[LeetCode] 81. Search in Rotated Sorted Array II 搜索旋转排序数组之二

There is an integer array nums sorted in non-decreasing order (not necessarily with distinct values).

Before being passed to your function, nums is rotated at an unknown pivot index k (0 <= k < nums.length) such that the resulting array is [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]] (0-indexed). For example, [0,1,2,4,4,4,5,6,6,7] might be rotated at pivot index 5 and become [4,5,6,6,7,0,1,2,4,4].

Given the array nums after the rotation and an integer target, return true if target is in nums, or false if it is not in nums.

You must decrease the overall operation steps as much as possible.

Example 1:

Input: nums = [2,5,6,0,0,1,2], target = 0
Output: true

Example 2:

Input: nums = [2,5,6,0,0,1,2], target = 3
Output: false

Constraints:

1 <= nums.length <= 5000
-10^4 <= nums[i] <= 10^4
nums is guaranteed to be rotated at some pivot.
-10^4 <= target <= 10^4

Follow up: This problem is similar to Search in Rotated Sorted Array, but nums may contain duplicates. Would this affect the runtime complexity? How and why?

这道是之前那道 Search in Rotated Sorted Array 的延伸，现在数组中允许出现重复数字，这个也会影响我们选择哪半边继续搜索，由于之前那道题不存在相同值，我们在比较中间值和最右值时就完全符合之前所说的规律：如果中间的数小于最右边的数，则右半段是有序的，若中间数大于最右边数，则左半段是有序的。而如果可以有重复值，就会出现来面两种情况，[3 1 1] 和 [1 1 3 1]，对于这两种情况中间值等于最右值时，目标值3既可以在左边又可以在右边，那怎么办么，对于这种情况其实处理非常简单，只要把最右值向左一位即可继续循环，如果还相同则继续移，直到移到不同值为止，然后其他部分还采用 Search in Rotated Sorted Array 中的方法，可以得到代码如下：

解法一：

class Solution {
public:
    bool search(vector<int>& nums, int target) {
        int n = nums.size(), left = 0, right = n - 1;
        while (left <= right) {
            int mid = (left + right) / 2;
            if (nums[mid] == target) return true;
            else if (nums[mid] < nums[right]) {
                if (nums[mid] < target && nums[right] >= target) left = mid + 1;
                else right = mid - 1;
            } else if (nums[mid] > nums[right]){
                if (nums[left] <= target && nums[mid] > target) right = mid - 1;
                else left = mid + 1;
            } else {
                --right;
            }
        }
        return false;
    }
};

当然对应的，我们也可以跟左边的数字比较，如果中间的数大于最左边的数，则左半段是有序的，若中间数小于最左边数，则右半段是有序的。同理，中间值等于最左值时，把最左值向右一位即可继续循环，如果还相同则继续移，直到移到不同值为止，然后其他部分还采用 Search in Rotated Sorted Array 中的方法，可以得到代码如下：

解法二：

class Solution {
public:
    int search(vector<int>& nums, int target) {
        int n = nums.size(), left = 0, right = n - 1;
        while (left <= right) {
            int mid = left + (right - left) / 2;
            if (nums[mid] == target) return true;
            if (nums[mid] > nums[left]) {
                if (nums[left] <= target && nums[mid] > target) right = mid - 1;
                else left = mid + 1;
            } else if (nums[mid] < nums[left]) {
                if (nums[mid] < target && nums[right] >= target) left = mid + 1;
                else right = mid - 1;
            } else {
                ++left;
            }
        }
        return false;
    }
};