Updates leetcode/binary-search/774-minimize-max-distance-to-gas-station.md

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Author: just4once

leetcode/binary-search/774-minimize-max-distance-to-gas-station.md

@@ -2,9 +2,9 @@
 
 [https://leetcode.com/problems/minimize-max-distance-to-gas-station/description/](https://leetcode.com/problems/minimize-max-distance-to-gas-station/description/)
 
-On a horizontal number line, we have gas stations at positions stations\[0\], stations\[1\], ..., stations\[N-1\], where N = stations.length.
+On a horizontal number line, we have gas stations at positions stations\[0\], stations\[1\], ..., stations\[N-1\], where N = stations.length.
 
-Now, we add K more gas stations so that D, the maximum distance between adjacent gas stations, is minimized.
+Now, we add K more gas stations so that D, the maximum distance between adjacent gas stations, is minimized.
 
 Return the smallest possible value of D.
 
@@ -32,7 +32,14 @@ Output: 0.500000
    4. Then the answer will be on top of the heap
    5. Time complexity O\(Klogn\)
    6. Space complexity O\(n\)
-3. ASD
+3. Binary Search
+   1. Using the boundaries of stations, the possible width will be in between 0 and 1e8
+   2. Perform binary search on the width within these boundaries, we will narrow down our search until these boundaries differ less than our desired delta
+   3. Now the conditions to narrow our search to left or right depends on a separate function possible\(mi, stations, K\), where it check if we can use less than or equal to K stations to achieve the mi distance
+   4. If possible return true, we set hi = mi to find better distance
+   5. Else we set lo = mi
+   6. Time complexity O\(nlogW\), where w = 1e8/1e-6 = 1e14
+   7. Space complexity O\(1\)
 
 ### Solution