crossword puzzle Algorithm

#include <bits/stdc++.h> 
using namespace std; 

// ways are to calculate the number of 
// possible ways to fill the grid 
int ways = 0; 

// this function is used to print 
// the resultant matrix 
void printMatrix(vector<string>& matrix, int n) 
{ 
	for (int i = 0; i < n; i++) 
		cout << matrix[i] << endl; 
} 

// this function checks for the current word 
// if it can be placed horizontally or not 
// x -> it represent index of row 
// y -> it represent index of column 
// currentWord -> it represent the 
// current word in word array 
vector<string> checkHorizontal(int x, int y, 
							vector<string> matrix, 
							string currentWord) 
{ 
	int n = currentWord.length(); 

	for (int i = 0; i < n; i++) { 
		if (matrix[x][y + i] == '#' || 
			matrix[x][y + i] == currentWord[i]) { 
			matrix[x][y + i] = currentWord[i]; 
		} 
		else { 

			// this shows that word cannot 
			// be placed horizontally 
			matrix[0][0] = '@'; 
			return matrix; 
		} 
	} 

	return matrix; 
} 

// this function checks for the current word 
// if it can be placed vertically or not 
// x -> it represent index of row 
// y -> it represent index of column 
// currentWord -> it represent the 
// current word in word array 
vector<string> checkVertical(int x, int y, 
							vector<string> matrix, 
							string currentWord) 
{ 
	int n = currentWord.length(); 

	for (int i = 0; i < n; i++) { 
		if (matrix[x + i][y] == '#' || 
			matrix[x + i][y] == currentWord[i]) { 
			matrix[x + i][y] = currentWord[i]; 
		} 
		else { 

			// this shows that word 
			// cannot be placed vertically 
			matrix[0][0] = '@'; 
			return matrix; 
		} 
	} 
	return matrix; 
} 

// this function recursively checks for every 
// word that can align vertically in one loop 
// and in another loop it checks for those words 
// that can align horizontally words -> it 
// contains all the words to fill in a crossword 
// puzzle matrix -> it contain the current 
// state of crossword index -> it represent 
// the index of current word n -> it represent 
// the length of row or column of the square matrix 
void solvePuzzle(vector<string>& words, 
				vector<string> matrix, 
				int index, int n) 
{ 
	if (index < words.size()) { 
		string currentWord = words[index]; 
		int maxLen = n - currentWord.length(); 

		// loop to check the words that can align vertically. 
		for (int i = 0; i < n; i++) { 
			for (int j = 0; j <= maxLen; j++) { 
				vector<string> temp = checkVertical(j, i, 
										matrix, currentWord); 

				if (temp[0][0] != '@') { 
					solvePuzzle(words, temp, index + 1, n); 
				} 
			} 
		} 

		// loop to check the words that can align horizontally. 
		for (int i = 0; i < n; i++) { 
			for (int j = 0; j <= maxLen; j++) { 
				vector<string> temp = checkHorizontal(i, j, 
									matrix, currentWord); 

				if (temp[0][0] != '@') { 
					solvePuzzle(words, temp, index + 1, n); 
				} 
			} 
		} 
	} 
	else { 
		// calling of print function to 
		// print the crossword puzzle 
		cout << (ways + 1) << " way to solve the puzzle "
			<< endl; 
		printMatrix(matrix, n); 
		cout << endl; 

		// increase the ways 
		ways++; 
		return; 
	} 
} 

// Driver Code 
int main() 
{ 
	// length of grid 
	int n1 = 10; 

	// matrix to hold the grid of puzzle 
	vector<string> matrix; 

	// take input of puzzle in matrix 
	// input of grid of size n1 x n1 
	matrix.push_back("*#********"); 
	matrix.push_back("*#********"); 
	matrix.push_back("*#****#***"); 
	matrix.push_back("*##***##**"); 
	matrix.push_back("*#****#***"); 
	matrix.push_back("*#****#***"); 
	matrix.push_back("*#****#***"); 
	matrix.push_back("*#*######*"); 
	matrix.push_back("*#********"); 
	matrix.push_back("***#######"); 

	vector<string> words; 

	// the words matrix will hold all 
	// the words need to be filled in the grid 
	words.push_back("PUNJAB"); 
	words.push_back("JHARKHAND"); 
	words.push_back("MIZORAM"); 
	words.push_back("MUMBAI"); 

	// initialize the number of ways 
	// to solve the puzzle to zero 
	ways = 0; 

	// recursive function to solve the puzzle 
	// Here 0 is the initial index of words array 
	// n1 is length of grid 
	solvePuzzle(words, matrix, 0, n1); 
	cout << "Number of ways to fill the grid is "
		<< ways << endl; 

	return 0; 
}