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# Find Minimum in Rotated Sorted Array

Updated: Mar 25, 2021

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, a, a, ..., a[n-1]] 1 time results in the array [a[n-1], a, a, a, ..., a[n-2]].

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

Example 1:

```Input: nums = [3,4,5,1,2]
Output: 1
Explanation: The original array was [1,2,3,4,5] rotated 3 times.

```

Example 2:

```Input: nums = [4,5,6,7,0,1,2]
Output: 0
Explanation: The original array was [0,1,2,4,5,6,7] and it was rotated 4 times.

```

Example 3:

```Input: nums = [11,13,15,17]
Output: 11
Explanation: The original array was [11,13,15,17] and it was rotated 4 times.

```

Constraints:

• n == nums.length

• 1 <= n <= 5000

• -5000 <= nums[i] <= 5000

• All the integers of nums are unique.

• nums is sorted and rotated between 1 and n times.

Solution:

Approach1 O(n):

```class Solution {
public int findMin(int[] nums) {
if(nums.length==1) return nums;
for(int i=0;i<nums.length;i++)
{
if(nums[i]>nums[(i+1)%nums.length])
{
return nums[(i+1)%nums.length];
}
}
return -1;
}
}```

Approach 2 O(log n) Binary Search:

```class Solution {
public int findMin(int[] nums) {
if(nums.length==1) return nums;
int start = 0, end=nums.length-1;
if(nums<nums[end]) return nums;

while(start<=end)
{
int mid = start+(end-start)/2;
if(nums[mid+1]<nums[mid]) return nums[mid+1];
if(nums[mid-1]>nums[mid]) return nums[mid];

if(nums[mid]>nums)
{
start = mid+1;
}
else end = mid-1;
}
return -1;

}
}```