<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>

class Solution:
    def findRadius(self, houses: List[int], heaters: List[int]) -> int:
        sorted_houses = sorted(houses)
        sorted_heaters = sorted(heaters)

        def find_closest_heater_index(target):
            heater_index = bisect.bisect_left(sorted_heaters, target)

            if heater_index == 0:
                return 0

            if heater_index == len(sorted_heaters):
                return len(sorted_heaters) - 1

            if abs(sorted_heaters[heater_index - 1] - target) <= abs(sorted_heaters[heater_index] - target):
                return heater_index - 1
            else:
                return heater_index


        max_heating_dist = -float('inf')
        for house in sorted_houses:
            heater_index = find_closest_heater_index(house)
            max_heating_dist = max(max_heating_dist, abs(house - sorted_heaters[heater_index]))

        return max_heating_dist

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