Traversal郭至軒（KuoE0）

KuoE0.tw@gmail.comKuoE0.ch

Latest update: Mar 13, 2013

Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)

http://creativecommons.org/licenses/by-sa/3.0/

Graph

Traversal

Traversal

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS (Depth-First Search)

DFS & stack

1

2

3 4

5 6

DFS & stack

1

2

3 4

5 6

1

1

DFS & stack

1

2

3 4

5 6

1

1

2

2

DFS & stack

1

2

3 4

5 6

1

1

2

23 3

DFS & stack

1

2

3 4

5 6

1

1

2

23 3

5

5

DFS & stack

1

2

3 4

5 6

1

1

2

23 3

55

DFS & stack

1

2

3 4

5 6

1

1

2

23

55

3

DFS & stack

1

2

3 4

5 6

1

1

2

23

55

3 4 4

DFS & stack

1

2

3 4

5 6

1

1

2

23

55

3 4 4

6

6

DFS & stack

1

2

3 4

5 6

1

1

2

23

55

3 4 4

66

DFS & stack

1

2

3 4

5 6

1

1

2

23

55

3 4

66

4

DFS & stack

1

2

3 4

5 6

1

1

2

3

55

3 4

66

4

2

DFS & stack

1

2

3 4

5 6

1

2

3

55

3 4

66

4

2

1

Source Code// There are n nodes.// g is an adjacent matrix.

void DFS( int now ) {if ( visited[ now ] == true )return;

visited[ now ] = true;for ( int i = 0; i < n; ++i ) {if ( g[ now ][ i ] == true )DFS( i );

}return;

}

Source Code// There are n nodes.// g is an adjacent matrix.

void DFS() {stack< int > stk;stk.push( 0 );while ( stk.empty() != true ) {

int now = stk.top();visited[ now ] = true;bool noleaf = true;for ( int i = 0; i < n; ++i )

if ( g[ now ][ i ] == true && visited[ i ] != true ) {stk.push( i );noleaf = false;break;

}if ( noleaf == true )

stk.pop();}

}

BFS (Breadth-First Search)

BFS (Breadth-First Search)

BFS (Breadth-First Search)

BFS (Breadth-First Search)

BFS (Breadth-First Search)

BFS & queue

1

2

3 4

5 6

1

BFS & queue

1

2

3 4

5 6

1 11

BFS & queue

1

2

3 4

5 6

1 11

BFS & queue

1

2

3 4

5 6

1 11

2

2

BFS & queue

1

2

3 4

5 6

11

2

2

BFS & queue

1

2

3 4

5 6

11

2

2

BFS & queue

1

2

3 4

5 6

11

2

2

3

3

BFS & queue

1

2

3 4

5 6

11

2

2

3

3

4

4

BFS & queue

1

2

3 4

5 6

11

2

3

3

4

4

BFS & queue

1

2

3 4

5 6

11

2

3

3

4

4

BFS & queue

1

2

3 4

5 6

11

2

3

3

4

4 5

5

BFS & queue

1

2

3 4

5 6

11

2

3 4

4 5

5

BFS & queue

1

2

3 4

5 6

11

2

3 4

4 5

5

BFS & queue

1

2

3 4

5 6

11

2

3 4

4 5

5 6

6

BFS & queue

1

2

3 4

5 6

11

2

3 4

5

5 6

6

BFS & queue

1

2

3 4

5 6

11

2

3 4

5

5 6

6

BFS & queue

1

2

3 4

5 6

11

2

3 4

5 6

6

BFS & queue

1

2

3 4

5 6

11

2

3 4

5 6

6

BFS & queue

1

2

3 4

5 6

11

2

3 4

5 6

Source Code// There are n nodes.// g is an adjacent matrix.

void BFS() {queue< int > que;que.push( 0 );while ( que.empty() != true ) {

int now = que.front();que.pop();visited[ now ] = true;for ( int i = 0; i < n; ++i )

if ( g[ now ][ i ] == true )que.push( i );

}}

Time Complexity

DFS O(V+E)

BFS O(V+E)

V: the number of nodesE: the number of edges

老鼠走迷宮 (DFS)

老鼠走迷宮 (DFS)

老鼠走迷宮 (BFS)

1

老鼠走迷宮 (BFS)

1

老鼠走迷宮 (BFS)

2

1

老鼠走迷宮 (BFS)

2 3

1

老鼠走迷宮 (BFS)

2 3 4

1

老鼠走迷宮 (BFS)

2 3 4 5

5

1

老鼠走迷宮 (BFS)

2 3 4 5 6

5

6

1

老鼠走迷宮 (BFS)

2 3 4 5 6 7

5

7 6 7

1

老鼠走迷宮 (BFS)

2 3 4 5 6 7

5 8

7 6 7

8

1

老鼠走迷宮 (BFS)

2 3 4 5 6 7

5 8 9

7 6 7 9

9 8

1

老鼠走迷宮 (BFS)

2 3 4 5 6 7

5 8 9 10

7 6 7 9

9 8 10

1

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11

5 8 9 10

7 6 7 9

9 8 10 11

1

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12

5 8 9 10

7 6 7 9

9 8 10 11 12

1

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13

5 8 9 10

7 6 7 9

9 8 10 11 12 13

1

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14

1

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15

1

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

11

老鼠走迷宮 (BFS)

2 3 4 5 6 7 11 12 13 14

5 8 9 10 14

7 6 7 9

9 8 10 11 12 13 14 15 16

2 3 4 5 6 7

8

9

10 11 12 13 14 15 16

Practice Now[UVa] 352 - The Seasonal War

352 - The Seasonal WarSample Input Sample Output

6100100001010 00000011000011100001010080110010101000001 00011000 0000001011000011101000101000000101100000

Image number 1 contains 3 war eagles. Image number 2 contains 6 war eagles.

352 - The Seasonal War

352 - The Seasonal War

352 - The Seasonal War

352 - The Seasonal War

Source Code#include <iostream>#include <cstdio>#include <cstring>using namespace std;

int n;char map[ 30 ][ 30 ];bool visited[ 30 ][ 30 ];int step[ 8 ][ 2 ] = { { 1, 1 }, { 1, 0 }, { 1, -1 }, { 0, 1 }, { 0, -1 }, { -1, 1 }, { -1, 0 }, { -1, -1 } };

void DFS( int r, int c );

int main() {int t = 0;while ( scanf( “%d”, &n ) != EOF ) {

int ret = 0;for ( int i = 0; i < n; ++i )

scanf( “%s”, map[ i ] );

memeset( visited, 0, sizeof( visited ) );

Source Codefor ( int i = 0; i < n; ++i )

for ( int j = 0; j < n; ++j )if ( map[ i ][ j ] == ‘1’ && visited[ i ][ j ] != true ) {

DFS( i, j );++ret;

}printf( “Image number %d contains %d war eagles.\n”, ++t, ret );

}return 0;

}void DFS( int r, int c ) {

if ( visited[ r ][ c ] == true )return;

visited[ r ][ c ] = true;for ( int i = 0; i < 8; ++i ) {

int r2 = r + step[ i ][ 0 ], c2 = c + step[ i ][ 1 ];if ( r2 >= 0 && r2 < n && c2 >= 0 && c2 < n && map[ r2 ][ c2 ] == ‘1’ )

DFS( r2, c2 );}

}

Practice Now[UVa] 260 - Il Gioco dell'X

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