Maximum Number of Achievable Transfer Requests

arraybacktrackingbit manipulation

Problem Statement

We have n buildings numbered from 0 to n - 1 . Each building has a number of employees. It's transfer season, and some employees want to change the building they reside in.

You are given an array requests where requests[i] = [from _i , to _i ] represents an employee's request to transfer from building from _i to building to _i .

All buildings are full , so a list of requests is achievable only if for each building, the net change in employee transfers is zero . This means the number of employees leaving is equal to the number of employees moving in . For example if n = 3 and two employees are leaving building 0 , one is leaving building 1 , and one is leaving building 2 , there should be two employees moving to building 0 , one employee moving to building 1 , and one employee moving to building 2 .

Return the maximum number of achievable requests .

Examples

Example 1

Input: n = 5, requests = [[0,1],[1,0],[0,1],[1,2],[2,0],[3,4]]
Output: 5
 Explantion: Let's see the requests:
From building 0 we have employees x and y and both want to move to building 1.
From building 1 we have employees a and b and they want to move to buildings 2 and 0 respectively.
From building 2 we have employee z and they want to move to building 0.
From building 3 we have employee c and they want to move to building 4.
From building 4 we don't have any requests.
We can achieve the requests of users x and b by swapping their places.
We can achieve the requests of users y, a and z by swapping the places in the 3 buildings.

Example 2

Input: n = 3, requests = [[0,0],[1,2],[2,1]]
Output: 3
 Explantion: Let's see the requests:
From building 0 we have employee x and they want to stay in the same building 0.
From building 1 we have employee y and they want to move to building 2.
From building 2 we have employee z and they want to move to building 1.
We can achieve all the requests.

Example 3

Input: n = 4, requests = [[0,3],[3,1],[1,2],[2,0]]
Output: 4

Constraints

1 <= n <= 20

1 <= requests.length <= 16

requests[i].length == 2

0 <= from _i , to _i < n

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBacktracking