最多的一次作业，67次提交

2021/2/1

今天完成的题（SPFA优化全部，差分约束全部，tarjan(剩两个)(最后一个为新知识 (2-SAT) )）

• 双调路径
• 虫洞
• 最小圈
• Easy SSSp
• 方伯伯运椰子
• Interval
• 出纳员问题
• 糖果
• 布局 latout
• 受欢迎的牛
• 最大强联通子图
• 网络协议
• 消息的传递
• 网络间谍

/*
  树状数组优化版本SPFA 
*/
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
#define N 1100
#define M 3100
#define C 10010
using namespace std;

const int A = 1e5 + 11;
const int B = 2050;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}
int n,m,s,t,head[N],cnt=0,dis[N][C],tree[N][C];
bool vis[N][C];
struct node{
  int v,nxt ;
  int w1;
  int w2;
} ed[B << 1];


void add(int u, int v, int c, int t){
  ed[++cnt].nxt = head[u]; 
  ed[cnt].v = v; 
  ed[cnt].w1 = c; 
  ed[cnt].w2 = t; 
  head[u] = cnt;
  return; 
}


int lowbit(int x) {return x & (-x);}

void change(int x, int y, int z){
  y++;
  while(y < 10100){
    tree[x][y] = min(tree[x][y], z);
    y +=  lowbit(y);
  }
  return; 
}

int ask(int x, int y){
  y++;
  int mn = 0x7fffffff;
  while(y >= 1){
    mn = min(mn, tree[x][y]);
    y -= lowbit(y);
  }
  return mn;
}

void spfa(){
  queue<pair<int,int> > q;
  memset(dis, 0x3f, sizeof(dis));
  memset(tree, 0x3f, sizeof(tree));
  memset(vis, 0, sizeof(vis));
  dis[s][0] = 0;  
  vis[s][0] = 1;
  q.push(make_pair(s, 0));
  change(s, 0, 0);
  while(!q.empty()){
    int w = q.front().second, u = q.front().first;
    q.pop();
    vis[u][w] = 0;
    for(int i = head[u]; i; i = ed[i].nxt){
      int v = ed[i].v, w1 = ed[i].w1, w2 = ed[i].w2;
      int ww = w + w1;
      if(ask(v,ww) > dis[u][w] + w2)
      {
        dis[v][ww] = dis[u][w] + w2;
        change(v, ww, dis[v][ww]);
        if(!vis[v][ww]){
          q.push(make_pair(v,ww));
          vis[v][ww] = 1;
        }
      }
    }
  }
  return;
}
int main() {
//  freopen(".in", "r", stdin);
//  freopen("cc.out", "w", stdout);
  cin >> n >> m >> s >> t;
  for (int i = 1; i <= m; i++){
    int u, v, w1, w2;
    cin >> u >> v >> w1 >> w2;
    add(u, v, w1, w2);
    add(v, u, w1, w2);
  } 
  spfa();
  int minx = 0x3f3f3f3f, ans = 0;
    for (int i = 1; i <= 10000; i++) {
      //cout << dis[t][i] << endl;
		if (dis[t][i] < minx)
            minx = dis[t][i], ans++;
           // cout << minx << endl;
    }
  printf("%d
",ans); 
  fclose(stdin);
  fclose(stdout);
  return 0;
  
}

//板子 
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
#define eps 1e-12
using namespace std;


const int A = 1e5 + 11;
const int B = 100005;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}
struct node{
  int v, nxt, w; 
} e[B << 1];

int t, head[B], cnt, vis[B], dis[B], n, m, k, flag = 0;

void add(int u, int v, int w){
  e[++cnt].nxt = head[u];
  e[cnt].v = v;
  e[cnt].w = w;
  head[u] = cnt;
}

