<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 israd(int rad,vector<int>& houses, vector<int>& heaters){
        int n = houses.size();
        int a = heaters.size();
        int i=0,j=0;
        while(i<n && j<a){
            if(rad>=abs(houses[i]-heaters[j])) i++;
            else{
                j++;
                
            }
        }
        if(i==n) return true;
        return false;
    }
    int findRadius(vector<int>& houses, vector<int>& heaters) {
        int n = houses.size();
        int a = heaters.size();

        // int max1=INT_MIN;
        // for(int i=0;i<n;i++){
        //     if(houses[i]>max1) max1=houses[i];
        // }

        // int min1=INT_MAX;
        // for(int i=0;i<n;i++){
        //     if(houses[i]<min1) min1=houses[i];
        // }

        // int max2=INT_MIN;
        // for(int i=0;i<a;i++){
        //     if(heaters[i]>max2) max2=heaters[i];
        // }        
        sort(houses.begin(),houses.end());
        sort(heaters.begin(),heaters.end());
        int h=1e9;
        int l=0,rad=0,range;
        while(l<=h){
            int mid=l+(h-l)/2;
            if(israd(mid,houses,heaters)==true){
                range=mid;
                h=mid-1;
            }
            else l=mid+1;
        }
        return range;
    }
};
29000