差分约束例题

编程语言 2018-09-22 14:54:27 阅读次数: 0
版权声明：本文为博主原创文章，未经博主允许不得转载。 https://blog.csdn.net/hhhhhhxh/article/details/82805367

poj 3159

#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
const int inf=0x3f3f3f3f;

const int maxn=30000+10;
const int maxm=150000+10;

int n,m;
int x,y,c;

struct Edge{
    int to,cost,next;
    bool operator < (const Edge &b) const{
        return cost>b.cost;
    }
}edge[maxm];
int head[maxn],cntE=0;

int d[maxn];
bool vis[maxn];

void init(){
    cntE=0;
    memset(head,-1,sizeof(head));
}

void addedge(int u,int v,int w){
    edge[cntE]=(Edge){v,w,head[u]};
    head[u]=cntE++;
}

void dijkstra(int start){
    for (int i=1;i<=n;i++)  d[i]=inf,vis[i]=false;
    d[start]=0;
    priority_queue <Edge> que;
    que.push((Edge){start,0,0});
    while (!que.empty()){
        Edge tmp=que.top();
        que.pop();
        int u=tmp.to;
        if (vis[u]) continue;
        vis[u]=true;
        for (int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;
            if (!vis[v]&&d[v]>d[u]+edge[i].cost){
                d[v]=d[u]+edge[i].cost;
                tmp=(Edge){v,d[v],0};
                que.push(tmp);
            }
        }
    }
}

int main(){
    init();
    scanf("%d %d",&n,&m);
    for (int i=1;i<=m;i++){
        scanf("%d %d %d",&x,&y,&c);
        addedge(x,y,c);
    }
    dijkstra(1);
    printf("%d\n",d[n]);
    return 0;
}

poj 3169

#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
const int inf=0x3f3f3f3f;

const int maxn=1000+10;
const int maxm=20000+10;

int n,m1,m2;
int x,y,c;

struct Edge{
    int to,cost,next;
    bool operator < (const Edge &b) const{
        return cost>b.cost;
    }
}edge[maxm];
int head[maxn],cntE=0;

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

void init(){
    cntE=0;
    memset(head,-1,sizeof(head));
}

void addedge(int u,int v,int w){
    edge[cntE]=(Edge){v,w,head[u]};
    head[u]=cntE++;
}

bool spfa(int start){
    for (int i=1;i<=n;i++)  d[i]=inf,vis[i]=false,cnt[i]=0;
    d[start]=0,cnt[start]=1,vis[start]=true;
    queue <int> q;
    q.push(start);
    while (!q.empty()){
        int u=q.front();
        q.pop();
        vis[u]=false;
        for (int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;
            if (d[v]>d[u]+edge[i].cost){
                d[v]=d[u]+edge[i].cost;
                if (!vis[v]){
                    if (++cnt[v]>n) return false;
                    vis[v]=true;
                    q.push(v);
                }
            }
        }
    }
    return true;
}

void dijkstra(int start){
    for (int i=1;i<=n;i++)  d[i]=inf,vis[i]=false;
    d[start]=0;
    priority_queue <Edge> que;
    que.push((Edge){start,0,0});
    while (!que.empty()){
        Edge tmp=que.top();
        que.pop();
        int u=tmp.to;
        if (vis[u]) continue;
        vis[u]=true;
        for (int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;
            if (!vis[v]&&d[v]>d[u]+edge[i].cost){
                d[v]=d[u]+edge[i].cost;
                tmp=(Edge){v,d[v],0};
                que.push(tmp);
            }
        }
    }
}

int main(){
    init();
    scanf("%d %d %d",&n,&m1,&m2);
    for (int i=1;i<=m1;i++){
        scanf("%d %d %d",&x,&y,&c);
        addedge(x,y,c);
    }
    for (int i=1;i<=m2;i++){
        scanf("%d %d %d",&x,&y,&c);
        addedge(y,x,-c);
    }
    bool ans=spfa(1);
    if (!ans)  printf("-1\n");
    else if (d[n]==inf)  printf("-2\n");
    else    printf("%d\n",d[n]);
    return 0;
}

poj 1716

#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
const int INF=0x3f3f3f3f;

const int maxn=50000+10;
const int maxm=150000+10;

int n;
int a[maxn],b[maxn];
int maxx=0;

struct Edge{
    int to,cost,next;
    bool operator < (const Edge &b) const{
        return cost>b.cost;
    }
}edge[maxm];
int head[maxn],cntE=0;

int d[maxn],cnt[maxn];
bool vis[maxn];

void init(){
    cntE=0;
    memset(head,-1,sizeof(head));
}

void addedge(int u,int v,int w){
    edge[cntE]=(Edge){v,w,head[u]};
    head[u]=cntE++;
}

bool spfa(int start){
    for (int i=0;i<=maxx;i++)  d[i]=INF,vis[i]=false,cnt[i]=0;
    d[start]=0,vis[start]=true,cnt[start]=1;
    queue <int> que;
    que.push(start);
    while (!que.empty()){
        int u=que.front();
        que.pop();
        vis[u]=false;
        for (int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;
            if (d[v]>d[u]+edge[i].cost){
                d[v]=d[u]+edge[i].cost;
                if (!vis[v]){
                    if (++cnt[v]>maxx) return false;
                    vis[v]=true;
                    que.push(v);
                }
            }
        }
    }
    return true;
}

