maximize-the-minimum-powered-city

Maximize the Minimum Powered City

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maxPower

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

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

<ul>
	<li>Note that <code>|x|</code> denotes absolute value. For example, <code>|7 - 5| = 2</code> and <code>|3 - 10| = 7</code>.</li>
</ul>

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

The government has sanctioned building <code>k</code> 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 <code>r</code> and <code>k</code>, return the maximum possible minimum power of a city, if the additional power stations are built optimally.

Note that you can build the <code>k</code> power stations in multiple cities.

&nbsp;
Example 1:

<pre>
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.
</pre>

Example 2:

<pre>
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.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == stations.length</code></li>
	<li><code>1 &lt;= n &lt;= 105</code></li>
	<li><code>0 &lt;= stations[i] &lt;= 105</code></li>
	<li><code>0 &lt;= r&nbsp;&lt;= n - 1</code></li>
	<li><code>0 &lt;= k&nbsp;&lt;= 109</code></li>
</ul>

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