<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>

#define pii pair<int,int>
class Solution {
public:
    int findRadius(vector<int>& houses, vector<int>& heaters){
        set<int>st(houses.begin(),houses.end());
        sort(heaters.begin(),heaters.end());
        vector<int> h(st.begin(),st.end());
        int ans=0;
        for(int i=0;i<h.size();i++){
            int right=upper_bound(heaters.begin(),heaters.end(),h[i])-heaters.begin();
            int left=lower_bound(heaters.begin(),heaters.end(),h[i])-heaters.begin();
            if(left>=heaters.size() or heaters[left]!=h[i]) left-=1;
            int distance=INT_MAX;
            if(left>=0) {
                int temp=abs(heaters[left]-h[i]);
                distance=min(distance,temp);
            }
            if(right<heaters.size()){
                int temp=abs(heaters[right]-h[i]);
                distance=min(distance,temp);
            }
            ans=max(ans,distance);
        }
        return ans;
    }
};
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