# 153    Find Minimum in Rotated Sorted Array

## 153. [Find Minimum in Rotated Sorted Array](https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/description/)

## 1. Question

Suppose an array sorted in ascending order 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`).

Find the minimum element.

You may assume no duplicate exists in the array.

## 2. Implementation

**(1) Binary Search**

思路：用二分查找，每次取中点，比较nums\[mid] 和 nums\[end]的大小关系，如果nums\[mid] > nums\[end], 说明最小值一定在\[mid + 1, end]之间，否则最小值在\[start, mid - 1]之间

```java
class Solution {
    public int findMin(int[] nums) {
        int start = 0, end = nums.length - 1, mid = 0;

        while (start + 1 < end) {
            mid = start + (end - start) / 2;

            if (nums[mid] > nums[end]) {
                start = mid + 1;
            }
            else {
                end = mid;
            }
        }
        return nums[start] < nums[end] ? nums[start] : nums[end];
    }
}
```

## 3. Time & Space Complexity

时间复杂度O(logn), 空间复杂度O(1)


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