POJ1201(差分约束)

Sn表示集合Z中小于等于i的元素个数

5
3 7 3
8 10 3
6 8 1
1 3 1
10 11 1

1.Z集合中范围在[ai,bi]的整数个数 S[bi] - S[ai - 1] 至少为 Ci，得不等式

S2 - S7 <= -3

S7 - S10 <= -3

S5 - S8 <= -1

S0 - S3 <=-1

S9 - S11 <= -1

2. S[i-1]到S[i]之间最多有1个数，最少有0个数

S[i] - S[i-1]  <= 1

S[i-1] - S[i]  <= 0

minm为所有区间左端点最小值， maxm为所有区间右端点最大值，最终要求 S[maxm] - S[minm] 的最小值   S[minm-1] - S[maxm] <= -M

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
#define N 50005
#define M 150005
#define inf 9999999
int dis[N],head[N],vis[N],in[N];
int n,size,maxm,minm;
struct Edge
{
    int v,w,next;
    Edge(){}
    Edge(int V,int W,int NEXT):v(V),w(W),next(NEXT){}
}edge[M];

void Init()
{
    size = 0;
    memset(head,-1,sizeof(head));
}

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

bool spfa()
{
    for(int i=minm-1; i<=maxm; i++)
    {
        dis[i] = inf;
        vis[i] = 0;
        in[i] = 0;
    }
    queue<int> Q;
    while(!Q.empty()) Q.pop();
    dis[maxm] = 0;
    in[maxm] = vis[maxm] = 1;
    Q.push(maxm);
    while(!Q.empty())
    {
        int u = Q.front();
        Q.pop();
        vis[u] = 0;
        for(int i=head[u]; i!=-1; i=edge[i].next)
        {
            int v = edge[i].v;
            if(dis[v] > dis[u] + edge[i].w)
            {
                dis[v] = dis[u] + edge[i].w ;
                if(!vis[v])
                {
                    vis[v] = 1;
                    in[v]++ ;
                    if(in[v]>n) return 0;
                    Q.push(v);
                }
            }
        }
    }
    return 1;
}

int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        Init();
        int u,v,w;
        maxm = 0 ; minm = 50050;
        for(int i=0; i<n; i++)
        {
            scanf("%d%d%d",&u,&v,&w);
            maxm = max(maxm,v);
            minm = min(minm,u);
            InsertEdge(v,u-1,-w);
        }
        for(int i=minm; i<=maxm; i++)
        {
            InsertEdge(i-1,i,1);
            InsertEdge(i,i-1,0);
        }
        if(spfa())
        printf("%d
",-dis[minm-1]);
    }
    return 0;
}