JZ-065 - Paths in Matrix

path in matrix

Topic description

Please design a function to determine whether there is a path containing all characters of a string in a matrix. The path can start from any cell in the matrix, and each step can move one cell left, right, up, and down in the matrix. If a path passes through a grid in the matrix, the path can no longer enter that grid. E.g

• a b c e
• s f c s
• a d e e
• The matrix contains a path to the string "bcced", but the matrix does not contain the path "abcb", because the first character b of the string occupies the first row of the matrix and after the second cell, the path cannot enter it again lattice.

title link : path in matrix

code

/**
 * 标题：矩阵中的路径
 * 题目描述
 * 请设计一个函数，用来判断在一个矩阵中是否存在一条包含某字符串所有字符的路径。路径可以从矩阵中的任意一个格子开始，每一步可以在矩阵中
 * 向左，向右，向上，向下移动一个格子。如果一条路径经过了矩阵中的某一个格子，则该路径不能再进入该格子。 例如
 * a b c e
 * s f c s
 * a d e e
 * 矩阵中包含一条字符串"bcced"的路径，但是矩阵中不包含"abcb"路径，因为字符串的第一个字符b占据了矩阵中的第一行第二个格子之后，路径不能
 * 再次进入该格子。
 * 题目链接：
 * https://www.nowcoder.com/practice/c61c6999eecb4b8f88a98f66b273a3cc?tpId=13&&tqId=11218&rp=1&ru=/ta/coding-interviews&qru=/ta/coding-interviews/question-ranking
 */
public class Jz65 {
    private final static int[][] next = {{0, -1}, {0, 1}, {-1, 0}, {1, 0}};
    private int rows;
    private int cols;

    /**
     * 回溯法
     *
     * @param matrix
     * @param rows
     * @param cols
     * @param str
     * @return
     */
    public boolean hasPath(char[] matrix, int rows, int cols, char[] str) {
        if (rows == 0 || cols == 0) {
            return false;
        }
        this.rows = rows;
        this.cols = cols;
        boolean[][] marked = new boolean[rows][cols];
        char[][] array = buildMatrix(matrix);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                if (backtracking(array, str, marked, 0, i, j)) {
                    return true;
                }
            }
        }
        return false;
    }

    private boolean backtracking(char[][] matrix, char[] str, boolean[][] marked, int pathLen, int r, int c) {
        if (pathLen == str.length) {
            return true;
        }

        if (r < 0 || r >= rows || c < 0 || c >= cols || matrix[r][c] != str[pathLen] || marked[r][c]) {
            return false;
        }

        marked[r][c] = true;
        for (int[] n : next) {
            if (backtracking(matrix, str, marked, pathLen + 1, r + n[0], c + n[1])) {
                return true;
            }
        }
        marked[r][c] = false;
        return false;
    }

    private char[][] buildMatrix(char[] array) {
        char[][] matrix = new char[rows][cols];
        for (int r = 0, idx = 0; r < rows; r++) {
            for (int c = 0; c < cols; c++) {
                matrix[r][c] = array[idx++];
            }
        }
        return matrix;
    }

    public static void main(String[] args) {
        Jz65 jz65 = new Jz65();
        Jz65 jz651 = new Jz65();
        char[] array = "abcesfcsadee".toCharArray();
        char[] array2 = "abcesfcsadee".toCharArray();
        boolean result1 = jz65.hasPath(array, 3, 4, "bcced".toCharArray());
        boolean result2 = jz651.hasPath(array2, 3, 4, "abcb".toCharArray());
        System.out.println(result1);
        System.out.println(result2);
    }
}

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