Maximize the Minimum Powered City
You are given a 0-indexed integer array stations of length n, where stations[i] represents the number of power stations in the ith city.
You are given a 0-indexed integer array stations of length n, where stations[i] represents the number of power stations in the ith 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.
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
- 1 <= n <= 10^5
- 0 <= stations[i] <= 10^5
- 0 <= r <= n - 1
- 0 <= k <= 10^9
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