Assign Campus Bikes to Workers

On a campus represented on the X-Y, there are n workers and m bikes (n <= m). You are given:

• workers: an array of length n, where workers[i] = [xi, yi] is the position of the ith worker
• bikes: an array of length m, where bikes[j] = [xj, yj] is the position of the jth bike

Assign a bike to each worker by pairing the worker and bike with the shortest Manhattan distance between them. If there are multiple pairs with the same distance, choose the pair with the smallest worker index, and if still tied, choose the pair with the smallest bike index. Return an array answer of length n, where answer[i] is the 0-indexed index of the bike assigned to the ith worker.

Note: The Manhattan distance between two points p1 and p2 is |p1.x - p2.x| + |p1.y - p2.y|.

Example:

Input: workers = [[0,0],[2,1]], bikes = [[1,2],[3,3]]
Output: [1,0]
Explanation: Worker 1 grabs Bike 0 as they are closest (without ties), and Worker 0 is assigned Bike 1. So the output is [1, 0].

Input: workers = [[0,0],[1,1],[2,0]], bikes = [[1,0],[2,2],[2,1]]
Output: [0,2,1]
Explanation: Worker 0 grabs Bike 0 at first. Worker 1 and Worker 2 share the same distance to Bike 2, thus Worker 1 is assigned to Bike 2, and Worker 2 will take Bike 1. So the output is [0,2,1].

Approach:

We want to organize the (worker, bike) pairs in ascending order, prioritizing their Manhattan distance, then worker index, and then bike index. Therefore, we will generate all possible (worker, bike) pairs and sort them according to the previously listed priorities. We will then iterate over the pairs, if both the worker and bike are available, assign the bike to the worker, and mark them both as unavailable. We will repeat this process until all workers have been assigned a bike.

Steps-by-step approach:

• Initialize Data Structures:
  • Create an array allTriplets to store tuples of (distance, worker, bike).
  • Create an arrayr bikeStatus to keep track of which bikes are taken.
  • Create an array workerStatus to keep track of which bike is assigned to each worker.
• Generate All Possible Pairs:
  • Iterate through all the workers and all the bikes.
  • For each worker-bike pair, calculate the Manhattan distance using the findDistance() function.
  • Add a tuple (distance, worker, bike) to the allTriplets array.
• Sort the Triplets:
  • Sort the allTriplets array based on the distance in ascending order.
• Assign Bikes to Workers:
  • Iterate through the sorted allTriplets.
  • For each tuple, check if the worker and the bike are both free.
  • If they are, assign the bike to the worker by updating the bikeStatus and workerStatus vectors.
  • Increment the pairCount variable.
  • If all workers have been assigned a bike, return the workerStatus vector.
• Return the Final Assignments:
  • After the loop, return the workerStatus vector, which contains the index of the bike assigned to each worker.

Below is the implementation of the above approach:

Worker assignments (bike index for each worker): 1 0 

Time complexity: O(NMlog⁡(NM)), Here, N is the number of workers, and M is the number of bikes.
Auxiliary Space: O(NM)