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.
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.
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.
if ( (a < c && a < d) || (b < c && b < d) ) // go left else // go right
- 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) { // one or two digits if ( i === j ) return nums[i]; let mid = i + Math.floor((j-i)/2); let a = nums[i]; let b = nums[mid]; let c = nums[mid+1]; let d = nums[j]; if ( (a < c && a < d) || (b < c && b < d) ) { // go left return findMinRecursive(nums, i, mid); } else { // go right return findMinRecursive(nums, mid+1, j); } } |
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