Suppose we have N number of cities, and they are numbered from 0 to N-1 and we also have the cities in which stations are located, we have to find the maximum distance between any city and its nearest station. We have to keep in mind that the cities with stations can be given in any order.
So, if the input is like N = 6 and stations = [2,4], then the output will be 2
To solve this, we will follow these steps −
station_present := a list of size N, and fill with False
for each city in station, do
station_present[city] := True
dist := 0, maximum_dist := minimum of station
for city in range 0 to N, do
if station_present[city] is True, then
maximum_dist := maximum of(dist + 1) / 2, maximum_dist
dist := 0
otherwise,
dist := dist + 1
return maximum of maximum_dist, dist
Example (Python)
Let us see the following implementation to get better understanding −
def get_max_dist(N, station): station_present = [False] * N for city in station: station_present[city] = True dist, maximum_dist = 0, min(station) for city in range(N): if station_present[city] == True: maximum_dist = max((dist + 1) // 2, maximum_dist) dist = 0 else: dist += 1 return max(maximum_dist, dist) N = 6 station = [2, 4] print(get_max_dist(N, station))
Input
6, [2,4]
Output
2