Drainage Ditches

题意：1是源点，m是汇点，求出来最大流量，没什么好说的就是练习最大流的模板题

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先用Edmonds-Karp的算法做一下试试吧
重边贡献了 1W，要加上所有的重边才算是两点间最大流量

***********************************************************************************************************************

/************************************/
/** 使用Edmonds-Karp 最短增广路算法*/
/** 邻接矩阵实现                   */
/** 2015/8/7/9:39                   */
/************************************/

#include<stdio.h>
#include<string.h>
#include<queue>
#include<algorithm>
using namespace std;

const int MAXN = 205;
const int oo = 1e9+7;

///1是源点，M是汇点，N条边
int G[MAXN][MAXN], M, N;
int pre[MAXN];///记录每个点的前驱，也就是父节点
bool used[MAXN];

///s代表源点，e代表汇点,可以到达汇返回true，否则返回false
bool BFS(int s, int e)
{
    memset(used, false, sizeof(used));
    queue<int> Q;
    Q.push(s);
    used[s] = true;

    while(Q.size())
    {
        s = Q.front();Q.pop();

        if(s == e) return true;

        for(int i=1; i<=M; i++)
        {
            if(G[s][i] && !used[i])
            {
                pre[i] = s;
                used[i] = true;
                Q.push(i);
            }
        }
    }

    return false;
}
int Karp(int s, int e)
{
    int MaxFlow = 0;

    while( BFS(s, e) == true )
    {///如果有增量
        int MinFlow = oo, v;

        v = e;

        while(v != s)
        {///求出来路径上最小流量
            MinFlow = min(MinFlow, G[pre[v]][v]);
            v = pre[v];
        }

        MaxFlow += MinFlow;
        v = e;

        while(v != s)
        {///边上的所有点减去最小流量，反边增加流量
            G[pre[v]][v] -= MinFlow;
            G[v][pre[v]] += MinFlow;

            v = pre[v];
        }
    }

    return MaxFlow;
}

int main()
{
    while(scanf("%d%d", &N, &M) != EOF)
    {
        int i, u, v, c;

        memset(G, false, sizeof(G));

        for(i=1; i<=N; i++)
        {
            scanf("%d%d%d", &u, &v, &c);
            G[u][v] += c;///有重边，两点间应该算上所有边
        }

        printf("%d
", Karp(1, M));
    }

    return 0;
}

邻接表实现

***********************************************************************************************************************

/************************************/
/// 使用Edmonds-Karp 最短增广路算法
/// 邻接表实现
/// 2015年8月7日10:13:55
/************************************/

#include<stdio.h>
#include<string.h>
#include<queue>
#include<algorithm>
using namespace std;

const int MAXN = 205;
const int oo = 1e9+7;

struct Edge{int u, v, Flow, next;}e[MAXN<<1];
int Head[MAXN], cnt;
int pre[MAXN], used[MAXN];

void InIt()
{
    memset(Head, -1, sizeof(Head));
    cnt = 0;
}
void AddEdge(int u, int v, int Flow)
{
    e[cnt].u = u;
    e[cnt].v = v;
    e[cnt].Flow = Flow;
    e[cnt].next = Head[u];
    Head[u] = cnt++;
}
bool BFS(int s, int End)
{
    memset(used, false, sizeof(used));
    memset(pre, -1, sizeof(pre));
    queue<int> Q;
    Q.push(s);
    used[s] = true;

    while(Q.size())
    {
        s = Q.front();Q.pop();

        if(s == End)return true;

        for(int i=Head[s]; i!=-1; i=e[i].next)
        {
            if(e[i].Flow && used[e[i].v] == false)
            {
                used[e[i].v] = true;
                pre[e[i].v] = i;///记录的是上面的边的位置
                Q.push(e[i].v);
            }
        }
    }

    return false;
}
int Karp(int s, int End)
{
    int MaxFlow = 0;

    while(BFS(s, End) == true)
    {
        int MinFlow = oo, v;

        v = pre[End];

        while(v != -1)
        {
            MinFlow = min(MinFlow, e[v].Flow);
            v = pre[e[v].u];///上个点来的位置
        }

        MaxFlow += MinFlow;
        v = pre[End];

        while(v != -1)
        {
            e[v].Flow -= MinFlow;
            e[v^1].Flow += MinFlow;
            v = pre[e[v].u];
        }
    }

    return MaxFlow;
}

int main()
{
    int N, M;

    while(scanf("%d%d", &N, &M) != EOF)
    {
        int i, u, v, Flow;

        InIt();

        for(i=1; i<=N; i++)
        {
            scanf("%d%d%d", &u, &v, &Flow);
            AddEdge(u, v, Flow);
            AddEdge(v, u, 0);///先添加一条反边的流量是0
        }

        printf("%d
", Karp(1, M));
    }

    return 0;
}

Dinic实现 

************************************************************************************************************************

#include<stdio.h>
#include<string.h>
#include<queue>
using namespace std;

const int MAXN = 205;
const int oo = 1e9+7;

struct Edge{int u, v, flow, next;}edge[MAXN*MAXN];
int Head[MAXN], cnt;
int layer[MAXN];///分层
int Start, End;///源点汇点

void AddEdge(int u, int v, int flow)
{
    edge[cnt].u = u;
    edge[cnt].v = v;
    edge[cnt].flow = flow;
    edge[cnt].next = Head[u];
    Head[u] = cnt++;
}
bool BfsLayer()///使用广搜进行分层
{
    bool used[MAXN]={0};queue<int> Q;
    memset(layer, -1, sizeof(layer));
    Q.push(Start);
    used[Start] = true;
    layer[Start] = 0;

