-
Notifications
You must be signed in to change notification settings - Fork 18
Expand file tree
/
Copy pathmax_flow.c
More file actions
110 lines (87 loc) · 2.11 KB
/
max_flow.c
File metadata and controls
110 lines (87 loc) · 2.11 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
/*
*
* 最大流算法 - 使用Edmonds-Karp (BFS)
*
* 问题：在流网络中找到从源点到汇点的最大流量
*
* 核心思想：
* - 使用BFS寻找最短增广路径
* - 沿增广路径增加流量
* - 更新残差网络
*
* 时间复杂度: O(VE²)
* 空间复杂度: O(V + E)
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#define MAX_V 100
int graph[MAX_V][MAX_V];
int V;
int bfs(int rGraph[MAX_V][MAX_V], int s, int t, int parent[]) {
int visited[MAX_V] = {0};
int queue[MAX_V];
int front = 0, rear = 0;
queue[rear++] = s;
visited[s] = 1;
parent[s] = -1;
while (front < rear) {
int u = queue[front++];
for (int v = 0; v < V; v++) {
if (!visited[v] && rGraph[u][v] > 0) {
queue[rear++] = v;
parent[v] = u;
visited[v] = 1;
if (v == t) {
return 1;
}
}
}
}
return 0;
}
int maxFlow(int s, int t) {
int u, v;
int rGraph[MAX_V][MAX_V];
int parent[MAX_V];
int max_flow = 0;
for (u = 0; u < V; u++) {
for (v = 0; v < V; v++) {
rGraph[u][v] = graph[u][v];
}
}
while (bfs(rGraph, s, t, parent)) {
int path_flow = INT_MAX;
for (v = t; v != s; v = parent[v]) {
u = parent[v];
path_flow = (path_flow < rGraph[u][v]) ? path_flow : rGraph[u][v];
}
for (v = t; v != s; v = parent[v]) {
u = parent[v];
rGraph[u][v] -= path_flow;
rGraph[v][u] += path_flow;
}
max_flow += path_flow;
}
return max_flow;
}
int main() {
printf("=== 最大流算法 ===\n");
V = 6;
memset(graph, 0, sizeof(graph));
graph[0][1] = 16;
graph[0][2] = 13;
graph[1][2] = 10;
graph[1][3] = 12;
graph[2][1] = 4;
graph[2][4] = 14;
graph[3][2] = 9;
graph[3][5] = 20;
graph[4][3] = 7;
graph[4][5] = 4;
int s = 0, t = 5;
int max_flow = maxFlow(s, t);
printf("最大流量: %d\n", max_flow);
return 0;
}