Given the number of cities n numbered from 0 to n-1 and the cities in which stations are located, the task is to find the maximum distance between any city and its nearest station. Note that the cities with stations can be given in any order.
Input: numOfCities = 6, stations = [1, 4] Output: 1 Input: numOfCities = 6, stations =  Output: 3 Input: numOfCities = 6, stations = [3, 1] Output: 2
- The below figure represents the first example containing 6 cities and the cities with stations highlighted with green color. In this case, the farthest cities from their nearest stations are 0, 2, 3 and 5 each at a distance of 1. Hence maximum distance is 1.
In the second example, the farthest city from its nearest station is 0 which is at a distance of 3. Hence maximum distance is 3.
In the third example, the farthest city from its nearest station is 5 which is at a distance of 2. Hence maximum distance is 2.
Approach: There are three possible cases in this problem:
- When the farthest city is between two stations.
- When the farthest city is on the left side of the first station.
- When the farthest city is on the right side of the last station.
Below is the algorithm to solve the above problem:
- Initialize a boolean array of size n (number of cities) with False. Then mark the values of cities with stations as True
- Initialize a variable dist with 0. Initialize another variable maxDist with value which is equal to the first city with station (used for case 2).
- Start looping through all the cities ony by one.
- If the current city has a station, then assign the maximum of (dist+1)//2 and maxDist to maxDist (used for case 1). Also, assign 0 to dist.
- Else, increment dist.
- At the end, return the maximum of dist and maxDist (used for case 3).
Below is the implementation of the above approach:
Max Distance: 2
Time Complexity: O(n)
Space Complexity: O(n)
- Find the maximum possible distance from origin using given points
- Find a rotation with maximum hamming distance
- Find the maximum distance covered using n bikes
- Pair with given sum and maximum shortest distance from end
- Maximum distance between two 1's in Binary representation of N
- Maximum subsequence sum such that all elements are K distance apart
- Maximum distance between two unequal elements
- Maximum distance between two occurrences of same element in array
- Minimal product subsequence where adjacent elements are separated by a maximum distance of K
- Find points at a given distance on a line of given slope
- Number of stopping station problem
- Find integral points with minimum distance from given set of integers using BFS
- Find the shortest distance between any pair of two different good nodes
- Find the integer points (x, y) with Manhattan distance atleast N
- Find distance between two nodes in the given Binary tree for Q queries
- Haversine formula to find distance between two points on a sphere
- Queries to find distance between two nodes of a Binary tree
- Find the distance covered to collect items at equal distances
- Find the side of the squares which are lined in a row, and distance between the centers of first and last square is given
- Find the minimum sum of distance to A and B from any integer point in a ring of size N
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.