How to Solve Maximum Manhattan Distance After K Changes Problem
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Maximum Manhattan Distance After K Changes
You are given a string s consisting of the characters 'N', 'S', 'E', and 'W', where s[i] indicates movements in an infinite grid: 'N' : Move north by 1 unit. 'S' : Move south by 1 unit. 'E' : Move eas...
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Understanding the Maximum Manhattan Distance After K Changes Problem
Let's break down this LeetCode problem and understand what makes it challenging in interview settings.
Problem Statement
You are given a string s consisting of the characters 'N', 'S', 'E', and 'W', where s[i] indicates movements in an infinite grid: 'N' : Move north by 1 unit. 'S' : Move south by 1 unit. 'E' : Move east by 1 unit. 'W' : Move west by 1 unit. Initially, you are at the origin (0, 0). You can change at most k characters to any of the four directions. Find the maximum Manhattan distance from the origin that can be achieved at any time while performing the movements in order. The Manhattan Distance between two cells (xi, yi) and (xj, yj) is |xi - xj| + |yi - yj|.
Maximum Manhattan Distance After K Changes
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Examples
s = "NWSE", k = 13Change s[2] from 'S' to 'N'. The string s becomes "NWNE". Movement Position (x, y) Manhattan Distance Maximum s[0] == 'N' (0, 1) 0 + 1 = 1 1 s[1] == 'W' (-1, 1) 1 + 1 = 2 2 s[2] == 'N' (-1, 2) 1 + 2 = 3 3 s[3] == 'E' (0, 2) 0 + 2 = 2 3 The maximum Manhattan distance from the origin that can be achieved is 3. Hence, 3 is the output.
s = "NSWWEW", k = 36Change s[1] from 'S' to 'N', and s[4] from 'E' to 'W'. The string s becomes "NNWWWW". The maximum Manhattan distance from the origin that can be achieved is 6. Hence, 6 is the output.
Constraints
1 <= s.length <= 1050 <= k <= s.lengths consists of only 'N', 'S', 'E', and 'W'.How Interview Coder Helps with Leetcode Problems
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