暑假集训-二分图,网络流,2-SAT

匈牙利算法DFS
　　

bool dfs(int u){
for(int i = 1; i <= n; i++){
if(a[u][i] && !visit[i]){
visit[i] = true;
if(match[i] == -1 || dfs(match[i])){
match[i] = u;
}
return true;
}
}
return false;
}

最优匹配KM算法

 

#include <iostream>
#include <cstdio>
#include <fstream>
#include <algorithm>
#include <cmath>
#include <deque>
#include <vector>
#include <queue>
#include <string>
#include <cstring>
#include <map>
#include <stack>
#include <set>
#define LL long long
#define eps 1e-8
#define INF 0x3f3f3f3f
#define OPEN_FILE
#define MAXM 1005
#define MAXN 205
using namespace std;
int n, m;
char s[MAXN][MAXM];
int a[MAXN][MAXN], match[MAXN], fx[MAXN], fy[MAXN];
bool x[MAXN], y[MAXN];

bool dfs(int u){
x[u] = true;
for(int i = 1; i <= n; i++){
if(y[i]) continue;
int p = fx[u] + fy[i] - a[u][i];
if(p == 0){
y[i] = true;
if(match[i] == -1 || dfs(match[i])){
match[i] = u;
return true;
}
}else{
m = min(m, p);
}
}
return false;
}
void KM(){
int i,j;
memset(fx,0,sizeof(fx));
memset(fy,0,sizeof(fy));
memset(match,-1,sizeof(match));
for(int i = 1; i <= n; i++){
for(int j = 1; j <= n; j++){
if(a[i][j] > fx[i]){
fx[i] = a[i][j];
}
}
}
for(int i = 1; i <= n; i++){
while(true){
memset(x, 0, sizeof(x));
memset(y, 0, sizeof(y));
m = INF;
if(dfs(i)) break;
for(int j = 1; j <= n; j++){
if(x[j]) fx[j] -= m;
if(y[j]) fy[j] += m;
}
}
}
}
int main()
{
#ifdef OPEN_FILE
//freopen("inD.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
#endif // OPEN_FILE
while(~scanf("%d", &n)){
memset(a, 0, sizeof(a));
for(int i = 1; i <= n; i++){
scanf("%s", s[i]);
}
for(int i = 1; i <= n; i++){
int p = strlen(s[i]);
for(int j = 1; j <= n; j++){
if(i == j) continue;
int q = strlen(s[j]) - 1;
int cnt = 0;
while(cnt < p && q >= 0 && s[i][cnt] == s[j][q]){
cnt++;
q--;
}
a[i][j] = cnt;
}
}
KM();
int ans = 0;
for(int i = 1; i <= n; i++){
ans += a[match[i]][i];
}
printf("%d\n", ans);
}
}

 

2-SAT

这里面的add_clause的作用式是针对 x=xval or y=yval的时候加边,建不同的图要加不同的边,这里要注意下!!

比如还有一个经典的题目 HDU1824, 建图的时候要格外注意.对于前面队内关系来说是相互的,必须要有一个留下,但是对于队友关系来说却不是相互的,之存在A留B走而不存在A走B必须留的情况,所以加边的里面要写成单向的.

struct TwoSAT{
int n;
vector<int> G[MAXN*2];
bool mark[MAXN*2];
int S[MAXN*2], c;

bool dfs(int x){
if(mark[x^1]) return false;
if(mark[x]) return true;
mark[x] = true;
S[c++] = x;
for(int i = 0; i < G[x].size(); i++){
if(!dfs(G[x][i])) return false;
}
return true;
}

void init(int n){
this->n = n;
for(int i = 0; i < n * 2; i++){
G[i].clear();
}
memset(mark, 0, sizeof(mark));
}

void add_clause(int x, int xval, int y, int yval){
x = x * 2 + xval;
y = y * 2 + yval;
G[x^1].push_back(y);
G[y^1].push_back(x);
}

bool solve(){
for(int i = 0; i < n * 2; i += 2){
if(!mark[i] && !mark[i + 1]){
c = 0;
if(!dfs(i)){
while(c > 0){
mark[S[--c]] = false;
}
if(!dfs(i + 1)){
return false;
}
}
}
}
return true;
}
};

