Find_the_longest_path_in_a_matrix_with_given_constraints.cpp

// C++ program to find the longest path in a matrix

#include <bits/stdc++.h>
#define n 3
using namespace std;


int findLongestFromACell(int i, int j, int mat[n][n],
						int dp[n][n])
{
	if (i < 0 || i >= n || j < 0 || j >= n)
		return 0;


	if (dp[i][j] != -1)
		return dp[i][j];

	int x = INT_MIN, y = INT_MIN, z = INT_MIN, w = INT_MIN;

	if (j < n - 1 && ((mat[i][j] + 1) == mat[i][j + 1]))
		x = 1 + findLongestFromACell(i, j + 1, mat, dp);

	if (j > 0 && (mat[i][j] + 1 == mat[i][j - 1]))
		y = 1 + findLongestFromACell(i, j - 1, mat, dp);

	if (i > 0 && (mat[i][j] + 1 == mat[i - 1][j]))
		z = 1 + findLongestFromACell(i - 1, j, mat, dp);

	if (i < n - 1 && (mat[i][j] + 1 == mat[i + 1][j]))
		w = 1 + findLongestFromACell(i + 1, j, mat, dp);

	return dp[i][j] = max({x, y, z, w, 1});
}


int finLongestOverAll(int mat[n][n])
{
	int result = 1; // Initialize result

	
	int dp[n][n];
	memset(dp, -1, sizeof dp);

	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			if (dp[i][j] == -1)
				findLongestFromACell(i, j, mat, dp);

			// Update result if needed
			result = max(result, dp[i][j]);
		}
	}

	return result;
}


int main()
{
	int mat[n][n]
		= { { 1, 2, 9 }, { 5, 3, 8 }, { 4, 6, 7 } };
	cout << "Length of the longest path is "
		<< finLongestOverAll(mat);
	return 0;
}