bool spfa(int s){
  vis[s] = 1;
  for(int i = head[s]; i; i = e[i].nxt)
  { 
    int v = e[i].v, w = e[i].w;
    if(dis[v] > dis[s] + w)
    {
      dis[v] = dis[s] + w;
      if(vis[v] || spfa(v)) return 1;
    }
  }
  vis[s] = 0;
  return 0;
}    
int main() {
//  freopen("dd.in", "r", stdin);
//  freopen(".out", "w", stdout);
   t = read();
   while(t--)
   {
      memset(vis, 0, sizeof(vis));
      memset(dis, 0, sizeof(dis));
      memset(head, 0, sizeof(head));
      cnt = 0;
     n = read(), m = read(), k = read();
     int a, b, c; 
     for (int i = 1; i <= m ; i++)
     {
       cin >> a >> b >> c;
       add(a, b, c);
       add(b, a, c);
     }
     for (int i = 1; i <= k; i++)
     {  
       cin >> a >> b >> c;
       add(a, b, -c);
     }
     flag = 0;
     for(int i = 1;i <= n; i++)
     {
       if(spfa(i))
       {
         flag = 1;
          break;
        }
     }
     if(flag) cout << "YES" << endl;
     else cout << "NO" << endl;
   }
  return 0;
}

/*
  错误： 边表数据类型int 代替 double
        SPFA数据类型 int 代替 double
   二分 定义类型错误   
*/
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
#define eps 1e-12
using namespace std;


const int A = 1e5 + 11;
const int B = 10005;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}
bool vis[B];
int  m, cnt,  head[B], k, nxt[B], to[B];
double ww[B];
double dis[B];
 void add(int u, int v, double w){
  nxt[++cnt] = head[u]; 
  to[cnt] = v; 
  ww[cnt] = w; 
  head[u] = cnt;
}
bool dfs(int u, double lim){
    vis[u] = 1;
    for (int i = head[u]; i; i = nxt[i]){
        int v = to[i];
        if(dis[v] > dis[u] + ww[i] - lim){
          dis[v] = dis[u] + ww[i] - lim;
          if(vis[v] ||dfs(v, lim)) return 1;
      }
    }
    vis[u] = 0;
    return 0;
}
bool check(double lim){
  memset(vis, 0, sizeof(vis));
  for(int i = 1; i <= k; i++) dis[i] = 0;
  for (int i = 1; i <= k; i++){
    if(dfs(i, lim)) return 1;
  }
  return 0; 
}
int main() {
  //freopen("dd.in", "r", stdin);
//  freopen(".out", "w", stdout);
    cin >> k >> m; 
    for (int i = 1; i <= m; i++){
      int u, v;
      double s;
      scanf("%d %d %lf", &u, &v, &s); 
      add(u, v, s);
    }
    double l = -1e7, r = 1e7;
    while(r - l > eps ){
      double mid = (l + r) / 2.0;
      if(check(mid)) r = mid ;
      else l = mid ;
    }
   printf("%.8lf
", r);
  return 0;
}

//板子 
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
#define eps 1e-12
using namespace std;


const int A = 1e5 + 11;
const int B = 100005;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}
struct node{
  int v, nxt, w; 
} e[B << 1];

int t, head[B], cnt, vis[B], dis[B], n, m, k, flag = 0;

void add(int u, int v, int w){
  e[++cnt].nxt = head[u];
  e[cnt].v = v;
  e[cnt].w = w;
  head[u] = cnt;
}

bool spfa(int s){
  vis[s] = 1;
  for(int i = head[s]; i; i = e[i].nxt)
  { 
    int v = e[i].v, w = e[i].w;
    if(dis[v] > dis[s] + w)
    {
      dis[v] = dis[s] + w;
      if(vis[v] || spfa(v)) return 1;
    }
  }
  vis[s] = 0;
  return 0;
}    
int main() {
  freopen("dd.in", "r", stdin);
//  freopen(".out", "w", stdout);
     n = read(), m = read(), k = read();
     int a, b, c; 
     for (int i = 1; i <= m ; i++)
     {
       cin >> a >> b >> c;
       add(a, b, c);
     }
     memset(dis, 0x3f, sizeof(dis));
     dis[k] = 0;
       if(spfa(k))
       {
          flag = 1;
        }
      if(head[1] == 0) flag = 1;
     if(flag) cout << -1 << endl;
     else{
      for (int i = 1;i <= n; i++)
      if(dis[i] == 1061109567)
      cout <<"NoPath" << endl;
      else cout<< dis[i] << endl;
    }
  return 0;
}

