<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 {
public:
    bool check(long radius,vector<int>&houses,vector<int>heaters,int n,int m){
        int i=0,j=0;
        for(;j<m;j++){
            long left = heaters[j]-radius;
            long right = heaters[j]+radius;
            if(houses[i]<left) return 0;
            while(i<n and houses[i]<=right){
                i++;
            }
            if(i==n) return 1;
        }
        return (i==n);
    }
    int findRadius(vector<int>& houses, vector<int>& heaters) {
        int n = houses.size();
        int m = heaters.size();
        sort(houses.begin(),houses.end());
        sort(heaters.begin(),heaters.end());
        long l = 0, r = max(heaters[m-1],houses[n-1]-min(heaters[0],houses[0])), radius,minRadius;
        while(l<=r){
            radius = l+(r-l)/2;
            if(check(radius,houses,heaters,n,m)){
                r=radius-1;
                minRadius = radius;
            }else{
                l=radius+1;
            }
        }
        return minRadius;
    }
};
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