the same as the brute force approach since the movement rules dictate that the fastest way to move between two points is to maximize diagonal movement first and then move straight. Thus, the same formula applies.

⚙️

Algorithm

5 steps

1Step 1: Initialize a variable to keep track of the total time.
2Step 2: Loop through each consecutive pair of points in the list.
3Step 3: For each pair, calculate the time taken to move from the first point to the second using the formula: max(abs(x2 - x1), abs(y2 - y1)).
4Step 4: Add the calculated time to the total time.
5Step 5: Return the total time after processing all points.

solution.py9 lines

1# Full working Python code
2
3def minTimeToVisitAllPoints(points):
4    total_time = 0
5    for i in range(len(points) - 1):
6        x1, y1 = points[i]
7        x2, y2 = points[i + 1]
8        total_time += max(abs(x2 - x1), abs(y2 - y1))
9    return total_time

ℹ

Complexity note: The time complexity remains O(n) as we still iterate through the list of points once, and the space complexity is O(1) since we only use a fixed amount of extra space.

1The fastest way to move between two points is to maximize diagonal movement first.
2The distance formula used here is based on the Chebyshev distance, which is appropriate for this problem.

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