Heaters
<p>Winter is coming! During the contest, your first job is to design a standard heater with a fixed warm radius to warm all the houses.</p>

<p>Every house can be warmed, as long as the house is within the heater&#39;s warm radius range.&nbsp;</p>

<p>Given the positions of <code>houses</code> and <code>heaters</code> on a horizontal line, return <em>the minimum radius standard of heaters&nbsp;so that those heaters could cover all houses.</em></p>

<p><strong>Notice</strong> that&nbsp;all the <code>heaters</code> follow your radius standard, and the warm radius will the same.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> houses = [1,2,3], heaters = [2]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The only heater was placed in the position 2, and if we use the radius 1 standard, then all the houses can be warmed.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> houses = [1,2,3,4], heaters = [1,4]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The two heaters were placed at positions 1 and 4. We need to use a radius 1 standard, then all the houses can be warmed.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> houses = [1,5], heaters = [2]
<strong>Output:</strong> 3
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= houses.length, heaters.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= houses[i], heaters[i] &lt;= 10<sup>9</sup></code></li>
</ul>
Array; Two Pointers; Binary Search; Sorting
class Solution:
    def findRadius(self, houses: List[int], heaters: List[int]) -> int:
        houses.sort()
        heaters.sort()

        def check(r):
            m, n = len(houses), len(heaters)
            i = j = 0
            while i < m:
                if j >= n:
                    return False
                mi = heaters[j] - r
                mx = heaters[j] + r
                if houses[i] < mi:
                    return False
                if houses[i] > mx:
                    j += 1
                else:
                    i += 1
            return True

        left, right = 0, int(1e9)
        while left < right:
            mid = (left + right) >> 1
            if check(mid):
                right = mid
            else:
                left = mid + 1
        return left
