You have n warehouses and n shops. At each warehouse, a truck is loaded with enough goods to supply one shop. There are m roads, each going from a warehouse to a shop, and driving along the ith road takes d i hours, where d i is an integer. Design a polynomial time algorithm to send the trucks to the shops, minimising the time until all shops are supplied.

Following are the steps of the polynomial-time algorithm:

Split the routes according to their categorizationAssuming that mid = di of the middle road, low = road with the least di, and high = road with the highest di, we may do a binary search on the sorted list.All shops must be approachable only using these roads for every road, from low to mid.Check if all shops can be reached from using only these roads.There is a solution if every shop can be reached by road only up to , but not up to mid.You can if all businesses aren't accessible using both roads.If every shop could be reached using both mid and mid+1, then set high to mid-1.With these layouts of businesses and roads, no response can be given because You can do this by The new low, mid, and high numbers are used in step (a).

In a minimum amount of time, this algorithm will determine the best strategy to supply all shops.

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polynomial-time algorithm:

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