Find Minimum in Rotated Sorted Array

Medium Binary Search Rotated Array Original on LeetCode

Find Minimum in Rotated Sorted Array is a medium binary search problem solved with the rotated array pattern. The best approach, optimal (binary search against nums[hi]), runs in O(log n) time and O(1) space. Below are 2 approaches in Java, from linear scan up.

Problem

A sorted array of distinct values was rotated at an unknown pivot. Return its minimum in O(log n) time.

Examples

Example 1

Input: nums = [4, 5, 6, 1, 2, 3]
Output: 1

Example 2

Input: nums = [2, 4, 8]
Output: 2

Constraints

1 <= nums.length <= 5000, distinct values.
O(log n).

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Solutions

Try it yourself first. Then compare: each approach lists its idea, the steps, its time and space, and the Java code.

Approach	Time	Space
Linear scan	`O(n)`	`O(1)`
Optimal (binary search against nums[hi])	`O(log n)`	`O(1)`

1Linear scan

TimeO(n)

SpaceO(1)

Return the smallest element.

Track the minimum.

Java

class Solution {
    public int findMin(int[] nums) {
        int min = nums[0];
        for (int x : nums) min = Math.min(min, x);
        return min;
    }
}

2Optimal (binary search against nums[hi])

TimeO(log n)

SpaceO(1)

If nums[mid] > nums[hi], the drop, and so the minimum, is to the right of mid. Otherwise the part mid..hi is sorted, so the minimum is at mid or to its left.

While lo < hi: if nums[mid] > nums[hi] lo = mid + 1, else hi = mid.
Return nums[lo].

Java

class Solution {
    public int findMin(int[] nums) {
        int lo = 0, hi = nums.length - 1;
        while (lo < hi) {
            int mid = (lo + hi) >>> 1;
            if (nums[mid] > nums[hi]) lo = mid + 1;
            else hi = mid;
        }
        return nums[lo];
    }
}

Edge cases to test

Not rotated
Two elements

Hints

Hint 1

Compare nums[mid] with nums[hi], not nums[lo].

FAQ

What is the best time complexity for Find Minimum in Rotated Sorted Array?

Optimal (binary search against nums[hi]) runs in O(log n) time and O(1) extra space.

Which pattern does Find Minimum in Rotated Sorted Array use?

It is a binary search problem that uses the rotated array pattern. Other problems with the same pattern: Find How Many Times Array is Rotated, Find Minimum in Rotated Sorted Array II, Search in Rotated Sorted Array.

Is there a brute force solution for Find Minimum in Rotated Sorted Array?

Yes. Linear scan takes O(n) time and O(1) space. Return the smallest element.

Which edge cases should I test for Find Minimum in Rotated Sorted Array?

Not rotated; Two elements.