int main(){
    /*
    f[a[i]-1]-f[b[i]]<=-c[i]
    f[i+1]-f[i]<=1
    f[i]-f[i+1]<=0
    */
    init();
    scanf("%d",&n);
    for (int i=1;i<=n;i++){
        scanf("%d %d",&a[i],&b[i]);
        a[i]++;
        b[i]++;
        maxx=max(maxx,b[i]);
        addedge(a[i]-1,b[i],-2);
    }
    for (int i=0;i<maxx;i++){
        addedge(i+1,i,1);
        addedge(i,i+1,0);
    }
    spfa(0);
    printf("%d\n",-d[maxx]);
}

poj 1201

#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
const int INF=0x3f3f3f3f;

const int maxn=50000+10;
const int maxm=150000+10;

int n;
int a[maxn],b[maxn],c[maxn];
int maxx=0;

struct Edge{
    int to,cost,next;
    bool operator < (const Edge &b) const{
        return cost>b.cost;
    }
}edge[maxm];
int head[maxn],cntE=0;

int d[maxn],cnt[maxn];
bool vis[maxn];

void init(){
    cntE=0;
    memset(head,-1,sizeof(head));
}

void addedge(int u,int v,int w){
    edge[cntE]=(Edge){v,w,head[u]};
    head[u]=cntE++;
}

bool spfa(int start){
    for (int i=0;i<=maxx;i++)  d[i]=INF,vis[i]=false,cnt[i]=0;
    d[start]=0,vis[start]=true,cnt[start]=1;
    queue <int> que;
    que.push(start);
    while (!que.empty()){
        int u=que.front();
        que.pop();
        vis[u]=false;
        for (int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;
            if (d[v]>d[u]+edge[i].cost){
                d[v]=d[u]+edge[i].cost;
                if (!vis[v]){
                    if (++cnt[v]>n) return false;
                    vis[v]=true;
                    que.push(v);
                }
            }
        }
    }
    return true;
}

int main(){
    /*
    f[a[i]-1]-f[b[i]]<=-c[i]
    f[i+1]-f[i]<=1
    f[i]-f[i+1]<=0
    */
    init();
    scanf("%d",&n);
    for (int i=1;i<=n;i++){
        scanf("%d %d %d",&a[i],&b[i],&c[i]);
        maxx=max(maxx,b[i]);
        addedge(a[i]-1,b[i],-c[i]);
    }
    for (int i=0;i<maxx;i++){
        addedge(i+1,i,1);
        addedge(i,i+1,0);
    }
    spfa(0);
    printf("%d\n",-d[maxx]);
}

hdu 6252

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int INF=0x3f3f3f3f;

const int maxn=2000+10;
const int maxm=10000+10;

int T;
int n,m;
int kase=0;
ll x;
int cnt[maxn];
ll d[maxn];
int A,B,C,D;
bool vis[maxn];
ll ans[maxn];

struct Edge{
    int to,next;
    ll cost;
    Edge(){}
    Edge(int _to,ll _cost,int _next):to(_to),cost(_cost),next(_next){}
}edge[maxm];
int head[maxn],cntE=0;

void init(){
    memset(head,-1,sizeof(head));
    cntE=0;
}

void addedge(int u,int v,ll cost){
    edge[cntE]=Edge(v,cost,head[u]);
    head[u]=cntE++;
}

bool spfa(int start){
    for (int i=1;i<=n;i++)    d[i]=INF,cnt[i]=0,vis[i]=false;
    d[start]=0,cnt[start]=1,vis[start]=true;
    queue <int> que;
    que.push(start);
    while (!que.empty()){
        int u=que.front();
        que.pop();
        vis[u]=false;
        for (int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;
            if (d[v]>d[u]+edge[i].cost){
                d[v]=d[u]+edge[i].cost;
                if (!vis[v]){
                    if (++cnt[v]>n)    return false;
                    vis[v]=true;
                    que.push(v);
                }
            }
        }
    }
    return true;
}

int main(){
    scanf("%d",&T);
    while (T--){
        init();
        scanf("%d %d %lld",&n,&m,&x);
        for (int i=1;i<=m;i++){
            scanf("%d %d %d %d",&A,&B,&C,&D);
            if (A==B&&C==D){
                addedge(A,C,-x);
                addedge(C,A,x);
            }
            else{
                addedge(A,D,-x-1);
                addedge(C,B,x-1);
            }
        }
        for (int i=1;i<=n-1;i++){
            addedge(i,i+1,-1);
        }
        bool flag=spfa(1);
        for (int i=1;i<=n-1;i++){
            ans[i]=d[i]-d[i+1];
        }
        if (!flag)    printf("Case #%d: IMPOSSIBLE\n",++kase);
        else{
            printf("Case #%d:",++kase);
            for (int i=1;i<=n-1;i++){
                printf(" %lld",ans[i]);
            }
            putchar('\n');
        }
    }
}

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