Longest Path In Matrix

LongestPathInMatrix.java

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+/ Java program to find the longest path in a matrix
+// with given constraints
+
+class LongestPathInMatrix
+{
+    public static int n = 3;
+
+    // Function that returns length of the longest path
+    // beginning with mat[i][j]
+    // This function mainly uses lookup table dp[n][n]
+    static int findLongestFromACell(int i, int j, int mat[][], int dp[][])
+    {
+        // Base case
+        if (i<0 || i>=n || j<0 || j>=n)
+            return 0;
+
+        // If this subproblem is already solved
+        if (dp[i][j] != -1)
+            return dp[i][j];
+
+        // Since all numbers are unique and in range from 1 to n*n,
+        // there is atmost one possible direction from any cell
+        if (j<n-1 && ((mat[i][j] +1) == mat[i][j+1]))
+            return dp[i][j] = 1 + findLongestFromACell(i,j+1,mat,dp);
+
+        if (j>0 && (mat[i][j] +1 == mat[i][j-1]))
+            return dp[i][j] = 1 + findLongestFromACell(i,j-1,mat,dp);
+
+        if (i>0 && (mat[i][j] +1 == mat[i-1][j]))
+            return dp[i][j] = 1 + findLongestFromACell(i-1,j,mat,dp);
+
+        if (i<n-1 && (mat[i][j] +1 == mat[i+1][j]))
+            return dp[i][j] = 1 + findLongestFromACell(i+1,j,mat,dp);
+
+        // If none of the adjacent fours is one greater
+        return dp[i][j] = 1;
+    }
+
+    // Function that returns length of the longest path
+    // beginning with any cell
+    static int finLongestOverAll(int mat[][])
+    {
+        // Initialize result
+        int result = 1;
+
+        // Create a lookup table and fill all entries in it as -1
+        int[][] dp = new int[n][n];
+        for(int i=0;i<n;i++)
+            for(int j=0;j<n;j++)
+                dp[i][j] = -1;
+
+        // Compute longest path beginning from all cells
+        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 = Math.max(result, dp[i][j]);
+            }
+        }
+
+        return result;
+    }
+
+    // driver program
+    public static void main (String[] args)
+    {
+        int  mat[][] = { {1, 2, 9},
+                {5, 3, 8},
+                {4, 6, 7} };
+        System.out.println("Length of the longest path is " +
+                finLongestOverAll(mat));
+    }
+}