/*
  P3288 [SCOI2014]方伯伯运椰子
*/
#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
#define N 5010
#define INF 0x3f3f3f3f
#define db double
using namespace std;

int n,m,bb,T;
db l,r,mid,d[N];
struct Bn
{
    int from,to;
    db quan;
}bn[10010],tmp[10010];

inline void add(int u,int v,int w)
{
    bb++;
    bn[bb].to=v;
    bn[bb].from=u;
    bn[bb].quan=(db)w;
}

inline bool check(db u)
{
    int i,j;
    bool have;
    for(i=1;i<=bb;i++) tmp[i].quan+=u;
    d[1]=0;
    for(i=2;i<=n+2;i++) d[i]=INF;
    for(i=1;i<=n+2;i++)
    {
        have=0;
        for(j=1;j<=bb;j++)
        {
            if(d[tmp[j].to]>d[tmp[j].from]+tmp[j].quan)
            {
                have=1;
                d[tmp[j].to]=d[tmp[j].from]+tmp[j].quan;
            }
        }
        if(!have) return 0;
    }
    return 1;
}

int main()
{
    int i,j,p,q,o,a,b,c,d;
    cin>>n>>m;
    for(i=1;i<=m;i++)
    {
        scanf("%d%d%d%d%d%d",&p,&q,&a,&b,&c,&d);
        if(c) add(q,p,a-d);
        add(p,q,b+d);
    }
    for(l=0,r=10000,T=200;T;T--)
    {
        for(i=1;i<=bb;i++) tmp[i]=bn[i];
        mid=(l+r)/2;
        check(mid)?l=mid:r=mid;
    }
    printf("%.2lf",l);
}

#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
using namespace std;

const int A = 1e5 + 11;
const int B = 1e6 + 11;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}
struct node{
  int nxt, v, w;
} e[B << 1];
int l, r;
int s[B], vis[B], cnt, dis[B], n, m, head[B], use[B], t, num[B];
void add(int u, int v, int w){
  e[++cnt].nxt = head[u];
  e[cnt].v = v;
  e[cnt].w = w;
  head[u] = cnt;
}
 queue<int> q;
int spfa(int s){
    memset(vis, 0, sizeof(vis));
    memset(dis, 0x3f, sizeof(dis));
    memset(use, 0, sizeof(use));
    dis[s] = 0, vis[s] = 1, q.push(s); 
    while(!q.empty()){
      int u = q.front();
      q.pop();
      vis[u] = 0;
      use[u]++;
      if(use[u] > n) return -1;
      for (int i = head[u]; i; i = e[i].nxt)
      {
        int v = e[i].v, w = e[i].w;
        if(dis[v] > dis[u] + w){
          dis[v] = dis[u] + w;
          //use[i]++;
          //if(use[i] > n - 1) return 0;
          if(!vis[v]){
            vis[v] = 1;
            q.push(v);
          }
        }
      }
    }
    if(dis[n] > 1e8)
    return -2;
    return dis[n];
}
int main() {
//  freopen(".in", "r", stdin);
//  freopen(".out", "w", stdout);
  n = read(), l = read(), r = read();
  int a, b, c;
  for (int i = 1; i <= l; i++){
    cin >> a >> b >> c;
    add(a, b, c);
  }
  for (int i = 1; i <= r; i++){
    cin >> a >> b >> c;
    add(b, a, -c);
  }
  memset(dis, 0x3f,sizeof(dis));
  for(int i = 1; i <= n; i++){
    add(0, i, 0);
  }
  for(int i = 1; i < n; i++)
  {
    add(i + 1, i, 0);
  }
  int sp = spfa(0);
  if(sp <= -1){
    cout << sp;
    return 0;
  }
  else cout << spfa(1) << endl;
  fclose(stdin);
  fclose(stdout);
  return 0;
}

/*
  不要用边表！！！！！！！！！！
  定义类型不要错！！！！！
  尤其是 tarjan void!!!!!!!!!! 
*/
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
using namespace std;

const int A = 1e5 + 11;
const int manx = 1e6 + 11;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}

vector<int> e[11000];
int zxs,head[manx],cnt,headd[manx],n,m,low[manx],lt[manx],dfs[manx],js,top,st[manx],cl[manx],zbc;
int id[manx],cd[manx];
int siz[manx];
int ans,sbw;

