# [Programming Problem] Find Minimum in Rotated Sorted Array II

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

• [4,5,6,7,0,1,4] if it was rotated 4 times.
• [0,1,4,4,5,6,7] 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 that may contain duplicates, return the minimum element of this array.

You must decrease the overall operation steps as much as possible.

Example 1:
Input: nums = [1,3,5]
Output: 1

Example 2:
Input: nums = [2,2,2,0,1]
Output: 0

We use a `modified` binary search to find the minimum element:-

• At every point, compare (‘i’, ‘mid’) with (‘mid+1’, ‘j’). Whichever section has the lower value, let’s move that direction. Because of duplicates, we might be in a situation where there’s no one clear winner. In that case, move in both directions.
```if ( (a < c && a < d) || (b < c && b < d) ) // go left else if ((c > a && c > b) || (d > a && d > b)) // go right else // go both directions.```
• Return the last number remaining in the recursion (when i === j)
```/** * @param {number[]} nums * @return {number} */ var findMin = function(nums) { return findMinRecursive(nums, 0, nums.length-1); };   var findMinRecursive = function(nums, i, j) { if (i === j) return nums[i];   let mid = i + Math.floor((j-i)/2); const a = nums[i]; const b = nums[mid]; const c = nums[mid + 1]; const d = nums[j];   let left = Number.MAX_VALUE; let right = Number.MAX_VALUE; if ((a < c && a < d) || (b < c && b < d)) { // go left left = findMinRecursive(nums, i, mid); } else if ((c > a && c > b) || (d > a && d > b)) { right = findMinRecursive(nums, mid+1, j); } else { // go both left = findMinRecursive(nums, i, mid); right = findMinRecursive(nums, mid+1, j); }   return Math.min(left, right); };```

### 28 thoughts on “[Programming Problem] Find Minimum in Rotated Sorted Array II”

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