<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>

#include <climits>
#include <algorithm>

class Solution {
public:
    int findRadius(vector<int>& houses, vector<int>& heaters) {
        sort(houses.begin(), houses.end());
        sort(heaters.begin(), heaters.end());
        vector<int> rhs(houses.size(), INT_MAX);
        for (int i = 0, j = 0; i < houses.size() && j < heaters.size();) {
            if (houses[i] <= heaters[j]) {
                rhs[i] = heaters[j] - houses[i];
                i++;
            } else {
                j++;
            }
        }
        vector<int> lhs(houses.size(), INT_MAX);
        
        for(int i=houses.size()-1,j=heaters.size()-1;i>=0 && j>=0;){
            if(houses[i]>=heaters[j]){
                lhs[i] = houses[i]-heaters[j];
                i--;
            }else{
                j--;
            }

        }
        vector<int> result(houses.size());
        for(int i=0;i<houses.size();i++){
            result[i] = min(rhs[i],lhs[i]);
        }

        for(int i=0;i<houses.size();i++){
            cout << rhs[i] << " " << lhs[i] << endl;
        }

        int final = *max_element(result.begin(),result.end());

        return final;
    }
};
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