UVA 11882 Biggest Number（搜索+剪枝）

You have a maze with obstacles and non-zero digits in it:

 

You can start from any square, walk in the maze, and finally stop at some square. Each step, you may only walk into one of the four neighbouring squares (up, down, left, right) and you cannot walk into obstacles or walk into a square more than once. When you finish, you can get a number by writing down the digits you encounter in the same order as you meet them. For example, you can get numbers 9784, 4832145, etc. The biggest number you can get is 791452384, shown in the picture above.

Your task is to find the biggest number you can get.

Input 

There will be at most 25 test cases. Each test begins with two integers R and C (2R,C15, R*C30), the number of rows and columns of the maze. The next R rows represent the maze. Each line contains exactly Ccharacters (without leading or trailing spaces), each of them will be either `#' or one of the nine non-zero digits. There will be at least one non-obstacle squares (i.e. squares with a non-zero digit in it) in the maze. The input is terminated by a test case with R = C = 0, you should not process it.

Output 

For each test case, print the biggest number you can find, on a single line.

 

题目大意：有一个R*C的矩阵，矩阵里面有1~9的数字（太好了不用处理前导0），或者是#（代表不能通过），先要从矩阵任意一点出发（之前英语抓鸡看成了边界，英语差的孩纸伤不起啊>_<），只能往上下左右四个方向移动，每个格子不能重复走，到达矩阵内任意一点。把这条路径的数字连起来变成一个很大的数字，求这个数字最大是什么。
思路：DP？记忆化搜索？30个点噢，时间吃得消内存都吃不消啦。所以呢？搜索。还是超时啊？剪枝啊。
剪枝1：假设当前答案为ans，那么当我们走到一个点(x, y)的时候，作一个小小的搜索预判。假设现在能从(x, y)走到的点，我们都能到达，这是最好的情况。设从(x, y)能走到的点数为maxlen，那么如果从出发点走到(x, y)经过的格子，加上maxlen，都没有ans的长度大，那么不管从(x, y)怎么搜，我们都不能取代我们现在的ans（长才是王道懂不懂），那么直接回溯，不要这个点了。这个剪枝效力还是不错的，但是还是TLE，我试过了QAQ。最近有点脑残，明明可以做一个数据测试一下非要交上去试一下……
剪枝2：同剪枝1，假设当前答案为ans，那么当我们走到一个点(x, y)的时候，搜到maxlen（同剪枝1），如果从出发点走到(x, y)经过的格子，加上maxlen，大于ans的长度，我们就只能继续搜了……如果等于呢？那么就再作一个最好预期的答案。把从(x, y)能走到的所有格子，从大到小排好序（我的代码是从小到大排序然后从后面开始取的……），都接在当前走到(x, y)的后面，这是从(x, y)可能搜到的最好的答案，如果这个都比ans要小，那么我们也就没有必要往下搜了，果断回溯。
PS：弄个结构体存答案很好写妥妥的。

 

代码（866MS）：

 1 #include <cstdio>

 2 #include <cstring>

 3 #include <iostream>

 4 #include <algorithm>

 5 #include <queue>

 6 using namespace std;

 7 typedef long long LL;

 8 

 9 const int MAXN = 33;

10 

11 struct Node {

12     int a[MAXN], len;

13     void clear() {

14         len = 0;

15     }

16     void print() {

17         //cout<<len<<endl;

18         for(int i = 0; i < len; ++i) printf("%d", a[i]);

19         printf("\n");

20     }

21     bool operator < (const Node &rhs) const {

22         if(len != rhs.len) return len < rhs.len;

23         for(int i = 0; i < len; ++i)

24             if(a[i] != rhs.a[i]) return a[i] < rhs.a[i];

25         return false;

26     }

27 };

28 

29 int fx[] = {1, 0, -1, 0};

30 int fy[] = {0, 1, 0, -1};

31 

32 Node ans, now, tmp;

33 char mat[MAXN][MAXN];

34 bool vis[MAXN][MAXN];

35 bool vis2[MAXN][MAXN];

36 int n, m;

37 int can[MAXN];

38 

39 int maxlen(int x, int y) {

40     queue<int> que; que.push(x * MAXN + y);

41     int ret = 1;

42     can[0] = mat[x][y] - '0';

43     memset(vis2, 0, sizeof(vis2));

44     vis2[x][y] = 1;

45     while(!que.empty()) {

46         int tmp = que.front(); que.pop();

47         int nx = tmp / MAXN, ny = tmp % MAXN;

48         for(int i = 0; i < 4; ++i) {

49             int px = nx + fx[i], py = ny + fy[i];

50             if(!isdigit(mat[px][py]) || vis[px][py] || vis2[px][py]) continue;

51             vis2[px][py] = true;

52             can[ret++] = mat[px][py] - '0';

53             que.push(px * MAXN + py);

54         }

55     }

56     return ret;

57 }

58 

59 void dfs(int x, int y) {

60     now.a[now.len++] = mat[x][y] - '0';

61     vis[x][y] = true;

62     for(int i = 0; i < 4; ++i) {

63         int px = x + fx[i], py = y + fy[i];

64         if(!isdigit(mat[px][py]) || vis[px][py]) continue;

65         int wantlen = maxlen(px, py);

66         if(now.len + wantlen < ans.len) continue;

67         if(now.len + wantlen == ans.len) {

68             sort(can, can + wantlen);

69             tmp = now;

70             for(int i = wantlen - 1; i >= 0; --i) tmp.a[tmp.len++] = can[i];

71             if(tmp < ans) continue;

72         }

73         dfs(px, py);

74     }

75     if(ans < now) ans = now;

76     --now.len;

77     vis[x][y] = false;

78 }

79 

80 int main() {

81     while(scanf("%d%d", &n, &m) != EOF) {

82         if(n + m == 0) break;

83         memset(mat, 0, sizeof(mat));

84         for(int i = 1; i <= n; ++i) scanf("%s", &mat[i][1]);

85         ans.clear(); now.clear();

86         for(int i = 1; i <= n; ++i) {

87             for(int j = 1; j <= m; ++j)

88                 if(isdigit(mat[i][j])) dfs(i, j);

89         }

90         ans.print();

91     }

92 }

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