差分约束

Posted 2023-01-03 sjsjsj-minus-si

例题1 interval

• 最长路
• 数组下标为-1怎么处理
• ”标准输出太巨怎么办“

/*
reference:
    
translation:
    
solution:
    
1---->在a[i]和b[i]+1之间连一条长度为c[i]的有向边

2---->在i和i+1之间连一条长度为0的有向边

3---->在i+1和i之间连一条长度为-1的有向边
trigger:
    
note:
    *我们在i-1和i之间连长度为0的有向边，在i和i-1之间连长度为-1的有向边
因为i的范围是0-50000所以i-1会变成负数，我们都知道，若数组的下标为负，程序会运行
错误，所以我们不妨给所有的变量加1，这样就不会出现负下标了
date:
    2019.09.05
*/
const int N=1e6+10;

int head[N],edge_num,maxx=INT_MIN,minn=INT_MAX;
int n,m,s;
int dis[N];
bool vis[N];

struct edge
    int v,w,next;
e[N];

inline void add(int u,int v,int w)e[++edge_num].v=v;e[edge_num].w=w;e[edge_num].next=head[u];head[u]=edge_num;

queue<int>q;
inline void spfa()
    mem(dis,-0x3f);
    mem(vis,0);
    q.push(0);
    vis[0]=1;
    dis[0]=0;
    while(!q.empty())
        int u=q.front();q.pop();
        vis[u]=0;
        ee(i,u)
            int v=e[i].v,w=e[i].w;
            if(dis[v]<dis[u]+w)
                dis[v]=dis[u]+w;
                if(!vis[v])
                    q.push(v);
                    vis[v]=1;
                
            
        
    
 

#undef int
int main()
#define int long long
    #ifdef WIN32
    freopen("interval.txt","r",stdin);
    #endif
    int T;rd(T);
    rep(cases,1,T)
        //初始化；
        mem(e,0);mem(head,0);
        edge_num=0,maxx=INT_MIN,minn=INT_MAX;
        rd(m);
        while(m--)
            int b,e,t;rd(b),rd(e),rd(t);
            add(b,e+1,t);
            maxx=max(maxx,e+1);
         
        rep(i,0,maxx)
            add(i+1,i,-1);
            add(i,i+1,0);
        
        spfa();
        if(cases<T)printf("%lld\n",dis[maxx]);
        else printf("%lld",dis[maxx]);
    
    return 0;

例二（看似很裸）poj 3159 candies

• poj 交的时候不能在文本末尾写注释
• spfa+queue竟然超时是什么鬼！！！，spfa只能加数组才能过！！！连加双端队列优化都不可以………………仙人板板

/*
reference:
    
translation:
    
solution:

trigger:
    
note:
    *
date:
    2019.09.04
*/
#include<iostream>
#include<cstdio>
#include<cctype>
#include<algorithm>
#include<queue>
#include<cstring>
using namespace std;
#define rep(i,a,b) for(int i=a;i<=b;++i)
#define dwn(i,a,b) for(int i=a;i>=b;--i) 
template <typename T> inline void rd(T &x)x=0;char c=getchar();int f=0;while(!isdigit(c))f|=c=='-';c=getchar();while(isdigit(c))x=(x<<1)+(x<<3)+(c^48);c=getchar();x=f?-x:x; 
#define ee(i,x) for(int i=head[x];i;i=e[i].next)
#define mem(a,b) memset(a,b,sizeof(a))

const int N = 30010,M = 150010;

int head[N],edge_num;
int n,m,dis[N];
bool vis[N];

struct edge
    int v,w,next;
e[M];

inline void add(int u,int v,int w)e[++edge_num].v=v;e[edge_num].w=w;e[edge_num].next=head[u];head[u]=edge_num;
//inline void adde(int u,int v)e[++edge_num].v=v;e[edge_num].next=head[u];head[u]=edge_num;
/*
deque<int>q;
inline void spfa()
    mem(dis,0x3f);
    mem(vis,0);
    q.push_back(1);
    vis[1]=1;
    dis[1]=0;
    while(!q.empty())
        int u=q.front();q.pop_front();
        vis[u]=0;
        ee(i,u)
            int v=e[i].v,w=e[i].w;
            if(dis[v]>dis[u]+w)
                dis[v]=dis[u]+w;
                if(q.empty() || dis[v]<dis[u])
                    q.push_front(v);
                else q.push_back(v);
                vis[v]=1;
            
        
    
*/

int q[N];
void spfa(int start,int n)

    int top=0;
    for(int v=1;v<=n;v++)//初始化
    
        if(v==start)
        
            q[top++]=v;
            vis[v]=true;
            dis[v]=0;
        
        else
        
            vis[v]=false;
            dis[v]=0x3f3f3f3f;
        
    
    while(top!=0)
        int u=q[--top];
        vis[u]=0;
        ee(i,u)
            int v=e[i].v,w=e[i].w;
            if(dis[v]>dis[u]+w)
                dis[v]=dis[u]+w;
                if(!vis[v])
                    vis[v]=true;
                    q[top++]=v;
                
            
        
    


int main()
    rd(n),rd(m);
    while(m--)
        int u,v,w;rd(u),rd(v),rd(w);
        add(u,v,w);
    
    spfa(1,n);
    printf("%d\n",dis[n]);
    return 0;

/*
2 2
1 2 5
2 1 4
*/
//5