This document discusses algorithms for solving maximum flow problems on graphs, including the Ford-Fulkerson, Dinic, and Push-Relabel algorithms. It provides time complexities of each algorithm, with Dinic having the best worst-case running time of O(V^2E) for finding the maximum flow in a flow network with V vertices and E edges. Examples of flow networks and applying the algorithms are also presented.

1. F
1

2. ❖ 101
❖ 1
❖ 1
”overfuro”

3. 1
❖
❖

4. 2
❖ 1
K
❖ 1
s2
s1
s3
s
INF
INF
INF

5. TLE
❖
❖ 1
❖ E O(E* )
FordFulkerson O(E2
F) Dinic O((VE)2
) F
❖ 1010

6. 3
❖
❖
❖

7. s
t
1
2
1 7
4
5
3 5
10
8
8
2

8. s
t
1
2
1 7
4
5
3 5
10
8
8
!!!
2

9. s
t
1
2
1 7
4
5
3 5
10
8
8
2
4

10. s
a
b
c
t
1
2
1 7
4
5
3 5
10
8
8
2
s t
s a b c

11. s
f
e
a
b
d
c
t
1
2
1 7
4
5
3 5
10
8
8
2
s t
d e f
t

12. s
f
e
a
b
d
c
t
1
2
1 7
4
5
3 5
10
8
8
2
s-a
d-t

13. ❖
❖ V
❖ O(V* )
❖ O(V2E) Dinic O(V3) Push-Relabel
Ford-Fulkerson

14. Dinic
❖ Dinic O(V2E)
❖ Dinic
AC
❖ Dinic
http://topcoder.g.hatena.ne.jp/Mi_Sawa/20140311/
1394730337

15. Writer
❖ C++ 119
❖ C++ 134
❖ FordFulkerson Dinic

16. ❖ FA
- tanzaku
- energy_star
❖ Accept/Submit
- 4/41(9.76%)