/*----------------------------*/
void tarjan(int u){
  low[u] = dfs[u] = ++js; st[++top] = u;
  for (int i = 0; i < e[u].size(); i++)
  {
    int v =e[u][i];
    if(!dfs[v]) { tarjan(v); low[u] = min(low[u], low[v]);}
    else if(!lt[v])
    {
      low[u] = min(low[u], dfs[v]);
    }
  }
  if(dfs[u] == low[u])
  {
    lt[u] = zxs++;
    while(st[top] != u){ siz[zxs]++; lt[st[top--]] = zxs; }
    siz[zxs]++;
    lt[st[top--]] = zxs;
  }
}
int main() {
//  freopen(".in", "r", stdin);
//  freopen(".out", "w", stdout);
  n = read(), m = read();
  for (int i = 1; i <= m; i++)
  {
    int x, y;
    cin >> x >> y;
    e[x].push_back(y);
  }
  for (int i = 1; i <= n; i++) if(!dfs[i]) tarjan(i);
  for (int i = 1; i <= n; i++)
    for(int j = 0; j < e[i].size(); j++)
    {
      int v = e[i][j];
      if(lt[i] != lt[v])
      {
        cd[lt[i]]++;
      }
    }
    int k = 0;
  for (int i = 1; i <= zxs; i++) 
    if(!cd[i])
  {
    if(k){ cout << "0"; return 0;}
    k = i;
  }
  cout << siz[k] << endl;
  return 0;
}

#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
using namespace std;

const int A = 1e5 + 11;
const int B = 1e6 + 11;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}
struct node{
  int nxt, v, w;
} e[B << 1];
int r[B],s[B], vis[B], cnt, dis[B], n, m, head[B], t, num[B];
void add(int u, int v, int w){
  e[++cnt].nxt = head[u];
  e[cnt].v = v;
  e[cnt].w = w;
  head[u] = cnt;
}
bool check(int lim){
    memset(head, 0, sizeof(head));
    memset(dis, 0, sizeof(dis));
    memset(vis, 0, sizeof(vis));
    cnt = 0;
    add(0, 24, lim);
    for (int i = 1; i <= 24; i++){
      add(i - 1, i, 0);
      add(i, i - 1, -num[i]);
      if(i > 8) add(i - 8, i, r[i]);
      else add(i + 16, i, r[i] - lim);
    }
    queue<int> q;
    q.push(0), dis[0] = 0, vis[0] = 0;
    while(!q.empty()){
      int u = q.front();
      q.pop();
      vis[u] = 0;
      for (int i = head[u]; i; i = e[i].nxt)
      {
        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] = 1;
            q.push(v);
          }
        }
      }
    }
    return dis[24] == lim;
}
    
int main() {
//  freopen(".in", "r", stdin);
//  freopen(".out", "w", stdout);
  t = read();
  while(t--){
    memset(num, 0, sizeof(num));
    for (int i = 1; i <= 24; i++) r[i] = read();
    n = read();
    for (int i = 1; i <= n ; i++){
      int x = read() + 1;
      num[x]++;
    }
    int l = 0, r = n, ans = 0;
    while(l <= r){
      int mid = (r + l) >> 1;
      if(check(mid)) ans = mid, r = mid - 1;
      else l = mid + 1;
    }
    if(ans == inf) cout << "No Solution" << endl;
    else cout << ans << endl;
  }
  fclose(stdin);
  fclose(stdout);
  return 0;
}

