HDU 4598 Difference

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由|a_i| < T for all i and ，(v_i, v_j) in E <=> |a_i - a_j| >= T,可知，相邻的边都是一正一负，dfs判断是否成立

差分约束判断是否有解，根据(v_i, v_j) in E <=> |a_i - a_j| >= T得，map[i][j]=0,|ai-aj|<T,map[i][j]=1,|ai-aj||>=T;|ai|<T,建图求解

#include <iostream>#include<cstdio>#include<cstring>#include<algorithm>#include<string>#include<queue>#define N 305#define M 90005#define INF 1<<29using namespace std;int map[N][N],cnt,head[N],vis[N],index[N],n,dis[N],mark[N];struct edge{    int v,next,w;}e[M];void init(){    memset(head,-1,sizeof(head));    memset(index,0,sizeof(index));    for(int i=1;i<=n;i++)    dis[i]=INF;    cnt=0;    memset(vis,0,sizeof(vis));}void addedge(int u,int v,int w){    e[cnt].v=v;e[cnt].w=w;e[cnt].next=head[u];head[u]=cnt++;}bool SPFA(int u){    queue<int> q;    int i,v,w;    q.push(u);    dis[u]=0;    while(!q.empty()){        u=q.front();        q.pop();        vis[u]=0;        for(i=head[u];i!=-1;i=e[i].next){            v=e[i].v;            w=e[i].w;            if(dis[u]+w<dis[v]){                dis[v]=dis[u]+w;                if(!vis[v]){                    vis[v]=1;                    q.push(v);                    if(++index[v]>n)                    return false;                }            }        }    }    return true;}bool judge(int u){    for(int i=1;i<=n;i++){        if(map[u][i]){            if(mark[i]==-1){                mark[i]=1-mark[u];                if(!judge(i))                return false;            }else {                if(mark[i]==mark[u])                return false;            }        }    }    return true;}int main(){    int i,j,t;    char str[N];    scanf("%d",&t);    while(t--){        scanf("%d",&n);        init();        memset(mark,-1,sizeof(mark));        for(i=1;i<=n;i++){            scanf("%s",str);            for(j=1;j<=n;j++){                map[i][j]=str[j-1]-'0';            }        }        mark[1]=0;        if(!judge(1)){            printf("No\n");            continue;        }        for(i=1;i<=n;i++){            for(j=1;j<=n;j++){                if(map[i][j]==1){                    if(mark[i])                    addedge(i,j,-N);                    else                    addedge(j,i,-N);                }else {                    if(mark[i])                    addedge(i,j,N-1);                    else                    addedge(j,i,N-1);                }            }        }        for(i=1;i<=n;i++){            addedge(0,i,N-1);        }        if(SPFA(0)){            printf("Yes\n");        }else {            printf("No\n");        }    }    return 0;}

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