Shortest Unsorted Continuous Subarray

Description

Given an integer array, you need to find one continuous subarray that if you only sort this subarray in ascending order, then the whole array will be sorted in ascending order, too.

You need to find the shortest such subarray and output its length.

Example 1:

Input: [2, 6, 4, 8, 10, 9, 15]
Output: 5
Explanation: You need to sort [6, 4, 8, 10, 9] in ascending order to make the whole array sorted in ascending order.

Note:

1. Then length of the input array is in range [1, 10,000].

2. The input array may contain duplicates, so ascending order here means <=.

Solution

Idea:

1. Find longest subarray nums[0..right] such that max(nums[0..right]) <= nums[right+1..n-1].

2. Find longest subarray nums[left..n-1] such that min(nums[left..n-1]) >= nums[0..left-1].

3. The shortest subarray we want to find is nums[left..right]. We can prove it by contradiction.

class Solution {
public:
    int findUnsortedSubarray(vector<int>& nums) {
        int n = nums.size();
        if(n < 2) return 0;
        int left = 1, right = 0;
        int max_num = INT_MIN, min_num = INT_MAX;
        for(int i = 0, j = n - 1; i < n; ++i, --j){
            if(max_num > nums[i])
                right = i;
            else
                max_num = nums[i];
            if(min_num < nums[j])
                left = j;
            else
                min_num = nums[j];
        }
        return right - left + 1;
    }
};