As an array lover, your friends have given you a challenge to solve a question on arrays, so the challenge goes as - :You are given an array 'r' consisting of 'x' integers. Unfortunately, the size of 'r' is too small. You want a bigger array! Your friends agree to give you a bigger array, but only if you are able to answer the following question correctly: is it possible to sort the array 'r' (in increasing order) by reversing exactly one segment of a? See definitions of segment and reversing in the notes.Input FormatThe first line of the input contains an integer x (1 ≤ x ≤ 10^5) — the size of array 'r'. The second line contains 'x' distinct space-separated integers.Constraints'x' distinct space-separated integers r[1], r[2], ..., r[x] (1 ≤ r[i] ≤ 10^9).Output FormatPrint "yes" or "no" (without quotes), depending on the answer.
Question
As an array lover, your friends have given you a challenge to solve a question on arrays, so the challenge goes as - :You are given an array 'r' consisting of 'x' integers. Unfortunately, the size of 'r' is too small. You want a bigger array! Your friends agree to give you a bigger array, but only if you are able to answer the following question correctly: is it possible to sort the array 'r' (in increasing order) by reversing exactly one segment of a? See definitions of segment and reversing in the notes.Input FormatThe first line of the input contains an integer x (1 ≤ x ≤ 10^5) — the size of array 'r'. The second line contains 'x' distinct space-separated integers.Constraints'x' distinct space-separated integers r[1], r[2], ..., r[x] (1 ≤ r[i] ≤ 10^9).Output FormatPrint "yes" or "no" (without quotes), depending on the answer.
Solution
To solve this problem, you can follow these steps:
- Read the size of the array 'x' from the input.
- Read the array 'r' from the input.
- Initialize two variables, 'start' and 'end', to -1. These will be used to keep track of the segment that needs to be reversed.
- Iterate over the array from the second element to the end. If the current element is smaller than the previous one and 'start' is -1, set 'start' to the index of the previous element. If the current element is larger than the previous one and 'start' is not -1 and 'end' is -1, set 'end' to the index of the previous element.
- If 'start' is -1, it means the array is already sorted, so print "yes" and return.
- If 'end' is -1, it means the segment to be reversed goes till the end of the array, so set 'end' to the last index of the array.
- Reverse the segment from 'start' to 'end' in the array.
- Check if the array is now sorted. If it is, print "yes", otherwise print "no".
This algorithm works because if it is possible to sort the array by reversing exactly one segment, that segment must be the only one that is not in increasing order. So we just need to find that segment, reverse it, and check if the array is sorted.
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