What does this variable do? - c++

Question

One day, Twilight Sparkle is interested in how to sort a sequence of
integers a1, a2, ..., an in non-decreasing order. Being a young
unicorn, the only operation she can perform is a unit shift. That is,
she can move the last element of the sequence to its beginning:
a1, a2, ..., an → an, a1, a2, ..., an - 1. Help Twilight Sparkle to
calculate: what is the minimum number of operations that she needs to
sort the sequence?
Input
The first line contains an integer n (2 ≤ n ≤ 105). The second
line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105).
Output
If it's impossible to sort the sequence output -1. Otherwise
output the minimum number of operations Twilight Sparkle needs to sort
it.
Examples
input
2
2 1
output
1
input
3
1 3 2
output
-1
input
2
1 2
output
0
Above is the problem and now I am confused because the solution down there used a variable called "s" and played around it for some reason but I don't know why was that variable used, if someone can tell me I'll be thankful.
#include <iostream>
#include <vector>
using namespace std;
int main()
{
int n, s, v(0);
cin >> n;
vector<int> a(n);
for (int i = 0; i < n; i++) cin >> a[i];
for (int i = 0; i < n - 1; i++) if (a[i] > a[i + 1]) s = i, v++;
if (a[n - 1] > a[0]) s = n - 1, v++;
if (v == 0) cout << 0 << endl;
else if (v > 1) cout << -1 << endl;
else cout << n - 1 - s << endl;
return 0;
}
Now here is my own solution, it works and everything except on a 10^5(and around that) size array but the question time limit is only 1000 ms, and mine exceeds that limit due to the nested loops making it go over O(10^8) which is 1000 ms on their systems.
#include <bits/stdc++.h>
#define fl(i,n) for(int i = 0; i < n; i++)
#define ll long long
#define nl endl
#define pb push_back
#define mp make_pair
#define PII pair<int,int>
#define EPS 1e-9
#define INF 1e9
using namespace std;
bool check(int a[], int n){
for(int i = 0; i < n-1; i++){
if(a[i] <= a[i+1]) continue;
return false;
}
return true;
}
int main()
{
int n;
cin >> n;
int a[n]; //is out of standard i know but it's accepted in the contest's compiler so we just use it
for(int i = 0; i < n; i++){
cin >> a[i];
}
if(check(a,n)){
cout << 0;
return 0;
}
int ret = 0;
for(int i = 0; i < n-1; i++){
ret++;
for(int j = n-1; j > 0; j--)
a[j] ^= a[j-1] ^= a[j] ^= a[j-1]; //is xor swap
if(check(a,n)){
cout << ret;
return 0;
}
}
cout << -1;
return 0;
}
PS: I TRACED the solution's code and even if I get the correct answers I simply don't know what it refers to.

Answer 1

The other person's implementation relies on an algorithmic insight. The only way a sequence can be sorted by moving back to front is if the sequence is made of two already-sorted sections. Then, the goal is to check how many unsorted discontinuities exist, and where they are. That's what s appears to be used for: the index of the (last) discontinuity of the sequence. v is the count of discontinuities.
If there are 0, it's already sorted. If more than 1, it's unsortable. If it's exactly one, then you can easily figure out how many shifts you need to perform to pull the discontinuity back to the front, using it's location (s) in the original sequence.
The only extra line of code is the special case of checking for the discontinuity around end of the sequence.
My recommendation: Generate a larger set of test sequences, and print v and s for each one.