UVA 705 - Slash Maze （Flood_Fill + DFS）

分析：

1. 可以知道的是，給定的 slash Maze 中只存在 ‘/’ 和 ‘\’ ，將斜線或反斜線離散化為 3 * 3 單位的方格，比如

    用數字 1 表示單位被覆蓋，數字 0 表示單位是空白，則 /

0	0	1
0	1	0
1	0	0

  也可以用 2 * 2 的單元格表示圖像，但是需要特判，而這種方法不需要特判，而且相對容易實現

2. 對圖像的邊界使用 Flood Fill 染色為數字 2，因為邊界部分不可能構成環（想一想），排除不構成環的部分

3. 第 2 步以后，對 slash Maze 數字為 0 的空格使用 dfs 找出最大的環長度，也可以使用 flood fill 直接找出

  1 /*

  2 PROG:   Slash Maze

  3 ID  :   yewei

  4 LANG:   C++

  5 */

  6 #pragma warnning (disable : 4786)

  7 

  8 #include <memory.h>

  9 #include <cstdio>

 10 #include <cstdlib>

 11 #include <cstring>

 12 #include <iostream>

 13 

 14 using namespace std;

 15 

 16 const int MAXN = 229;

 17 const int dx[] = {-1, 1, 0, 0};

 18 const int dy[] = {0, 0, -1, 1};

 19 

 20 int w, h, cycles, grids, maxGrids, cas = 1;

 21 int graph[MAXN][MAXN];

 22 bool vis[MAXN][MAXN], hash[MAXN][MAXN];

 23 

 24 void debug() {

 25     for (int i = 0; i < h; ++i) {

 26         for (int j = 0; j < w; ++j) {

 27             if (graph[i][j] == 1) {

 28                 printf("*");

 29             } else if (graph[i][j] == 2) {

 30                 printf("#");

 31             } else if (graph[i][j] == 0) {

 32                 printf(" ");

 33             }

 34         }

 35         printf("\n");

 36     }

 37     printf("\n");

 38 }

 39 

 40 void readGraph() {

 41     char ch;

 42     

 43     h *= 3, w *= 3;

 44     for (int i = 1; i < h; i += 3) {

 45         getchar();

 46         for (int j = 1; j < w; j += 3) {

 47             scanf("%c", &ch);

 48             if (ch == '\\') {

 49                 graph[i][j] = 1;

 50                 graph[i - 1][j - 1] = graph[i + 1][j + 1] = 1;

 51                 graph[i - 1][j] = graph[i + 1][j] = 0;

 52                 graph[i][j - 1] = graph[i][j + 1] = 0;

 53                 graph[i - 1][j + 1] = graph[i + 1][j - 1] = 0;

 54             } else if (ch == '/') {

 55                 graph[i][j] = 1;

 56                 graph[i - 1][j + 1] = graph[i + 1][j - 1] = 1;

 57                 graph[i - 1][j] = graph[i + 1][j] = 0;

 58                 graph[i][j - 1] = graph[i][j + 1] = 0;

 59                 graph[i - 1][j - 1] = graph[i + 1][j + 1] = 0;

 60             }

 61         }

 62     }

 63     // debug();

 64 }

 65 

 66 bool isBoundary(int &x, int &y) {

 67     return (x == 0 || y == 0 || x == h - 1 || y == w - 1);

 68 }

 69 

 70 bool isOut(int &x, int &y) {

 71     return (x < 0 || y < 0 || x >= h || y >= w);

 72 }

 73 

 74 void flood_fill(int x, int y, int color) {

 75     vis[x][y] = true;

 76     graph[x][y] = color;

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

 78         int nx = x + dx[i];

 79         int ny = y + dy[i];

 80         if (!isOut(nx, ny) && !vis[nx][ny] && !graph[nx][ny]) {

 81             flood_fill(nx, ny, color);

 82         }

 83     }

 84 }

 85 

 86 void colorBoundary() {

 87     for (int i = 0; i < h; ++i) {

 88         for (int j = 0; j < w; ++j) {

 89             if (isBoundary(i, j) && !vis[i][j] && !graph[i][j]) {

 90                 flood_fill(i, j, 2);

 91             }

 92         }

 93     }

 94     // debug();

 95 }

 96 

 97 void dfs(int x, int y) {

 98     ++grids;

 99     hash[x][y] = true;

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

101         int nx = x + dx[i];

102         int ny = y + dy[i];

103         if (!isOut(nx, ny) && !graph[nx][ny] && !hash[nx][ny]) {

104             dfs(nx, ny);

105         }

106     }

107 }

108 

109 void solve() {

110     cycles = 0, maxGrids = -1;

111     for (int i = 0; i < h; ++i) {

112         for (int j = 0; j < w; ++j) {

113             if (!graph[i][j] && !hash[i][j]) {

114                 ++cycles;

115                 grids = 0;

116                 dfs(i, j);

117                 if (grids > maxGrids) {

118                     maxGrids = grids;

119                 }

120             }

121         }

122     }

123 }

124 

125 void solve();

126 

127 int main() {

128     while (~scanf("%d %d", &w, &h) && w + h != 0) {

129         memset(vis, false, sizeof(vis));

130         memset(hash, false, sizeof(hash));

131         memset(graph, -1, sizeof(graph));

132         

133         readGraph();

134         colorBoundary();

135         solve();

136         

137         printf("Maze #%d:\n", cas++);

138         if (cycles) {

139             printf("%d Cycles; the longest has length %d.\n", cycles, maxGrids / 3);

140         } else {

141             printf("There are no cycles.\n");

142         }

143         printf("\n");

144     }// End of while

145 

146     return 0;

147 }

148 /*

149 #         Problem     Verdict     Language     Run Time     Submission Date

150 10592483     705     Slash Maze     Accepted     C++     0.036     2012-09-12 03:01:16

151 */