【板子】最短路

例题：hdu的1874

FLOYD

a->b有两种走法，1、a->k->b，2、a->b

这是主要思想。那每次保留最短路径即可。

dp[i][j] = min(dp[i][j] , dp[i][k] + dp[k][j])

#include<iostream>
#include<vector>
#include<queue>
#include<algorithm>
using namespace std;
const int maxn = 205;

int n,m;
int mp[maxn][maxn];

void init(int n){
    for(int i = 0; i < n ;i++){
        for(int j = 0 ; j < n ;j++){
            if(i == j)
                mp[i][j] = 0;
            else
                mp[i][j] = 1e9;
        }
    }
}

int main(){

    while(cin>>n>>m){
        init(n);
        int x,y,z;

        for(int i = 1; i <= m ;i++){
            cin>>x>>y>>z;
            mp[x][y] = min(z,mp[x][y]);
            mp[y][x] = min(z,mp[y][x]);
        }

        int s,t;
        cin>>s>>t;

        for(int k = 0; k < n ;k++){
            for(int i = 0; i < n ;i++){
                for(int j = 0; j < n ;j++){
                    mp[i][j] = min(mp[i][j],mp[i][k] + mp[k][j]);
                    //cout<<mp[i][j]<<endl;
                }
            }
        }
        //cout<<mp[1][2]<<endl;
        if(mp[s][t] == 1e9)
            cout<<-1<<endl;
        else
            cout<<mp[s][t]<<endl;
    }

    return 0;
}

SPFA

基于dp的思想。十分有趣的板子

e[]　　　　存边

d[]　　　　存距离

inq[]　　　判断是否在queue里。

主要的dp思想就是

dp[v] = max(dp[now] + e[now][i].second  , dp[v])

#include<iostream>
#include<stack>
#include<vector>
#include<queue>
#include<algorithm>
using namespace std;
const int maxn = 2e5+7;

vector< pair<int,int> > e[maxn];

int n,m;
int d[maxn],inq[maxn];

void init(){
    for(int i = 0; i < maxn; i++)
        e[i].clear();
    for(int i = 0 ;i < maxn ; i++)
        inq[i] = 0;
    for(int i = 0 ; i < maxn ; i++)
        d[i] = 1e9;
}

int main(int argc, const char * argv[]) {
    while(cin>>n>>m){
        init();
        int x,y,z;
        for(int i = 0; i < m ;i++){
            cin>>x>>y>>z;
            e[x].push_back(make_pair(y,z));
            e[y].push_back(make_pair(x,z));
        }
        int s,t;
        cin>>s>>t;
        queue<int>Q;
        Q.push(s);d[s] = 0 ;inq[s] = 1;
        while( !Q.empty() ){
            int now = Q.front();
            Q.pop();
            inq[now] = 0;
            for(int i = 0; i < e[now].size() ; i++){
                int v = e[now][i].first;
                if(d[v] > d[now] + e[now][i].second){
                    d[v] = d[now] + e[now][i].second;
                    if(inq[v] == 1)
                        continue;
                    inq[v] = 1;
                    Q.push(v);
                }
            }

        }
        if(d[t] == 1e9)
            cout<<-1<<endl;
        else{
            cout<<d[t]<<endl;
        }
    }
    return 0;
}

更新一下kb大神的板子。

#include<bits/stdc++.h>
using namespace std;

const int maxn = 1e5+7;
const int inf = 0x3f3f3f3f;

struct Edge{
    int v;
    int cost;
    Edge(int _v = 0,int _cost = 0):v(_v),cost(_cost){}
};

vector<Edge> e[maxn];

void addedge(int u,int v,int w){
    e[u].push_back(Edge(v,w));
}

bool vis[maxn];
int cnt[maxn];
int dis[maxn];

int n,m,c;

bool spfa(int s){
    memset(vis,false,sizeof(vis));
    for(int i = 1; i <= n; i++) dis[i] = inf;

    vis[s] = true;
    dis[s] = 0;
    queue<int> Q;
    while(!Q.empty())   Q.pop();
    Q.push(s);
    memset(cnt,0,sizeof(cnt));
    cnt[s] = 1;

    while(!Q.empty()){
        int u = Q.front();
        Q.pop();
        vis[u] = false;
        for(int i = 0; i < e[u].size();i++){
            int v = e[u][i].v;
            if(dis[v] > dis[u] + e[u][i].cost){
                dis[v] = dis[u] + e[u][i].cost;
                if(!vis[v]){
                    vis[v] = true;
                    Q.push(v);
                    if(++cnt[v] > n)    return false;
                    //cnt[i]
                }
            }
        }
    }

    return true;
}

DIJSTRA

其实就是在spfa上做了优先队列的改进，省略了inq[]数组。

第一次用这个优先队列，感觉很妙。

#include<iostream>
#include<stack>
#include<vector>
#include<queue>
#include<algorithm>
using namespace std;
const int maxn = 2e5+7;

vector< pair<int,int> > e[maxn];

int n,m;
int d[maxn];

void init(){
    for(int i = 0; i < maxn; i++)
        e[i].clear();
    for(int i = 0 ; i < maxn ; i++)
        d[i] = 1e9;
}

int main(int argc, const char * argv[]) {
    while(cin>>n>>m){
        init();
        int x,y,z;
        for(int i = 0; i < m ;i++){
            cin>>x>>y>>z;
            e[x].push_back(make_pair(y,z));
            e[y].push_back(make_pair(x,z));
        }
        int s,t;
        cin>>s>>t;
        priority_queue <pair<int,int> >Q;
        d[s] = 0;
        Q.push( make_pair(-d[s],s) );
        while( !Q.empty() ){
            int now = Q.top().second;
            Q.pop();

            for(int i = 0; i < e[now].size() ; i++){
                int v = e[now][i].first;
                if(d[v] > d[now] + e[now][i].second){
                    d[v] = d[now] + e[now][i].second;
                    Q.push( make_pair(-d[v],v));
                }
            }

        }
        if(d[t] == 1e9)
            cout<<-1<<endl;
        else{
            cout<<d[t]<<endl;
        }
    }
    return 0;
}

 kb大神的板子

#include<bits/stdc++.h>
using namespace std;
const int maxn = 1e5+7;
const int inf = 0x3f3f3f3f;

struct node{
    int v;
    int c;
    node(int _v = 0,int _c = 0):v(_v),c(_c){}
    bool operator < (const node &r)const{
        return c > r.c;
    }    

};


struct Edge{
    int v,cost;
    Edge(int _v = 0, int _cost = 0):v(_v),cost(_cost){}
};

vector< Edge > e[maxn];
bool vis[maxn];
int dis[maxn];
int n,m,c;

void addedge(int u,int v,int w){
    e[u].push_back(Edge(v,w));
}

void dij(int s){
    memset(vis,false,sizeof(vis));
    for(int i = 1; i <= n ;i++) dis[i] = inf;
    priority_queue <node> Q;
 
    while(!Q.empty()) Q.pop();
    dis[s] = 0;
    Q.push(node(s,0));
    node tmp;

    while( !Q.empty() ){
      tmp = Q.top();
      Q.pop();
      int u = tmp.v;
      if(vis[u])  continue;
      vis[u] = true;
      for(int i = 0; i < e[u].size(); i++){
        int v = e[tmp.v][i].v;
        int cost = e[u][i].cost;
        if(!vis[v] && dis[v] > dis[u] + cost){
          dis[v] = dis[u] + cost;
          Q.push(node(v,dis[v]));
        }
      }
    }
}