    while(Q.size())
    {
        int s = Q.front();Q.pop();

        if(s == End)return true;

        for(int i=Head[s]; i!=-1; i=edge[i].next)
        {
            int v = edge[i].v;

            if(edge[i].flow && !used[v])
            {
                used[v] = true;
                layer[v] = layer[s] + 1;
                Q.push(v);
            }
        }
    }

    return false;
}
int dfs(int u, int MaxFlow)
{///MaxFlow 记录的是这条路径上能经过的最大流量
    if(u == End)return MaxFlow;

    int uFlow = 0;///这个点最多能经过多少流量

    for(int i=Head[u]; i!=-1; i=edge[i].next)
    {
        int v = edge[i].v, flow = edge[i].flow;

        if(layer[v]-1 == layer[u] && flow)
        {
            flow = min(MaxFlow-uFlow, flow);
            flow = dfs(v, flow);

            edge[i].flow -= flow;
            edge[i^1].flow += flow;
            uFlow += flow;
            if(uFlow == MaxFlow)
                break;///已经等于最大流量的时候注意结束
        }
    }

    return uFlow;
}
int Dinic()///用dinic算法求最大流
{
    int MaxFlow = 0;

    while(BfsLayer() == true)
    {
        MaxFlow += dfs(Start, oo);
    }

    return MaxFlow;
}

int main()
{
    int N, M;

    while(scanf("%d%d", &N, &M) != EOF)
    {
        int i, u, v, flow;

        Start = 1, End = M, cnt = 0;
        memset(Head, -1, sizeof(Head));

        for(i=1; i<=N; i++)
        {
            scanf("%d%d%d", &u, &v, &flow);
            AddEdge(u, v, flow);
            AddEdge(v, u, 0);
        }

        printf("%d
", Dinic());
    }

    return 0;
}

SAP实现

*************************************************************************************************************************

#include<stdio.h>
#include<string.h>
#include<queue>
using namespace std;

const int MAXN = 205;
const int oo = 1e9+7;

struct Edge{int u, v, flow, next;}edge[MAXN*MAXN];
int Head[MAXN], cnt;
int Layer[MAXN];///分层
int start, End;///源点汇点
int cur[MAXN], Stack[MAXN],gap[MAXN];
int sumV;///节点的总个数

void AddEdge(int u, int v, int flow)
{
    edge[cnt].u = u;
    edge[cnt].v = v;
    edge[cnt].flow = flow;
    edge[cnt].next = Head[u];
    Head[u] = cnt++;
}

void BFS()
{
    memset(Layer, -1, sizeof(Layer));
    memset(gap, 0, sizeof(gap));
    queue<int> Q;
    Q.push(End);
    Layer[End] = 0, gap[0] = 1;

    while(Q.size())
    {
        int u = Q.front();
        Q.pop();

        for(int j=Head[u]; j!=-1; j=edge[j].next)
        {
            int v = edge[j].v;

            if(Layer[v] == -1)
            {
                Layer[v] = Layer[u] + 1;
                gap[Layer[v]]++;
                Q.push(v);
            }
        }
    }
}

int SAP()
{
    int j, top=0, u = start, MaxFlow=0;

    BFS();

    memcpy(cur, Head, sizeof(Head));

    while(Layer[start] < sumV)
    {///源点的层次小于总结点数,汇点是0层

        if(u == End)
        {
            int MinFlow = oo, location;///记录下最小流量边的位置，出栈时候用

            for(j=0; j<top; j++)
            {
                int i = Stack[j];
                if(MinFlow > edge[i].flow)
                {
                    MinFlow = edge[i].flow;
                    location = j;
                }
            }
            for(j=0; j<top; j++)
            {///所有的边减去路径上的最小流量
                int i = Stack[j];

                edge[i].flow -= MinFlow;
                edge[i^1].flow += MinFlow;
            }

            MaxFlow += MinFlow;
            top = location;///退栈
            u = edge[Stack[top]].u;
        }
        else if(gap[Layer[u]-1] == 0)
            break;///u所在的层下面的层没有了，出现了断层，也就没有了可行弧

        for(j=cur[u]; j!=-1; j=edge[j].next)
        {///如果u有可行弧就停止
            if(Layer[u]==Layer[edge[j].v]+1 && edge[j].flow)
                break;
        }

        if(j != -1)
        {///找到了可行弧
            cur[u] = j;///u点的可行弧是j
            Stack[top++] = j;///记录下这条边
            u = edge[j].v;
        }
        else
        {///没有找到可行弧，修改标号
            int MinIndex = sumV;

            for(j=Head[u]; j!=-1; j=edge[j].next)
            {///查找与u相连的最小的层是多少
                if(edge[j].flow && MinIndex > Layer[edge[j].v])
                {///记录下这条可行弧,下次可以直接访问这条边
                    MinIndex = Layer[edge[j].v];
                    cur[u] = j;
                }
            }

            gap[Layer[u]] -= 1;///u改变层，所以u原来所在层的点数减去1
            Layer[u] = MinIndex + 1;
            gap[Layer[u]] += 1;

            if(u != start)
            {///返回上一层
                u = edge[Stack[--top]].u;
            }
        }
    }

    return MaxFlow;
}

int main()
{
    int N, M;

    while(scanf("%d%d", &N, &M) != EOF)
    {
        int i, u, v, flow;
        sumV = M;
        start = 1, End = M, cnt = 0;
        memset(Head, -1, sizeof(Head));

        for(i=1; i<=N; i++)
        {
            scanf("%d%d%d", &u, &v, &flow);
            AddEdge(u, v, flow);
            AddEdge(v, u, 0);
        }

        printf("%d
", SAP());
    }

    return 0;
}