153 Find Minimum in Rotated Sorted Array

153. Find Minimum in Rotated Sorted Array

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 7might become4 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

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)