Max-Flow(Dinic)

struct Dinic{
int n, m, i, s, t;
Edge e;
vector<Edge> edges;
vector<int> G[MAXN];
int d[MAXN], cur[MAXN];
bool vis[MAXN];
void init(int n){
this->n = n;
for (i = 0; i <= n; i++){
G[i].clear();
}
edges.clear();
}
void AddEdge(int from, int to, int cap){
edges.push_back(Edge{ from, to, cap, 0 });
edges.push_back(Edge{ to, from, 0, 0 });
m = edges.size();
G[from].push_back(m - 2);
G[to].push_back(m - 1);
}
bool BFS(){
memset(vis, 0, sizeof(vis));
queue<int> Q;
Q.push(s);
d[s] = 0;
vis[s] = 1;
while (!Q.empty()){
int x = Q.front();
Q.pop();
for (i = 0; i < G[x].size(); i++){
Edge& e = edges[G[x][i]];
if (!vis[e.to] && e.cap > e.flow){
vis[e.to] = true;
d[e.to] = d[x] + 1;
Q.push(e.to);
}
}
}
return vis[t];
}
int DFS(int x, int a){
if (x == t || a == 0) return a;
int flow = 0, f;
for (int& i = cur[x]; i < G[x].size(); i++){
Edge& e = edges[G[x][i]];
if (d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap - e.flow))) > 0){
e.flow += f;
edges[G[x][i] ^ 1].flow -= f;
flow += f;
a -= f;
if (a == 0) break;
}
}
return flow;
}
int MaxFlow(int s, int t, int need){
int flow = 0;
this->s = s;
this->t = t;
while (BFS()){
memset(cur, 0, sizeof(cur));
flow += DFS(s, INF);
if (flow > need) return flow;
}
return flow;
}
bool checkFull(int s){
for (int i = 0; i < G[s].size(); i++){
if (edges[G[s][i]].flow != edges[G[s][i]].cap){
return false;
}
}
return  true;
}
};

MCMF

struct Edge{
int u,v,c,cost,next;
}edge[E];
int head[V],cnt;

void init(){
cnt=0;
memset(head,-1,sizeof(head));
}
void addedge(int u,int v,int c,int cost)
{
edge[cnt].u=u;edge[cnt].v=v;edge[cnt].cost=cost;
edge[cnt].c=c;edge[cnt].next=head[u];head[u]=cnt++;

edge[cnt].u=v;edge[cnt].v=u;edge[cnt].cost=-cost;
edge[cnt].c=0;edge[cnt].next=head[v];head[v]=cnt++;
}

bool spfa(int begin,int end){
int u,v;
queue<int> q;
for(int i=0;i<=end+2;i++){
pre[i]=-1;
vis[i]=0;
dist[i]=inf;
}
vis[begin]=1;
dist[begin]=0;
q.push(begin);
while(!q.empty()){
u=q.front();
q.pop();
vis[u]=0;
for(int i=head[u];i!=-1;i=edge[i].next){
if(edge[i].c>0){
v=edge[i].v;
if(dist[v]>dist[u]+edge[i].cost){
dist[v]=dist[u]+edge[i].cost;
pre[v]=i;
if(!vis[v]){
vis[v]=true;
q.push(v);
}
}
}
}
}
return dist[end]!=inf;
}

int MCMF(int begin,int end){
int ans=0,flow;
int flow_sum=0;
while(spfa(begin,end)){
flow=inf;
for(int i=pre[end];i!=-1;i=pre[edge[i].u])
if(edge[i].c<flow)
flow=edge[i].c;
for(int i=pre[end];i!=-1;i=pre[edge[i].u]){
edge[i].c-=flow;
edge[i^1].c+=flow;
}
ans+=dist[end];
flow_sum += flow;
}
//cout << flow_sum << endl;
return ans;
}