<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>

//BINARY SEARCH ON ANSWER 

class Solution {
public:
    int findRadius(vector<int>& houses, vector<int>& heaters) {       
        int heat = heaters.size();
        int hou = houses.size();
        sort(houses.begin(), houses.end());
        sort(heaters.begin(), heaters.end());
        int l = 0;
        int h = max(abs(houses[0]-heaters[heat-1]), abs(houses[hou-1]-heaters[0]));
        int ans = -1;
        int mid = l+(h-l)/2;
        while(l <= h)
        {
            mid = l+(h-l)/2;
            if(solve(houses, heaters, mid))
            {
               ans = mid;
               h = mid-1;
            }else
            {
                l = mid+1;
            }
        }
        return ans;
    }

    bool solve(vector<int>& houses, vector<int>& heaters, int rad)
    {
       bool found = true;
       for(int i = 0;i < houses.size(); i++)
       {
         auto it1 = lower_bound(heaters.begin(), heaters.end(), houses[i]-rad);
         if(it1 == heaters.end())
         {
            return false;
         }
         if(*it1 > houses[i]+rad)
         {
            return false;
         }
       }
       return true;
    }
};
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