<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:
    int findRadius(vector<int>& houses, vector<int>& heaters) {
        int maxi=INT_MAX;
        vector<int>v;
        sort(heaters.begin(),heaters.end());
    for(int i=0; i<houses.size(); i++){
     int ind=lower_bound(heaters.begin(),heaters.end(),houses[i])-heaters.begin();
     int left=ind-1; 
  
         int maxi=0;
      
      int a=INT_MAX;
     if(ind<heaters.size()) a=abs(houses[i]-heaters[ind]);
         int b=INT_MAX;
        if(left>=0)b=abs(houses[i]-heaters[left]);
         maxi=min(a,b);
         
         v.push_back(maxi);
         cout<<v[i];
        }

    
    int ans=0;
    for(int i=0; i<v.size(); i++){
      
        ans=max(ans,v[i]);
    }
    return ans;
    }
};


// class Solution {
// public:
//     int findRadius(vector<int>& houses, vector<int>& heaters) {
//         vector<int> v;
//         sort(heaters.begin(), heaters.end()); // Sort the heaters array

//         for (int i = 0; i < houses.size(); i++) {
//             int ind = lower_bound(heaters.begin(), heaters.end(), houses[i]) - heaters.begin();
//             int right = ind; // `ind` is already the right position due to `lower_bound`

//             // Calculate distance to the nearest heaters on both sides
//             int a = (ind < heaters.size()) ? abs(houses[i] - heaters[ind]) : INT_MAX;
//             int b = (ind > 0) ? abs(houses[i] - heaters[ind - 1]) : INT_MAX;

//             // Minimum distance to a heater for this house
//             int value = min(a, b);

//             // Store the minimum distance
//             v.push_back(value);
//         }

//         int ans = 0;
//         for (int i = 0; i < v.size(); i++) {
//             ans = max(ans, v[i]);
//         }

//         return ans;
//     }
// };

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