leetcode_gym/_problems/findMinInSortedArray.md

layout, title, last_solved, category, leetcode_url, status

layout	title	last_solved	category	leetcode_url	status
page	Find Min in Sorted Array	2020-07-27	binary search	https://leetcode.com/problems/find-minimum-in-rotated-sorted-array	Attempted

Problem

Suppose an array sorted in ascending order is rotated at some pivot unknown to you beforehand.

(i.e.,  [0,1,2,4,5,6,7] might become  [4,5,6,7,0,1,2]).

Find the minimum element.

You may assume no duplicate exists in the array.

Example 1:

Input: [3,4,5,1,2] 
Output: 1
Example 2:

Input: [4,5

Solution

Try a more concise solution:

{% highlight python %}

l, r = 0, len(nums) - 1 while nums[l] > nums[r]: mid = int((l+r)/2)
if nums[mid] >= nums[l]: l = mid + 1 else: r = mid return nums[l]

{% endhighlight %}

Think of examples with each of the if statements

if nums[mid] > nums[mid+1]:

mid = 1, nums=1 [2,1,3]

{% highlight python %}

arr = [4,5,6,7,2,3]

def findMin(nums):

# 1-elem array
if len(nums)==1:
    return nums[0]

left = 0
right = len(nums)-1

# this condition means arr is already sorted, so just return first element
if nums[right] > nums[0]:
    return nums[0]


while right>=left:

    mid = left + (right-left) // 2

    # min found: case 1
    if nums[mid] > nums[mid+1]:     # 3 4 5 1 2 where 5 is mid
        return nums[mid+1]

    # min found: case 2
    if nums[mid-1] > nums[mid]:     # 4 5 1 2 3 where 1 is mid
        return nums[mid]


    ### min not found cases below
    # mid is greater than first elem so ignore left half
    if nums[mid] > nums[0]:
        left = mid+1

    # mid is less than first elem, ignore right half
    else:
        right = mid-1

print(findMin(arr))

{% endhighlight %}

____________-

Using the powerful binary search template

{% highlight python %}

def findMin(self, nums: List[int]) -> int:

left, right = 0, len(nums)-1

while left<right:
    
    mid = (left+right)//2
    
    if nums[mid]<nums[right]:   # this is the condition that we want to satisfy w.r.t. mid
        
        right = mid
    
    else:
        
        left = mid+1
        
return nums[left]

{% endhighlight %}