Assign Mice to Holes
The Assign Mice to Holes problem is a classic problem in computer science and mathematics. It involves a scenario where there are 'n' mice and 'n' holes placed in a line. Each mouse must be assigned to a hole, and the goal is to minimize the time taken for all the mice to reach their respective holes. Each mouse moves at a certain speed, and the time it takes for a mouse to reach its hole is proportional to the distance between the mouse and the hole.
Problem Statement and Example
Given the positions of mice and holes along a line, and the speed of each mouse, the task is to find the arrangement of mice in the holes that minimizes the maximum time taken for any mouse to reach its hole. Each mouse should be assigned to a unique hole, and the order of mice and holes should be preserved.
For example, consider the following scenario:
 Mice Positions: 3, 7, 5, 9, 16
 Hole Positions: 1, 9, 15, 4, 14
The goal is to arrange the mice in the holes in a way that minimizes the maximum time taken for any mouse to reach its hole.
Idea to Solve the Problem
To solve this problem, we can follow these steps:
 Sort the positions of mice and holes in ascending order.
 Iterate through the sorted arrays and calculate the absolute difference between each mouse's position and its corresponding hole's position.
 Track the maximum absolute difference during the iteration.
 The maximum absolute difference represents the time it takes for the mouse to reach its hole in the optimal arrangement.
Algorithm Explanation
 Sort both the
mices
andholes
arrays in ascending order.  Initialize a variable
result
to store the maximum absolute difference (time taken).  Iterate through the arrays from 0 to
n1
(wheren
is the length of the arrays): a. Calculate the absolute difference betweenmices[i]
andholes[i]
. b. Updateresult
if the calculated difference is greater than the currentresult
.  Print the
result
, which represents the minimum time taken for the mice to reach their holes in an optimal arrangement.
Code Solution

1) Assigning mice to holes in java
2) Assigning mice to holes in c++
3) Assigning mice to holes in c#
4) Assigning mice to holes in php
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6) Assigning mice to holes in ruby
7) Assigning mice to holes in scala
8) Assigning mice to holes in swift
9) Assigning mice to holes in golang
10) Assigning mice to holes in kotlin
11) Assigning mice to holes in vb.net
12) Assigning mice to holes in node js
Time Complexity
The time complexity of this algorithm is O(n log n), where 'n' is the number of mice (or holes). This is because the algorithm involves sorting the mice and holes arrays, which takes O(n log n) time using a standard sorting algorithm. The subsequent iteration through the arrays takes linear time O(n), resulting in a total complexity of O(n log n).
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