Problem:
Suppose a sorted array is rotated at some pivot unknown to you beforehand.
(i.e., 0 1 2 4 5 6 7 might become 4 5 6 7 0 1 2).
You are given a target value to search. If found in the array return its index, otherwise return -1.
You may assume no duplicate exists in the array.
My analysis:
The idea behind binary search is beautiful and elegenat: we only search the possible result in the possible part.
If we stick to this principle, we would finally end up in finding out the right result.
For this question, even the sorted array was rotated, but we could use extra checking to guarantee we still iterate on the right partion of the array.
1. we firstly find out the mid element in which partion.
(either left or right partion is perfectly ordered)
a. the perfectly ordered partion.
b. the mixed partion.
2. we make our decision on iterating which part based on the comparsion in the sorted partion. we could not make the decsion based on the mixed partion, because we do not know the boundary.
a. iff the target is in the ordered partion, we search the target in it.
b. otherwise, we search the target in other partion. (which means the target must in this partion)
Note the checking condition is "if (A[low] <= A[mid])", rather than "if (A[low] < A[mid]) "
cause we should treat A[low] = A[mid] as the left partion sorted !!!
My solution:
public class Solution { public int search(int[] A, int target) { if (A.length == 0) return -1; int low = 0; int high = A.length - 1; int mid = -1; while (low <= high) { mid = (low + high) / 2; if (A[mid] == target) return mid; if (A[low] <= A[mid]) { //either left partion or right partion is perfectly sorted. if (A[low] <= target && target < A[mid]) high = mid - 1; else low = mid + 1; } else{ if (A[mid] < target && target <= A[high]) low = mid + 1; else high = mid - 1; } } return -1; } }