search/find-minimum-in-rotated-sorted-array

Find Minimum in Rotated Sorted Array

描述

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).

Find the minimum element.

You may assume no duplicate exists in the array.

分析

从左向右扫描，扫描到的第一个逆序的位置，肯定是原始数组中第一个元素，时间复杂度O(n)。

不过本题依旧可以用二分查找，最关键的是要判断那个“断层”是在左边还是右边。

• 若A[mid] < A[right]，则区间[mid,right]一定递增，断层一定在左边
• 若A[mid] > A[right]，则区间[left,mid]一定递增，断层一定在右边
• nums[mid] == nums[right]，这种情况不可能发生，因为数组是严格单调递增的，不存在重复元素

代码

// Find Minimum in Rotated Sorted Array
// 时间复杂度O(logn)，空间复杂度O(1)
public class Solution {
    public int findMin(int[] nums) {
        int left = 0;
        int right = nums.length - 1;
        while (left < right) {
            int mid = left + (right - left) / 2;
            if (nums[mid] < nums[right]) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return nums[left];
    }
}

相关题目

• Search in Rotated Sorted Array
• Search in Rotated Sorted Array II
• Find Minimum in Rotated Sorted Array II