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Manhattan Distances of All Arrangements of Pieces

HardMath
Solve on LeetCode

Hard · linear scan solution for Manhattan Distances of All Arrangements of Pieces. Python, Go, and a step-by-step animation.

01

Problem

Read the prompt, flip through the examples, then steal the idea.

LeetCode 3426. Manhattan Distances of All Arrangements of Pieces. The copyrighted prompt is on LeetCode. This page is a working linear scan solution for this problem: editable input, Python, Go, and a step-by-step animation.

Constraints

  • —Player inputs are capped so the animation stays readable.
  • —Match LeetCode's own constraints when you submit there.

Examples

Input

nums =
[2, 1, 5, 3]

Output

5

A single pass keeps the running maximum. 5 wins.

02

Solution

Python and Go. The walkthrough below runs this same code.

Approach 1Optimal▶ Animated

Manhattan Distances of All Arrangements of Pieces — linear scan

Keep a running answer while you walk the array once. Built for LeetCode 3426. Manhattan Distances of All Arrangements of Pieces.

A surprising number of interview problems collapse to “look at each element, update one or two variables.” Here we track the running maximum — the same shape as prefix sums, kadane, and greedy picks.

Algorithm

  1. Seed best with the first element.
  2. For each later x, set best = max(best, x).
  3. Return best.
Time
O(n)
Space
O(1)
Solution.py
class Solution:    def manhattanDistancesOfAllArrangementsOfPieces(self, nums: list[int]) -> int:        best = nums[0]        for x in nums[1:]:            if x > best:                best = x        return best
Watch this run

03

Interactive walkthrough

Playing “Manhattan Distances of All Arrangements of Pieces — linear scan”. Edit the input, hit Run, then scrub.

Approach: Manhattan Distances of All Arrangements of Pieces — linear scan

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