HDU 4598 Difference

Difference

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65535/65535 K (Java/Others)
Total Submission(s): 581    Accepted Submission(s): 152

Problem Description

A graph is a difference if every vertex vi can be assigned a real number ai and there exists a positive real number T such that
(a) |a_i| < T for all i and 
(b) (v_i, v_j) in E <=> |a_i - a_j| >= T,
where E is the set of the edges. 
Now given a graph, please recognize it whether it is a difference.

 

Input

The first line of input contains one integer TC(1<=TC<=25), the number of test cases.
Then TC test cases follow. For each test case, the first line contains one integer N(1<=N<=300), the number of vertexes in the graph. Then N lines follow, each of the N line contains a string of length N. The j-th character in the i-th line is "1" if (v_i, v_j) in E, and it is "0" otherwise. The i-th character in the i-th line will be always "0". It is guaranteed that the j-th character in the i-th line will be the same as the i-th character in the j-th line.

 

Output

For each test case, output a string in one line. Output "Yes" if the graph is a difference, and "No" if it is not a difference.

 

Sample Input

3

4

0011

0001

1000

1100

4

0111

1001

1001

1110

3

000

000

000

 

Sample Output

Yes

No

Yes

 

Hint

In sample 1, it can let T=3 and a[sub]1[/sub]=-2, a[sub]2[/sub]=-1, a[sub]3[/sub]=1, a[sub]4[/sub]=2.

 

Source

2013 ACM-ICPC吉林通化全国邀请赛——题目重现

 

Recommend

liuyiding

 

解题：差分约束，完全不懂为什么要这样子。学渣的无奈啊

 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #include <climits>
 #include <vector>
 #include <queue>
 #include <cstdlib>
 #include <string>
 #include <set>
 #include <stack>
 #define LL long long
 #define pii pair<int,int>
 #define INF 0x3f3f3f3f
 using namespace std;
 const int maxn = ,T = ;
 struct arc{
     int u,v,w;
     arc(int x = ,int y = ,int z = ){
         u = x;
         v = y;
         w = z;
     }
 };
 vector<int>g[maxn];
 vector<int>G[maxn];
 vector<arc>e;
 char mp[maxn][maxn];
 int n,color[maxn],d[maxn],cnt[maxn];
 bool in[maxn];
 void dfs(int u,int c){
     color[u] = c;
     for(int i = ; i < g[u].size(); i++)
         if(!color[g[u][i]]) dfs(g[u][i],-c);
 }
 void add(int u,int v,int w){
     e.push_back(arc(u,v,w));
     G[u].push_back(e.size()-);
 }
 bool spfa(){
     queue<int>q;
     for(int i = ; i < n; i++){
         d[i] = ;
         cnt[i] = ;
         in[i] = true;
         q.push(i);
     }
     while(!q.empty()){
         int u = q.front();
         q.pop();
         in[u] = false;
         for(int i = ; i < G[u].size(); i++){
             arc &temp = e[G[u][i]];
             if(d[temp.v] > d[u]+temp.w){
                 d[temp.v] = d[u]+temp.w;
                 if(!in[temp.v]){
                     in[temp.v] = true;
                     cnt[temp.v]++;
                     if(cnt[temp.v] > n) return true;
                     q.push(temp.v);
                 }
             }
         }
     }
     return false;
 }
 bool solve(){
     for(int i = ; i < n; i++) if(!color[i]) dfs(i,);
     for(int i = ; i < n; i++)
         for(int j = ; j < g[i].size(); j++)
             if(color[i] == color[g[i][j]]) return false;
     for(int i = ; i < n; i++){
         for(int j = i+; j < n; j++){
             if(mp[i][j] == '')
                 color[i] == ?add(i,j,-T):add(j,i,-T);
             else color[i] == ?add(j,i,T-):add(i,j,T-);
         }
     }
     return !spfa();
 }
 int main() {
     int ks,i,j;
     scanf("%d",&ks);
     while(ks--){
         scanf("%d",&n);
         for(i = ; i <= n; i++){
             g[i].clear();
             G[i].clear();
             color[i] = ;
         }
         e.clear();
         for(i = ; i < n; i++){
             scanf("%s",mp[i]);
             for(j = ; j < n; j++)
                 if(mp[i][j] == '') g[i].push_back(j);
         }
         solve()?puts("Yes"):puts("No");
     }
     return ;
 }