[LeetCode] Find Minimum in Rotated Sorted Array

As explained in the Solution tag, the key to solving this problem is to use invariants. We set two pointers: l for the left and r for the right. One key invariant is nums[l] > nums[r]. If this invariant does not hold, then we know the array has not been rotated and the minimum is justnums[l]. Otherwise, we reduce the search range by a half each time via comparisons betweennums[l], nums[r] and nums[(l + r) / 2], denoted as nums[mid]:

1. If nums[mid] > nums[r], then mid is in the first larger half and r is in the second smaller half. So the minimum will be right to mid, update l = mid + 1;
2. If nums[mid] <= nums[r], then the minimum is at least nums[mid] and elements right tomid cannot be the minimum. So update r = mid (note that it is not mid - 1 since midmay also be the index of the minimum).

When l == r or the invariant does not hold, we have found the answer, which is just nums[l].

Putting these togerther, we have the following codes.

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C (0 ms)

1 int findMin(int* nums, int numsSize) {
2     int l = 0, r = numsSize - 1;
3     while (l < r && nums[l] > nums[r]) {
4         int mid = (l & r) + ((l ^ r) >> 1);
5         if (nums[mid] > nums[r]) l = mid + 1;
6         else r = mid; 
7     }
8     return nums[l];
9 }

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C++ (4 ms)

 1 class Solution {
 2 public:
 3     int findMin(vector<int>& nums) {
 4         int l = 0, r = nums.size() - 1;
 5         while (l < r && nums[l] > nums[r]) {
 6             int mid = (l & r) + ((l ^ r) >> 1); 
 7             if (nums[mid] > nums[r]) l = mid + 1;
 8             else r = mid;
 9         }
10         return nums[l];
11     }
12 };

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Python (48 ms)

 1 class Solution:
 2     # @param {integer[]} nums
 3     # @return {integer}
 4     def findMin(self, nums):
 5         l, r = 0, len(nums) - 1
 6         while l < r and nums[l] > nums[r]:
 7             mid = (l & r) + ((l ^ r) >> 1)
 8             if nums[mid] > nums[r]:
 9                 l = mid + 1
10             else:
11                 r = mid
12         return nums[l]