Careercup

2014-05-06 07:11

题目链接

原题：

Find a shortest path in a N*N matrix maze from (0,0) to (N,N), assume 1 is passable, 0 is not, 3 is destination, use memorization to cache the result. Here is my code. I am not sure if I am caching it right.

题目：给定一个N * N的矩阵，找出从(0, 0)到(n - 1, n - 1)的最短路径。此人在后面还贴上了自己的代码，从代码水平上看此人实力基本不足以参加Google的面试，此人叫“Guy”。

解法：对于这种移动距离限于一格的最短路径问题，最直接的思想就是BFS了。而这位老兄居然还把自己四路DFS的代码贴出来，多余的也就没必要评论了。此题要求得到完整的最短路径，所以进行BFS的同时，需要记录每个点的回溯位置。这样就可以从目的地一直回溯到出发点，得到一条完整的最短路径。算法的整体时间复杂度是O(n^2)的。

代码：

// http://www.careercup.com/question?id=5634470967246848
#include <cstdio>
#include <queue>
#include <vector>
using namespace std;

int main()
{
    int n;
    vector<vector<int> > v;
    queue<int> q;
    int i, j, k;
    int x, y;
    int dx, dy;
    int d[4][2] = {
        {-1, 0}, 
        {+1, 0}, 
        {0, -1}, 
        {0, +1}
    };
    int back[4] = {1, 0, 3, 2};
    vector<vector<int> > trace;
    vector<int> path;
    int tmp;
    
    while (scanf("%d", &n) == 1 && n > 0) {
        v.resize(n);
        trace.resize(n);
        for (i = 0; i < n; ++i) {
            v[i].resize(n);
            trace[i].resize(n);
        }
        
        for (i = 0; i < n; ++i) {
            for (j = 0; j < n; ++j) {
                scanf("%d", &v[i][j]);
                if (v[i][j] == 3) {
                    dx = i;
                    dy = j;
                }
            }
        }
        
        v[0][0] = -1;
        q.push(0);
        while (v[dx][dy] > 0 && !q.empty()) {
            tmp = q.front();
            q.pop();
            i = tmp / n;
            j = tmp % n;
            for (k = 0; k < 4; ++k) {
                x = i + d[k][0];
                y = j + d[k][1];
                if (x < 0 || x > n - 1 || y < 0 || y > n - 1) {
                    continue;
                }
                if (v[x][y] > 0) {
                    v[x][y] = v[i][j] - 1;
                    trace[x][y] = back[k];
                    q.push(x * n + y);
                }
            }
        }
        while (!q.empty()) {
            q.pop();
        }
        
        if (v[dx][dy] < 0) {
            x = dx;
            y = dy;
            while (x || y) {
                path.push_back(x * n + y);
                i = x + d[trace[x][y]][0];
                j = y + d[trace[x][y]][1];
                x = i;
                y = j;
            }
            path.push_back(0);
            while (!path.empty()) {
                x = path.back() / n;
                y = path.back() % n;
                printf("(%d, %d)", x, y);
                path.pop_back();
            }
            putchar('
');
        } else {
            printf("Unreachable.
");
        }
        
        for (i = 0; i < n; ++i) {
            v[i].clear();
            trace[i].clear();
        }
        v.clear();
        trace.clear();
        path.clear();
    }
    
    return 0;
}