Question

我正在尝试编写一个递归函数来查找排序矩阵中的值。

public static void main(String[] args) {
        System.out.println("yeah");

        int[][] matrix = {{1, 2, 3, 4, 5},{6, 7, 8, 9, 10},
                          {11, 12, 13, 14, 15},{16, 17, 18, 19, 20},{21,22,23,24,25}};
        printMatrix(matrix);
        int[][] testmatrix = {{1,2},{3,4}};
        findValue(matrix, 19, 0, 4, 0, 4);
    }

    //write a print matrix function
    public static void printMatrix(int[][] matrix) {
        for(int i=0; i<matrix.length; i++) {
            for (int j=0; j<matrix[i].length; j++) {
                System.out.print(matrix[i][j] + " ");
            }
            System.out.println("");
        }
    }

    //sorted matrix and value, efficient algo to find value
    private static void findValue(int[][] matrix, int k, int rowLow, int rowHigh, int colLow, int colHigh) {
        // 1 element left
        if ((rowLow==rowHigh) && (colLow==colHigh)) {
            if ((matrix[rowLow][colLow])==k) {
                System.out.println("position of key: "+rowLow+","+colLow);
                return;
            }
            else {
                System.out.println("not found");
                return;
            }
        }

        // take care of the case with 2 elements left
        else if ((rowLow==rowHigh) && (colLow+1==colHigh)) {
            if ((matrix[rowLow][colLow])==k) {
                System.out.println("position of key: "+rowLow+","+colLow);
                return;
            }
            else if ((matrix[rowLow][colHigh])==k) {
                System.out.println("position of key: "+rowLow+","+colHigh);
                return;
            }
            else {
                System.out.println("not found");
                return;
            }
        }


        else {
            while (rowHigh > rowLow) {
                int rowMid = (rowLow+rowHigh)/2;
                //check last value of rowMid
                if (matrix[rowMid][colHigh] > k) {
                    findValue(matrix, k, rowLow, rowMid, colLow, colHigh);
                }
                else {
                    findValue(matrix, k, rowMid+1, rowHigh, colLow, colHigh);
                }
            }

            while (colHigh > colLow) {
                int colMid = (colLow+colHigh) /2 ;

                if  ((matrix[rowLow][colMid])==k) {
                    System.out.println("position of key: "+rowLow+","+colMid);
                    return;
                }
                else if (matrix[rowLow][colMid] > k) {
                    findValue(matrix, k, rowLow, rowHigh, colLow, colMid);
                }
                else {
                    findValue(matrix, k, rowLow, rowHigh, colMid+1, colHigh);
                }
            }

        }

    }

它确实有效，但问题在于它会无限地保持打印位置。

我发现它很奇怪，因为我在打印基础案例中的位置后调用了返回。任何人都可以指出这段代码有什么问题吗？

Answer 1

我的猜测是你的while循环中有一些错误，导致它永远不会停止执行。在递归调用之后添加返回似乎可以解决问题：

//sorted matrix and value, efficient algo to find value
    private static void findValue(int[][] matrix, int k, int rowLow, int rowHigh, int colLow, int colHigh) {
        // 1 element left
        if ((rowLow==rowHigh) && (colLow==colHigh)) {
            if ((matrix[rowLow][colLow])==k) {
                System.out.println("position of key: "+rowLow+","+colLow);
                return;
            }
            else {
                System.out.println("not found");
                return;
            }
        }

        // take care of the case with 2 elements left
        else if ((rowLow==rowHigh) && (colLow+1==colHigh)) {
            if ((matrix[rowLow][colLow])==k) {
                System.out.println("position of key: "+rowLow+","+colLow);
                return;
            }
            else if ((matrix[rowLow][colHigh])==k) {
                System.out.println("position of key: "+rowLow+","+colHigh);
                return;
            }
            else {
                System.out.println("not found");
                return;
            }
        }


        else {
            while (rowHigh > rowLow) {
                int rowMid = (rowLow+rowHigh)/2;
                //check last value of rowMid
                if (matrix[rowMid][colHigh] > k) {
                    findValue(matrix, k, rowLow, rowMid, colLow, colHigh);
                    return;
                }
                else {
                    findValue(matrix, k, rowMid+1, rowHigh, colLow, colHigh);
                    return;
                }
            }

            while (colHigh > colLow) {
                int colMid = (colLow+colHigh) /2 ;

                if  ((matrix[rowLow][colMid])==k) {
                    System.out.println("position of key: "+rowLow+","+colMid);
                    return;
                }
                else if (matrix[rowLow][colMid] > k) {
                    findValue(matrix, k, rowLow, rowHigh, colLow, colMid);
                    return;
                }
                else {
                    findValue(matrix, k, rowLow, rowHigh, colMid+1, colHigh);
                    return;
                }
            }

        }

收率：

yeah
1 2 3 4 5 
6 7 8 9 10 
11 12 13 14 15 
16 17 18 19 20 
21 22 23 24 25 
position of key: 3,3

Answer 2

哇，这是一个疯狂的算法。它需要递归吗？这可能具有相同的复杂性，但代码少得多（意味着更少的错误）

public static void findValue(int[][] matrix, int n, int x){
    int i = 0, j = n-1;  //set indexes for top right element
    while ( i < n && j >= 0 ){
        if ( matrix[i][j] == x ){
            System.out.println("position of key: " + i + "," + j);
            return;
        }
        if ( matrix[i][j] > x ){
            j--;
        }else {
            i++;
        }
    }
    System.out.println("not found");
}

...
findValue(matrix, 4, 19);
...

输出：

yeah
1 2 3 4 5 
6 7 8 9 10 
11 12 13 14 15 
16 17 18 19 20 
21 22 23 24 25 
position of key: 3,3

这个递归函数在排序矩阵中查找值有什么问题？

2 个答案: