153. Find Minimum in Rotated Sorted Array

Prompt

Suppose an array of length n sorted in ascending order is rotated between 1 and n times. For example, the array nums = [0,1,2,4,5,6,7] might become:

• [4,5,6,7,0,1,2] if it was rotated 4 times.
• [0,1,2,4,5,6,7] if it was rotated 7 times.

Notice that rotating an array [a[0], a[1], a[2], ..., a[n-1]] 1 time results in the array [a[n-1], a[0], a[1], a[2], ..., a[n-2]].

Given the sorted rotated array nums of unique elements, return the minimum element of this array.

You must write an algorithm that runs in O(log n) time.

Solution

In C++

int findMin(vector<int>& nums) {
  int l = 0; int r = nums.size() - 1;
  int n = nums.size();
  while (l < r) {
	int m = (r - l) / 2 + l;
	if (nums[m] > nums[r]) l = m + 1;
	else r = m;
  }
  return nums[l];
}

Explanation

W use the regular binary search algorithm with a modifying index to handle to rotation. The find pivot is a little different because the middle pointer can also have the minimum.

Big O Analysis

Time Complexity

$O(\log n)$

Auxiliary Space Complexity

$O(1)$