Maximize the Minimum Powered City

arraybinary searchgreedy

Problem Statement

You are given a 0-indexed integer array stations of length n , where stations[i] represents the number of power stations in the i ^th city.

Each power station can provide power to every city in a fixed range . In other words, if the range is denoted by r , then a power station at city i can provide power to all cities j such that |i - j| <= r and 0 <= i, j <= n - 1 .

Note that |x| denotes absolute value. For example, |7 - 5| = 2 and |3 - 10| = 7 .

The power of a city is the total number of power stations it is being provided power from.

The government has sanctioned building k more power stations, each of which can be built in any city, and have the same range as the pre-existing ones.

Given the two integers r and k , return the maximum possible minimum power of a city, if the additional power stations are built optimally.

Note that you can build the k power stations in multiple cities.

Examples

Example 1

Input: stations = [1,2,4,5,0], r = 1, k = 2
Output: 5
One of the optimal ways is to install both the power stations at city 1. 
So stations will become [1,4,4,5,0].
- City 0 is provided by 1 + 4 = 5 power stations.
- City 1 is provided by 1 + 4 + 4 = 9 power stations.
- City 2 is provided by 4 + 4 + 5 = 13 power stations.
- City 3 is provided by 5 + 4 = 9 power stations.
- City 4 is provided by 5 + 0 = 5 power stations.
So the minimum power of a city is 5.
Since it is not possible to obtain a larger power, we return 5.

Example 2

Input: stations = [4,4,4,4], r = 0, k = 3
Output: 4
It can be proved that we cannot make the minimum power of a city greater than 4.

Constraints

n == stations.length

1 <= n <= 10 ^5

0 <= stations[i] <= 10 ^5

0 <= r <= n - 1

0 <= k <= 10 ^9

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBinary Search