#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;

bool hasSingleCycle(vector<int> array) {

	//doesn't matter where you start in the cycle
	//if there is a cycle, all elements will be in the valid cycle
	vector<int> visitedIndex;
	int currIndex = 0;
	int indexVal = array.at(0);
	visitedIndex.push_back(0);

	while (visitedIndex.size() != array.size() + 1) {
		currIndex = currIndex + indexVal;
		if (currIndex < 0) {
			cout << currIndex << " % " << array.size() << endl;
			currIndex = currIndex % array.size();
			cout << currIndex << endl;
			currIndex = array.size() + currIndex;
			cout << currIndex << endl;
		}
		else if (currIndex >= array.size()) {
			currIndex = currIndex % array.size();
		}
		visitedIndex.push_back(currIndex);
		indexVal = array.at(currIndex);
	}
	
	for (int i = 0; i < array.size(); i++) {
		if (find(visitedIndex.begin(), visitedIndex.end(), i) == visitedIndex.end()) {
			return false;
		}
	}
	
	if (visitedIndex.at(array.size()) != 0) {
		return false;
	}
	return true;
}

int main() {
	// int z = -1%3;
	// cout << z << endl;
	vector<int> x = {-1, 2, 2};
	bool y = hasSingleCycle(x);
	return 0;
}