<p>Given a <strong>sorted</strong> integer array <code>arr</code>, two integers <code>k</code> and <code>x</code>, return the <code>k</code> closest integers to <code>x</code> in the array. The result should also be sorted in ascending order.</p>

<p>An integer <code>a</code> is closer to <code>x</code> than an integer <code>b</code> if:</p>

<ul>
	<li><code>|a - x| &lt; |b - x|</code>, or</li>
	<li><code>|a - x| == |b - x|</code> and <code>a &lt; b</code></li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> arr = [1,2,3,4,5], k = 4, x = 3
<strong>Output:</strong> [1,2,3,4]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> arr = [1,2,3,4,5], k = 4, x = -1
<strong>Output:</strong> [1,2,3,4]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= arr.length</code></li>
	<li><code>1 &lt;= arr.length &lt;= 10<sup>4</sup></code></li>
	<li><code>arr</code> is sorted in <strong>ascending</strong> order.</li>
	<li><code>-10<sup>4</sup> &lt;= arr[i], x &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
 public:
 //this is binary search solution
int leastDistanceIndex(vector<int>arr,int x){
    int start=0;
    int end=arr.size()-1;
    int ans=end;
    while(start<=end){
        int mid=start+(end-start)/2;
        if(arr[mid]>=x){
            ans=mid;
            end=mid-1;
        }else{
            start=mid+1;
        }
    }
    return ans;
}
vector<int> binarySearch(vector<int>arr,int k, int x){
    int high=leastDistanceIndex(arr,x);
    int low=high-1;
    while(k--){
        if(low<0){
            high++;
        }
        else if(high==arr.size()){
            low--;
        }
        else if(high>arr.size()-1){
            low++;
        }
       else if(x-arr[low]>arr[high]-x){
            high++;
        }else{
            low--;
        }
    }
    return vector<int>(arr.begin()+low+1,arr.begin()+high);
}



//commented line is first method where we minimize the size of window.
// vector<int> findRange(vector<int>arr,int k,int x){
//     int low=0;
//     int high=arr.size()-1;
//     while(high-low>=k){
//         if(x-arr[low]>arr[high]-x){
//             low++;
//         }else{
//             high--;
//         }
//     }
//     return vector<int>(arr.begin() + low,arr.begin()+high+1);
// }
   vector<int> findClosestElements(vector<int>& arr, int k, int x) {
          return binarySearch(arr,k,x);



//        return findRange(arr,k,x);
     }
 };
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