#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
using namespace std;

const int A = 1e5 + 11;
const int B = 1e6 + 11;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}
struct node{
  int v, nxt, w;
} e[B];
int vis[B], dis[B];
int head[B], cnt, n, m, minx = inf, manx = -inf;
void add(int u, int v, int w){
  e[++cnt].nxt = head[u];
  e[cnt].v = v;
  e[cnt].w = w;
  head[u] = cnt;
}
void spfa(int s){
  memset(vis, 0, sizeof(vis));
  memset(dis, -inf, sizeof(dis));
  queue<int> q;
  dis[s] = 0, vis[s] = 1, q.push(s);
  while(!q.empty()){
    int u = q.front();
    q.pop();
    vis[u] = 0;
    for (int i = head[u]; i; i = e[i].nxt){
      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] = 1;
          q.push(v);
        }
      }
    }
  }
}
int main() {
//  freopen(".in", "r", stdin);
//  freopen(".out", "w", stdout);
  m = read();
  while(m--){
    memset(head, 0, sizeof(head));
    minx = inf;
    manx = -inf;
    cnt = 0;
  n = read();
  for(int i = 1; i <= n; i++){
    int a, b, c;
    cin >> a >> b >> c;
    add(a - 1, b, c);
    minx = min(minx, a - 1);
    manx = max(manx, b);
  }
  for(int i = minx; i <= manx; i++){
    add(i, i + 1, 0);
    add(i + 1, i, -1);
  }
  spfa(minx);
  cout << dis[manx] << endl;
  if(m) printf("
");
}
  fclose(stdin);
  fclose(stdout);
  return 0;
}

/*
  做烦了 
*/
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
using namespace std;

const int A = 1e5 + 11;
const int B = 1e6 + 11;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}
struct node{
  bool f;
  int mon;
} vx[B];
vector<int> e[B];
int r, dfn[B], n, m, js, st[B], top, m, low[B], lt[B], sum, in[B], out[B];
int ans, minx[B];
void tarjan(int u){
  low[u] = dfn[u] = ++js; st[++top] = u;
  for(int i = 0; i < e[u].size(); i++){
    int v = e[u][i];
    if(!dfn[v]){ tarjan(v); low[u] = min(low[u], low[v]);}
    else if(!lt[v]){low[u] = min(low[u], dfn[v]);}
  }
    if(dfn[u] == low[u]){
      lt[u] = sum++;
      if(vx[u].f)
        minx[sum] = min(minx[sum], vx[x].mon);
      while(st[top] != u)
      {
        if(vx[st[top--]].f)
        minx[sum] = min(minx[sum], vx[st[top--]].mon);  
        lt[st[top]] = sum;
      }
      lt[st[top--]] = sum;
    }
}    
int main() {
//  freopen(".in", "r", stdin);
//  freopen(".out", "w", stdout);
  memset(minx, inf, sizeof(minx));
  n = read();
  m = read();
  for(int i = 1; i <= m; i++){
    int x, mon;
    cin >> x >> mon;
    vx[x].f = 1, vx[x].cost = mon;
  }
  r = read();
  for(int i = 1; i <= r; i++){
    int x, y;
    cin >> x >> y;
    e[x].push_back(y);
  } 
  for(int i = 1; i <= n; i++)if(!dfn[i]) tarjan(i);
  for(int i = 1; i <= n; i++)
    for(int j = 0; j < e[i].size(); j++){
      int v = e[i][j];
      if(lt[i] != lt[v]){
        in[lt[v]]++;
      }
    }
  for(int i = 1; i <= sum; i++){
    if(!in[i]){
      
  }
  cout << ans << endl;
  return 0;
}

#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
using namespace std;

const int A = 1e5 + 11;
const int B = 1e6 + 11;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}
vector<int> e[B];
int  dfn[B], n, js, st[B], top, m, low[B], lt[B], sum, in[B], out[B];
int ans;
void tarjan(int u){
  low[u] = dfn[u] = ++js; st[++top] = u;
  for(int i = 0; i < e[u].size(); i++){
    int v = e[u][i];
    if(!dfn[v]){ tarjan(v); low[u] = min(low[u], low[v]);}
    else if(!lt[v]){low[u] = min(low[u], dfn[v]);}
  }
    if(dfn[u] == low[u]){
      lt[u] = sum++;
      while(st[top] != u) lt[st[top--]] = sum;
      lt[st[top--]] = sum;
    }
}    
int main() {
//  freopen(".in", "r", stdin);
//  freopen(".out", "w", stdout);
  n = read();
  for(int i = 1; i <= n; i++)
    for(int j = 1; j <= n; j++){
      int x = read();
      if(x)  e[i].push_back(j);
    }
  for(int i = 1; i <= n; i++)if(!dfn[i]) tarjan(i);
  for(int i = 1; i <= n; i++)
    for(int j = 0; j < e[i].size(); j++){
      int v = e[i][j];
      if(lt[i] != lt[v]){
        in[lt[v]]++;
      }
    }
  for(int i = 1; i <= sum; i++){
    if(!in[i]) ans++;
  }
  cout << ans << endl;
  return 0;
}

