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

maxDistance.js

/**
 * Calculates the maximum Manhattan distance from the origin
 * that can be achieved while moving in a grid, with the option
 * to change up to 'k' directions.
 *
 * @param {string} s - String of movement directions: 'N', 'S', 'E', 'W'.
 * @param {number} k - Number of allowed direction changes.
 * @return {number} - Maximum distance from the origin at any point.
 */
var maxDistance = function(s, k) {
    let x = 0, y = 0;       // Current coordinates on the grid
    let maxDist = 0;        // Tracks the farthest distance from origin

    for (let i = 0; i < s.length; i++) {
        const ch = s[i];

        // Update coordinates based on current move
        if (ch === 'N') y += 1;
        else if (ch === 'S') y -= 1;
        else if (ch === 'E') x += 1;
        else if (ch === 'W') x -= 1;

        // At most k changes allowed, but we can’t change more than i + 1 steps so far
        const changes = Math.min(k, i + 1);

        // Each change can increase distance by up to 2 units (reversing direction fully)
        const maxPossibleDist = Math.abs(x) + Math.abs(y) + 2 * changes;

        // Cap the distance by the total number of steps taken so far
        const cappedDist = Math.min(maxPossibleDist, i + 1);

        maxDist = Math.max(maxDist, cappedDist);
    }

    return maxDist;
};