#1066 - Campus Bikes II

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Array Dynamic Programming Bit Manipulation Backtracking Bitmask

Problem Description

On a campus represented as a 2D grid, there are n workers and m bikes, with n <= m.

Each worker and bike is a 2D coordinate on this grid.

We assign one unique bike to each worker so that the sum of the Manhattan distances between each worker and their assigned bike is minimized.

Return the minimum possible sum of Manhattan distances between each worker and their assigned bike.

The Manhattan distance between two points p1 and p2 is Manhattan(p1, p2) = |p1.x - p2.x| + |p1.y - p2.y|.

Solution

/**
 * @param {number[][]} workers
 * @param {number[][]} bikes
 * @return {number}
 */
var assignBikes = function(workers, bikes) {
  const n = workers.length;
  const m = bikes.length;
  const memo = new Map();

  return dfs(0, 0);

  function getDistance(worker, bike) {
    return Math.abs(workers[worker][0] - bikes[bike][0])
      + Math.abs(workers[worker][1] - bikes[bike][1]);
  }

  function dfs(workerIndex, usedBikes) {
    if (workerIndex === n) return 0;

    const key = `${workerIndex}-${usedBikes}`;
    if (memo.has(key)) return memo.get(key);

    let minDistance = Infinity;

    for (let bikeIndex = 0; bikeIndex < m; bikeIndex++) {
      if ((usedBikes & (1 << bikeIndex)) === 0) {
        const distance = getDistance(workerIndex, bikeIndex)
          + dfs(workerIndex + 1, usedBikes | (1 << bikeIndex));
        minDistance = Math.min(minDistance, distance);
      }
    }

    memo.set(key, minDistance);
    return minDistance;
  }
};