import java.io.*;
import java.util.Scanner;

public class floyd {

    // Infinity parameter - you might need a large value that will not interfere with actual path costs
    public static final int INF = Integer.MAX_VALUE / 2;

    public static void main(String[] args) throws FileNotFoundException {
        if (args.length != 1) {
            System.err.println("Usage: Floyd <graph-file>");
            return;
        }

        String inputFile = args[0];
        Scanner scanner = new Scanner(new File(inputFile));
        PrintWriter writer = new PrintWriter("output.txt");

        while (scanner.hasNextLine()) {
            String line = scanner.nextLine().trim();
            if (line.startsWith("Problem") && line.contains("n =")) {
                String problemId = line.split(" ")[0]; // to Storing the problem id, e.g., "Problem1"
                int n = Integer.parseInt(line.split("n =")[1].trim());

                // Initialize the adjacency and next matrix
                int[][] dist = new int[n][n];
                int[][] next = new int[n][n];

                // Initially, no paths are known, so fill with INF and -1 respectively, except diagonal elements
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < n; j++) {
                        if (i == j) dist[i][j] = 0;
                        else dist[i][j] = INF;
                        next[i][j] = -1; // Using -1 to indicate no path
                    }
                }

                // Read the matrix
                for (int i = 0; i < n; i++) {
                    if (scanner.hasNextLine()) {
                        line = scanner.nextLine().trim();
                        String[] parts = line.split("\\s+");
                        for (int j = 0; j < n; j++) {
                            int val = Integer.parseInt(parts[j]);
                            // Only set distances for non-zero (assuming non-zero means path exists) and non-diagonal elements
                            if (val != 0 && i != j) {
                                dist[i][j] = val;
                                next[i][j] = j; // Initially, the next vertex on the path is the target itself
                            }
                        }
                    }
                }

                // Floyd-Warshall algorithm
                for (int k = 0; k < n; ++k) {
                    for (int i = 0; i < n; ++i) {
                        for (int j = 0; j < n; ++j) {
                            // We also need to check for potential integer overflow
                            if (dist[i][k] < INF && dist[k][j] < INF && dist[i][j] > dist[i][k] + dist[k][j]) {
                                dist[i][j] = dist[i][k] + dist[k][j];
                                next[i][j] = next[i][k];
                            }
                        }
                    }
                }

                writer.println(problemId + ": n = " + n); // Include the problem ID in the output

                // Print Pmatrix indicating direct path found from i to j
                writer.println("Pmatrix:");
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < n; j++) {
                        writer.print(next[i][j] + "  ");
                    }
                    writer.println();
                }

