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g2501_2600.s2528_maximize_the_minimum_powered_city.readme.md Maven / Gradle / Ivy

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 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`.

*   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`
*   1 <= n <= 105
*   0 <= stations[i] <= 105
*   `0 <= r <= n - 1`
*   0 <= k <= 109