Pile

#include <stdio.h> // include before iostream for faster scanf
#include <iostream>
#include <vector>
#include <string>
#include <map>
#include <unordered_map>
#include <algorithm>
#include <utility>
#include <set>
#include <unordered_set>
#include <cmath>
#include <math.h>
#include <queue>
#include <stdlib.h>
#include <string.h>
#include <sstream>
#include <tuple>
#include <utility>
#include <iomanip>
#include <iterator>

using namespace std;
typedef long long LL;

#define printv(printVec) for (auto printVecIter : (printVec)) cout << printVecIter << " "; cout << endl;

// g++-4.8 -Wall -Wshadow -std=c++11 a.cpp && ./a.out

int main() {
	std::ios::sync_with_stdio(false);cin.tie(0);
	int n;
	cin >> n;
	vector<int> v(n);
	for (int i = 0; i < n; i++) {
		cin >> v[i]; v[i]--;
	}
	int idx = 0;
	set<int> inpile;
	deque<int> pile;
	for (int i = 0; i < n; i++) {
		inpile.insert(i);
		pile.push_back(i);
		while (pile.size() && idx < n && v[idx] == pile.back()) {
			pile.pop_back();
			inpile.erase(i);
			idx++;
		}
		if (idx < n && inpile.count(v[idx])) {
			cout << "Cheater"; return 0;
		}
	}
	if (idx < n) {
		cout << "Cheater"; return 0;
	} else {
		cout << "Not a proof"; return 0;
	}
	
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED