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16.16. Sub Sort

Description

Given an array of integers, write a method to find indices m and n such that if you sorted elements m through n, the entire array would be sorted. Minimize n - m (that is, find the smallest such sequence).

Return [m,n]. If there are no such m and n (e.g. the array is already sorted), return [-1, -1].

Example: 


Input:  [1,2,4,7,10,11,7,12,6,7,16,18,19]

Output:  [3,9]

Note:

  • 0 <= len(array) <= 1000000

Solutions

Solution 1: Two Passes

We first traverse the array $array$ from left to right, and use $mx$ to record the maximum value encountered so far. If the current value $x$ is less than $mx$, it means that $x$ needs to be sorted, and we record the index $i$ of $x$ as $right$; otherwise, update $mx$.

Similarly, we traverse the array $array$ from right to left, and use $mi$ to record the minimum value encountered so far. If the current value $x$ is greater than $mi$, it means that $x$ needs to be sorted, and we record the index $i$ of $x$ as $left$; otherwise, update $mi$.

Finally, return $[left, right]$.

The time complexity is $O(n)$, where $n$ is the length of the array $array$. The space complexity is $O(1)$.

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class Solution:
    def subSort(self, array: List[int]) -> List[int]:
        n = len(array)
        mi, mx = inf, -inf
        left = right = -1
        for i, x in enumerate(array):
            if x < mx:
                right = i
            else:
                mx = x
        for i in range(n - 1, -1, -1):
            if array[i] > mi:
                left = i
            else:
                mi = array[i]
        return [left, right]

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class Solution {
    public int[] subSort(int[] array) {
        int n = array.length;
        int mi = <