                // Reconstructing paths
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < n; j++) {
                        if (i != j && dist[i][j] != INF) { // Ensure a path exists
                            int u = i;
                            writer.print(problemId + " V" + (i + 1) + "-V" + (j + 1) + ": shortest path and length\nV" + (i + 1));
                            while (u != j) {
                                u = next[u][j];
                                writer.print(" V" + (u + 1));
                            }
                            writer.println(": " + dist[i][j]);
                        }
                    }
                }
            }
        }
        scanner.close();
        writer.close();
    }
}
 the program is giving the output as Problem1: n = 7
Pmatrix:
-1  1  2  3  4  5  6  
0  -1  2  3  4  5  6  
0  1  -1  3  4  5  6  
0  1  2  -1  4  5  6  
0  1  2  3  -1  5  6  
0  1  2  3  4  -1  6  
0  1  2  3  4  5  -1  
Problem1 V1-V2: shortest path and length
V1 V2: 6
Problem1 V1-V3: shortest path and length
V1 V3: 5
Problem1 V1-V4: shortest path and length
V1 V4: 4
Problem1 V1-V5: shortest path and length
V1 V5: 6
Problem1 V1-V6: shortest path and length
V1 V6: 3
Problem1 V1-V7: shortest path and length
V1 V7: 6
Problem1 V2-V1: shortest path and length
V2 V1: 6
Problem1 V2-V3: shortest path and length
V2 V3: 6
Problem1 V2-V4: shortest path and length
V2 V4: 4
Problem1 V2-V5: shortest path and length
V2 V5: 5
Problem1 V2-V6: shortest path and length
V2 V6: 5
Problem1 V2-V7: shortest path and length
V2 V7: 3
Problem1 V3-V1: shortest path and length
V3 V1: 5
Problem1 V3-V2: shortest path and length
V3 V2: 6
Problem1 V3-V4: shortest path and length
V3 V4: 3
Problem1 V3-V5: shortest path and length
V3 V5: 1
Problem1 V3-V6: shortest path and length
V3 V6: 4
Problem1 V3-V7: shortest path and length
V3 V7: 6
Problem1 V4-V1: shortest path and length
V4 V1: 4
Problem1 V4-V2: shortest path and length
V4 V2: 4
Problem1 V4-V3: shortest path and length
V4 V3: 3
Problem1 V4-V5: shortest path and length
V4 V5: 4
Problem1 V4-V6: shortest path and length
V4 V6: 1
Problem1 V4-V7: shortest path and length
V4 V7: 4
Problem1 V5-V1: shortest path and length
V5 V1: 6
Problem1 V5-V2: shortest path and length
V5 V2: 5
Problem1 V5-V3: shortest path and length
V5 V3: 1
Problem1 V5-V4: shortest path and length
V5 V4: 4
Problem1 V5-V6: shortest path and length
V5 V6: 5
Problem1 V5-V7: shortest path and length
V5 V7: 5
Problem1 V6-V1: shortest path and length
V6 V1: 3
Problem1 V6-V2: shortest path and length
V6 V2: 5
Problem1 V6-V3: shortest path and length
V6 V3: 4
Problem1 V6-V4: shortest path and length
V6 V4: 1
Problem1 V6-V5: shortest path and length
V6 V5: 5
Problem1 V6-V7: shortest path and length
V6 V7: 3
Problem1 V7-V1: shortest path and length
V7 V1: 6
Problem1 V7-V2: shortest path and length
V7 V2: 3
Problem1 V7-V3: shortest path and length
V7 V3: 6
Problem1 V7-V4: shortest path and length
V7 V4: 4
Problem1 V7-V5: shortest path and length
V7 V5: 5
Problem1 V7-V6: shortest path and length
V7 V6: 3
Problem2: n = 6
Pmatrix:
-1  1  2  3  4  5  
0  -1  2  3  4  5  
0  1  -1  3  4  5  
0  1  2  -1  4  5  
0  1  2  3  -1  5  
0  1  2  3  4  -1  
Problem2 V1-V2: shortest path and length
V1 V2: 1
Problem2 V1-V3: shortest path and length
V1 V3: 2
Problem2 V1-V4: shortest path and length
V1 V4: 1
Problem2 V1-V5: shortest path and length
V1 V5: 3
Problem2 V1-V6: shortest path and length
V1 V6: 4
Problem2 V2-V1: shortest path and length
V2 V1: 1
Problem2 V2-V3: shortest path and length
V2 V3: 3
Problem2 V2-V4: shortest path and length
V2 V4: 2
Problem2 V2-V5: shortest path and length
V2 V5: 2
Problem2 V2-V6: shortest path and length
V2 V6: 3
Problem2 V3-V1: shortest path and length
V3 V1: 2
Problem2 V3-V2: shortest path and length
V3 V2: 3
Problem2 V3-V4: shortest path and length
V3 V4: 3
Problem2 V3-V5: shortest path and length
V3 V5: 3
Problem2 V3-V6: shortest path and length
V3 V6: 6
Problem2 V4-V1: shortest path and length
V4 V1: 1
Problem2 V4-V2: shortest path and length
V4 V2: 2
Problem2 V4-V3: shortest path and length
V4 V3: 3
Problem2 V4-V5: shortest path and length
V4 V5: 3
Problem2 V4-V6: shortest path and length
V4 V6: 5
Problem2 V5-V1: shortest path and length
V5 V1: 3
Problem2 V5-V2: shortest path and length
V5 V2: 2
Problem2 V5-V3: shortest path and length
V5 V3: 3
Problem2 V5-V4: shortest path and length
V5 V4: 3
Problem2 V5-V6: shortest path and length
V5 V6: 5
Problem2 V6-V1: shortest path and length
V6 V1: 4
Problem2 V6-V2: shortest path and length
V6 V2: 3
Problem2 V6-V3: shortest path and length
V6 V3: 6
Problem2 V6-V4: shortest path and length
V6 V4: 5
Problem2 V6-V5: shortest path and length
V6 V5: 5
 which is wrong. The correct and expected output that the program should give is Problem1: n = 7
Pmatrix: 
0  0  0  6  3  0  6  
0  0  5  0  0  4  0  
0  5  0  0  0  0  5  
6  0  0  0  3  0  6  
3  0  0  3  0  3  0  
0  4  0  0  3  0  0  
6  0  5  6  0  0  0 

