2528 - Maximize the Minimum Powered City.

Hard

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

Example 1:

Input: stations = 1,2,4,5,0, r = 1, k = 2

Output: 5

Explanation:

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

Explanation: It can be proved that we cannot make the minimum power of a city greater than 4.

Constraints:

• n == stations.length

• <code>1 <= n <= 10⁵</code>

• <code>0 <= stationsi<= 10⁵</code>

• 0 <= r <= n - 1

• <code>0 <= k <= 10⁹</code>