Create Search in Rotated Sorted Array.java

Author: Lokesh598

Array/Binary Search/Search in Rotated Sorted Array.java

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+class Solution {
+    public int search(int[] A, int target) {
+         int n = A.length;
+        int lo=0,hi=n-1;
+        // find the index of the smallest value using binary search.
+        // Loop will terminate since mid < hi, and lo or hi will shrink by at least 1.
+        // Proof by contradiction that mid < hi: if mid==hi, then lo==hi and loop would have been terminated.
+        while(lo<hi){
+            int mid=(lo+hi)/2;
+            if(A[mid]>A[hi]) lo=mid+1;
+            else hi=mid;
+        }
+        // lo==hi is the index of the smallest value and also the number of places rotated.
+        int rot=lo;
+        lo=0;hi=n-1;
+        // The usual binary search and accounting for rotation.
+        while(lo<=hi){
+            int mid=(lo+hi)/2;
+            int realmid=(mid+rot)%n;
+            if(A[realmid]==target)return realmid;
+            if(A[realmid]<target)lo=mid+1;
+            else hi=mid-1;
+        }
+        return -1;
+    }
+}