最长路径算法

问题描述

目前，我有一个能找到最长路径的有效算法。但是，当我尝试打印出路径时，它会打印出找到最长路径所需的所有路径。我该如何解决？

我厌倦了走回原路，这导致了错误的答案，但输出却少了一些（在这种情况下，输出少了大约400条）。还是应该制作另一个ArrayList来存储正确的路径？既然代码运行起来，我应该怎么做才能想到所有可能。还是我应该以某种方式修改代码？

import java.util.*;
import java.awt.Point;

class Main
{
    // M x N matrix
    private static final int M = 10;
    private static final int N = 10;
    static ArrayList<Point> Path = new ArrayList<Point>();

    // check if it is possible to go to position (x,y) from
    // current position. The function returns false if the cell
    // has value 0 or it is already visited.
    private static boolean isSafe(int mat[][],int visited[][],int x,int y) {
        if (mat[x][y] == 0 || visited[x][y] != 0)
            return false;

        return true;
    }

    // if not a valid position,return false
    private static boolean isValid(int x,int y) {
        if (x < M && y < N && x >= 0 && y >= 0)
            return true;

        return false;
    }

    // Find Longest Possible Route in a Matrix mat from source
    // cell (0,0) to destination cell (x,y)
    // 'max_dist' stores length of longest path from source to
    // destination found so far and 'dist' maintains length of path from
    // source cell to the current cell (i,j)
    public static int findLongestPath(int mat[][],int i,int j,int y,int max_dist,int dist) {
        // if destination not possible from current cell
        if (mat[i][j] == 0) {
            return 0;
        }

        // if destination is found,update max_dist
        if (i == x && j == y) {
            return Integer.max(dist,max_dist);
        }

        // set (i,j) cell as visited
        visited[i][j] = 1;

        // go to bottom cell
        if (isValid(i + 1,j) && isSafe(mat,visited,i + 1,j)) {
            max_dist = findLongestPath(mat,j,x,y,max_dist,dist + 1);
        }

        // go to right cell
        if (isValid(i,j + 1) && isSafe(mat,i,j + 1)) {
            max_dist = findLongestPath(mat,j + 1,dist + 1);
        }

        // go to top cell
        if (isValid(i - 1,i - 1,dist + 1);
        }

        // go to left cell
        if (isValid(i,j - 1) && isSafe(mat,j - 1)) {
            max_dist = findLongestPath(mat,j - 1,dist + 1);
        }

        // Backtrack - Remove (i,j) from visited matrix
        visited[i][j] = 0;

        Point temp = new Point(i,j);
        Path.add(temp);

        return max_dist;
    }

    public static void main(String[] args)
    {
        // input matrix
        int mat[][] =
        {
                { 1,1,1 },{ 1,{ 0,0 },0 }
        };

        // construct a matrix to keep track of visited cells
        int[][] visited= new int[N][N];

        // (0,0) are the source cell coordinates and (5,7) are the
        // destination cell coordinates
        int max_dist = findLongestPath(mat,5,7,0);

        System.out.println("Maximum length path is " + max_dist);
        
        Collections.reverse(Path);
        int i = 1;
        for (Point point : Path) {
            System.out.println(i + " " + point.toString());
            i++;
        }

    }
}

解决方法

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