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3443. Maximum Manhattan Distance After K Changes
- Given a string s representing movements on an infinite grid with 'N', 'S', 'E', and 'W' characters, find the maximum Manhattan distance from the origin that can be achieved by changing at most k characters.
- Approach involves iterating through the string, updating position based on directions, calculating Manhattan distance at each step, accounting for changes allowed, and updating the maximum distance accordingly.
- The solution efficiently determines the maximum Manhattan distance with the constraint of at most k changes to the movement directions in the string.
- The algorithm runs in linear time, making it suitable for large inputs.
- Example scenarios such as changing 'S' to 'N' in 'NWSE' to get a distance of 3 and changing 'NSWWEW' result in an output of 6 are provided.
- Constraints include 1 <= s.length <= 105 and 0 <= k <= s.length, with hints suggesting brute forcing directions and maximizing distance changes.
- The algorithm involves optimizing movements by potentially changing directions to increase the Manhattan distance from the origin.
- Code example in PHP showcases the implementation and testing with test cases to demonstrate the solution.
- The approach efficiently balances distance optimization with the constraints of allowed changes and total movements in the string.
- The solution offers a systematic way to determine the maximum Manhattan distance achievable with limited direction changes.
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