King(差分约束)

http://poj.org/problem?id=1364

题意：输入i，n，gt(lt),k; 判断是否存在这样一个序列，从第 i 项加到第 n+i 项的和 <(lt) k 或 >(gt) k.

思路: 由题意知

gt: Sn+i - Si > k;.......(1)

lt: Si - Sn+i < k;........(2)

由(1)(2)得 ：

gt: Si - Sn+i <= -k-1;

lt: Si - Sn+i <= k-1;

根据<n+i,i,-k-1> <n+i,i,k-1>建图。

 #include <stdio.h>
 #include <string.h>
 const int N=;
 const int INF=<<;
 struct node
 {
     int u,v,w;
 } edge[N];
 int cnt,n,m;
 int dis[N];
 void add(int u,int v,int w)
 {
     edge[cnt].u = u;
     edge[cnt].v = v;
     edge[cnt++].w = w;

 }
 int bellman_ford( )
 {
     for (int i = ; i <= n; i++)
         dis[i] = ;//将源点到各点的距离初始化为零，
                    //因为根据不等式知源点到各点的最短距离肯定小于零
     for (int i = ; i < n; i ++)
     {
         for (int j = ; j < cnt; j ++)
         {
             int u = edge[j].u;
             int v = edge[j].v;
             if (dis[v] > dis[u]+edge[j].w)//更新各点到源点的距离
                 dis[v] = dis[u]+edge[j].w;
         }
     }
     for (int j =  ; j < cnt; j ++)//判断负环
     {
         int u = edge[j].u;
         int v = edge[j].v;
         if (dis[v] > dis[u]+edge[j].w)
             return false;
     }
     return true;
 }
 int main()
 {
     char s[];
     int u,v,w;
     while(~scanf("%d",&n)&&n)
     {
         cnt = ;
         scanf("%d",&m);
         for (int i = ; i < m; i++)
         {
             scanf("%d %d %s %d",&u,&v,s,&w);
             if (s[]=='g')
                 add(u+v,u-,-w-);
             else
                 add(u-,u+v,w-);
         }
         if (!bellman_ford())
             printf("successful conspiracy\n");
         else
             printf("lamentable kingdom\n");
     }
     return ;
 }