java - 检查矩阵内的总和并递归地将路径保留在第二个数组上

Question

这个问题是在我对 Java 的期末考试中：

给定一个正数矩阵（未排序）m，一个整数sum和另一个p填充满的矩阵0。递归检查内部是否有一条路径m，它的总和等于sum。

规则：

您只能在数组中向下、向上、向左或向右移动。

找到路径后，矩阵将在正确的路径上p填充。1's

只有 1 条路径

所有其他单元格p应该0在方法完成之后。

如果没有办法得到这笔钱，你会p在得到他时离开。

例子：

        int[][] p = {{0,0,0,0},
                     {0,0,0,0},
                     {0,0,0,0},
                     {0,0,0,0}};

在一开始的时候。

矩阵是：

        int [][] hill = {{3,8,7,1},
                         {5,15,2,4},
                         {12,14,-13,22},
                         {13,16,17,52}};

如果您在该方法上调用该方法，sum = 23则该方法将返回 true ，并且p将是：

        int[][] p = {{1,0,0,0},
                     {1,1,0,0},
                     {0,0,0,0},
                     {0,0,0,0}};

该方法必须是递归的

这个问题简直让测试像地狱一样......

希望你能弄清楚，也许能帮助我理解它！谢谢

我的进步：

    public static boolean findSum(int[][] mat , int sum , int[][]path){
    return findSum(mat,sum,path,0,0);
}

private static boolean findSum(int[][] m, int sum, int[][] p, int i, int j) {
    if (i>=m.length || j>= m[i].length) return false;


    boolean op1 = finder(m,sum-m[i][j],p,i,j);
    boolean op2 = findSum(m,sum,p,i+1,j);
    boolean op3 = findSum(m,sum,p,i,j+1);

    if (op1) return true;
    else if (op2) return true;
    return op3;
}

private static boolean finder(int[][] m, int sum,int[][]p , int i, int j) {

    if (sum==0) {
        p[i][j]=1;
        return true;
    }
    p[i][j]=1;
    boolean op1=false,op2=false,op3=false,op4=false;
    if (i>0 && p[i-1][j]==0 && sum-m[i][j]>=0) op1 = finder(m, sum - m[i][j], p, i - 1, j);
    if (i<m.length-1 && p[i+1][j]==0&& sum-m[i][j]>=0) op2 = finder(m, sum - m[i][j], p, i + 1, j);
    if (j>0 && p[i][j-1]==0&& sum-m[i][j]>=0) op3 = finder(m, sum - m[i][j], p, i, j - 1);
    if (j<m[i].length-1 && p[i][j+1]==0&& sum-m[i][j]>=0) op4 = finder(m, sum - m[i][j], p, i, j + 1);
    else p[i][j]=0;
    return op1||op2||op3||op4;

}

标签： javarecursionbacktracking

Answer 1

我真的很喜欢解决这个问题。我已经在 python 中完成了它，但您可以轻松地将它扩展到 Java。我已经评论了代码以供您理解。让我知道是否有任何您没有得到或可以改进的地方。

顺便说一句，在您的示例中，一个总和有多个路径，下面的代码可以找到所有路径。

hill = [[3,8,7,1],[5,15,2,4],[12,14,-13,22],[13,16,17,52]]
p = [ [0 for x in range (4)] for y in range(4)]
num = 23

def checkPath(p, r, c): #Check boundaries
    res = []
    if r+1<len(p):
        res.append(p[r+1][c] == 0)
    if r-1>=0:
        res.append(p[r-1][c] == 0)
    if c+1<len(p[0]):
        res.append(p[r][c+1] == 0)
    if c-1>=0:
        res.append(p[r][c-1] == 0)
    return res


def pathF(tot, hill, p, r, c):
    p[r][c] = 1 #mark visited
    tot = tot + hill[r][c]    #update total

    if tot == num: #solution found
        print("Found", p)
    else:
        if any (checkPath(p,r,c)):
            if r+1<len(p) and p[r+1][c] == 0: #move right checking if it wasnt visited
                  pathF(tot,hill,p,r+1,c)
            if r-1>=0 and p[r-1][c] == 0:
                pathF(tot,hill,p,r-1,c)
            if c+1<len(p[0]) and p[r][c+1] == 0:
                pathF(tot,hill,p,r,c+1)
            if c-1>=0 and p[r][c-1] == 0:
                pathF(tot,hill,p,r,c-1)
    p[r][c]=0 #mark unvisited
    tot = tot - hill[r][c]     #set total to original       


for x in range(len(hill)): #iterate over every starting point possible
    for y in range(len(hill[0])):
        pathF(0,hill,p,x,y)

这是 num = 23 的输出

Found [[1, 0, 0, 0], [1, 0, 1, 0], [1, 1, 1, 0], [0, 0, 0, 0]]
Found [[1, 0, 0, 0], [1, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
Found [[1, 1, 1, 1], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0]]
Found [[0, 1, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
Found [[0, 1, 1, 1], [0, 0, 1, 1], [0, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[1, 1, 1, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 0], [1, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[1, 1, 1, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
Found [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 1, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
Found [[1, 0, 0, 0], [1, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 0], [0, 0, 0, 0]]
Found [[1, 0, 0, 0], [1, 0, 1, 0], [1, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[1, 1, 1, 1], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0]]
Found [[0, 0, 0, 0], [0, 0, 1, 1], [0, 1, 1, 0], [0, 1, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 0], [1, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 1, 1, 1], [0, 0, 1, 1], [0, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 1, 1], [0, 0, 0, 0]]
Found [[0, 0, 0, 0], [0, 0, 1, 1], [0, 1, 1, 0], [0, 1, 0, 0]]