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edmonds_karp.go
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/*
*
* Edmonds-Karp算法 - 使用BFS的最大流算法
*
* 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)
*/
package main
import (
"fmt"
)
const MAX_V = 100
var graph [MAX_V][MAX_V]int
var V int
func bfs(rGraph [MAX_V][MAX_V]int, s int, t int, parent []int) bool {
visited := make([]bool, V)
queue := []int{s}
visited[s] = true
parent[s] = -1
for len(queue) > 0 {
u := queue[0]
queue = queue[1:]
for v := 0; v < V; v++ {
if !visited[v] && rGraph[u][v] > 0 {
queue = append(queue, v)
parent[v] = u
visited[v] = true
if v == t {
return true
}
}
}
}
return false
}
func edmondsKarp(s int, t int) int {
rGraph := [MAX_V][MAX_V]int{}
parent := make([]int, V)
max_flow := 0
for u := 0; u < V; u++ {
for v := 0; v < V; v++ {
rGraph[u][v] = graph[u][v]
}
}
for bfs(rGraph, s, t, parent) {
path_flow := 1 << 30
for v := t; v != s; v = parent[v] {
u := parent[v]
if rGraph[u][v] < path_flow {
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
}
func main() {
fmt.Println("=== Edmonds-Karp算法 ===")
V = 6
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
s := 0
t := 5
max_flow := edmondsKarp(s, t)
fmt.Printf("最大流量: %d\n", max_flow)
}