V1-Vj: shortest path and length
V1 V1: 0
V1 V2: 6
V1 V3: 5
V1 V6 V4: 4
V1 V3 V5: 6
V1 V6: 3
V1 V6 V7: 6

V2-Vj: shortest path and length
V2 V1: 6
V2 V2: 0
V2 V5 V3: 6
V2 V4: 4
V2 V5: 5
V2 V4 V6: 5
V2 V7: 3

V3-Vj: shortest path and length
V3 V1: 5
V3 V5 V2: 6
V3 V3: 0
V3 V4: 3
V3 V5: 1
V3 V6: 4
V3 V5 V7: 6

V4-Vj: shortest path and length
V4 V6 V1: 4
V4 V2: 4
V4 V3: 3
V4 V4: 0
V4 V3 V5: 4
V4 V6: 1
V4 V6 V7: 4

V5-Vj: shortest path and length
V5 V3 V1: 6
V5 V2: 5
V5 V3: 1
V5 V3 V4: 4
V5 V5: 0
V5 V3 V6: 5
V5 V7: 5

V6-Vj: shortest path and length
V6 V1: 3
V6 V4 V2: 5
V6 V3: 4
V6 V4: 1
V6 V3 V5: 5
V6 V6: 0
V6 V7: 3

V7-Vj: shortest path and length
V7 V6 V1: 6
V7 V2: 3
V7 V5 V3: 6
V7 V6 V4: 4
V7 V5: 5
V7 V6: 3
V7 V7: 0

Problem2: n = 6
Pmatrix:
0  0  0  0  2  2  
0  0  1  1  0  0  
0  1  0  1  0  2  
0  1  1  0  0  2  
2  0  0  0  0  2  
2  0  2  2  2  0  

V1-Vj: shortest path and length
V1 V1: 0
V1 V2: 1
V1 V3: 2
V1 V4: 1
V1 V2 V5: 3
V1 V2 V6: 4

V2-Vj: shortest path and length
V2 V1: 1
V2 V2: 0
V2 V1 V3: 3
V2 V1 V4: 2
V2 V5: 2
V2 V6: 3

V3-Vj: shortest path and length
V3 V1: 2
V3 V1 V2: 3
V3 V3: 0
V3 V1 V4: 3
V3 V5: 3
V3 V1 V2 V6: 6

V4-Vj: shortest path and length
V4 V1: 1
V4 V1 V2: 2
V4 V1 V3: 3
V4 V4: 0
V4 V5: 3
V4 V1 V2 V6: 5

V5-Vj: shortest path and length
V5 V2 V1: 3
V5 V2: 2
V5 V3: 3
V5 V4: 3
V5 V5: 0
V5 V2 V6: 5

V6-Vj: shortest path and length
V6 V2 V1: 4
V6 V2: 3
V6 V2 V1 V3: 6
V6 V2 V1 V4: 5
V6 V2 V5: 5
V6 V6: 0