#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
using namespace std;

const int A = 1e5 + 11;
const int B = 1e6 + 11;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}
struct node{
  int nxt, v, w;
} e[B << 1];
int r[B],s[B], vis[B], cnt, dis[B], n, m, head[B], use[B], t, num[B];
void add(int u, int v, int w){
  e[++cnt].nxt = head[u];
  e[cnt].v = v;
  e[cnt].w = w;
  head[u] = cnt;
}
 queue<int> q;
bool spfa(){
    while(!q.empty()){
      int u = q.front();
      q.pop();
      vis[u] = 0;
      use[u] = 0;
      for (int i = head[u]; i; i = e[i].nxt)
      {
        int v = e[i].v, w = e[i].w;
        if(dis[v] < dis[u] + w){
          dis[v] = dis[u] + w;
          use[i]++;
          if(use[i] > n - 1) return 0;
          if(!vis[v]){
            vis[v] = 1;
            q.push(v);
          }
        }
      }
    }
    return 1;
}
int main() {
//  freopen(".in", "r", stdin);
//  freopen(".out", "w", stdout);
  n = read(), m = read();
  for (int i = 1; i <= m; i++)
  {
    int x, a, b;
    cin >> x >> a >> b;
    if(x == 1) add(b, a, 0), add(a, b, 0);
    else if(x == 2) add(a, b, 1);
    else if(x == 3) add(b, a, 0);
    else if(x == 4) add(b, a, 1);
    else if(x == 5) add(a, b, 0);
    if(x % 2 == 0 && a == b){
      cout << -1 << endl;
      return 0;
    }
  }
  for(int i = 1; i <= n; i++){
    vis[i] = 1;
    dis[i] = 1;
    use[i] = 1;
    q.push(i);
  }
  if(!spfa())
  {
    cout << -1 << "
";
    return 0;
  }
  ll ans = 0;
  for(int i = 1; i <= n; i++){
    ans += dis[i];
  }
  cout << ans << endl;
  fclose(stdin);
  fclose(stdout);
  return 0;
}

//板子 
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
#define eps 1e-12
using namespace std;


const int A = 1e5 + 11;
const int B = 100005;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;

inline int read() {
  char c = getchar();
  int x = 0, f = 1;
  for ( ; !isdigit(c); c = getchar()) if (c == '-') f = -1;
  for ( ; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  return x * f;
}
struct node{
  int v, nxt, w; 
} e[B << 1];

int t, head[B], cnt, vis[B], dis[B], n, m, k, flag = 0;

void add(int u, int v, int w){
  e[++cnt].nxt = head[u];
  e[cnt].v = v;
  e[cnt].w = w;
  head[u] = cnt;
}

bool spfa(int s){
  vis[s] = 1;
  for(int i = head[s]; i; i = e[i].nxt)
  { 
    int v = e[i].v, w = e[i].w;
    if(dis[v] > dis[s] + w)
    {
      dis[v] = dis[s] + w;
      if(vis[v] || spfa(v)) return 1;
    }
  }
  vis[s] = 0;
  return 0;
}    
int main() {
  freopen("dd.in", "r", stdin);
//  freopen(".out", "w", stdout);
     n = read(), m = read(), k = read();
     int a, b, c; 
     for (int i = 1; i <= m ; i++)
     {
       cin >> a >> b >> c;
       add(a, b, c);
     }
     memset(dis, 0x3f, sizeof(dis));
     dis[k] = 0;
       if(spfa(k))
       {
          flag = 1;
        }
      if(head[1] == 0) flag = 1;
     if(flag) cout << -1 << endl;
     else{
      for (int i = 1;i <= n; i++)
      if(dis[i] == 1061109567)
      cout <<"NoPath" << endl;
      else cout<< dis[i] << endl;
    }
  return 0;
}