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DSA/Find_the_longest_path_in_a_matrix_with_given_constraints.cpp

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+// 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;
+}