[Question]: 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.
Example 1:
Input: nums = [3,4,5,1,2] Output: 1 Explanation: The original array was [1,2,3,4,5] rotated 3 times.
// TC: O(log(N))
// SC: O(1)
func findMin(_ nums: [Int]) ->Int {
var low = 0
var high = nums.count - 1
var ans = Int.max
while low <= high {
let mid = (low + high) / 2
//search space is already sorted
//then arr[low] will always be
//the minimum in that search space:
if nums[low] <= nums[high] {
ans = min(ans, nums[low])
break
}
// If left part is sorted:
if nums[low] <= nums[mid] {
// Keep the minimum:
ans = min(ans, nums[low])
// Eliminate left half:
low = mid + 1
} else { // If right part is sorted:
// Keep the minimum:
ans = min(ans, nums[mid])
// Eliminate right half:
high = mid - 1
}
}
return ans
}
let rotArrayInput = [4, 5, 6, 7, 0, 1, 2, 3]
let rotArrayOutput = findMin(rotArrayInput)
print("The minimum element is: ", rotArrayOutput)// 0