oj.uz

Submission #834621

# Submission time Handle Problem Language Result Execution time Memory
834621 2023-08-22T16:08:44 Z kwongweng Passport (JOI23_passport) C++17
100 / 100
 808 ms 16056 KB 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef long double ld;
typedef pair<ll, ll> pll;
#define FOR(i, a, b) for(int i = a; i < b; i++)
#define ROF(i, a, b) for(int i = a; i >= b; i--)
#define ms memset
#define pb push_back
#define fi first
#define se second

/* Consider directed graph formed by constructing edge i -> j for all j in [l[i], r[i]]
problem becomes finding for each 1<=i<=n :
min # vertices to pass through to reach vertex 1 and vertex n
there are 2 cases:
1) 2 disjoint paths, one from i to 1, one from i to n
2) another vertex j, 3 disjoint paths, (i to j, j to 1, j to n)

So we can find use bfs to find min dist from each i to 1 and to n
Then a third bfs to deal with the cases. (smth similar to dijkstra)
* note : directions are reversed here

Issue : There are O(n^2) edges, so total runtime is O(n^2) with naive bfs
Solution : we need smarter bfs which ignores useless edge
How can bfs be smarter?
Let u be current vertex, we need to efficiently find v so that u->v and v not visited
Obs : u-> v if
1) v < u and r[v] >= u
2) u < v and l[v] <= u
Hence we can efficiently maintain 2 segment trees to find v in O(log n)
1) find v so that r[v]=max(1<=w<=u, w not visited).
2) find v so that l[v]=min(u<=w<=n, w not visited).

Finally, the third bfs can employ the same idea to finish.
*/

struct segtree{
  int sz; vi mx; vi a;
  void build(int v, int tl, int tr){
    if (tl==tr) {mx[v]=tl; return;}
    int tm=(tl+tr)/2;
    build(2*v,tl,tm); build(2*v+1,tm+1,tr);
    if (a[mx[2*v]] >= a[mx[2*v+1]]) mx[v]=mx[2*v];
    else mx[v]=mx[2*v+1];
  }
  void init(int n, vi A){
    sz=n; mx.assign(4*n,-1); a=A; build(1,0,n-1);
  }
  void rem(int v, int tl, int tr, int pos){
    if (tl==tr){mx[v]=-1; return;}
    int tm=(tl+tr)/2;
    if (pos<=tm) rem(2*v,tl,tm,pos);
    else rem(2*v+1,tm+1,tr,pos);
    if (mx[2*v] != -1 && mx[2*v+1] != -1){
      if (a[mx[2*v]] >= a[mx[2*v+1]]) mx[v]=mx[2*v];
      else mx[v]=mx[2*v+1];
    }else{
      if (mx[2*v]==-1) mx[v]=mx[2*v+1];
      else mx[v]=mx[2*v];
    }
  }
  void rem(int pos){rem(1,0,sz-1,pos);}
  int qry(int v, int tl, int tr, int l, int r){
    if (tl==l && tr==r) return mx[v];
    if (l>r) return -1;
    int tm=(tl+tr)/2;
    int L=qry(2*v,tl,tm,l,min(r,tm)), R=qry(2*v+1,tm+1,tr,max(l,tm+1),r);
    if (L==-1) return R;
    if (R==-1) return L;
    if (a[L]>=a[R]) return L;
    return R;
  }
  int qry(int l, int r){return qry(1,0,sz-1,l,r);}
};

void solve(){
  int n; cin>>n;
  vi l(n+1), r(n+1);
  FOR(i,1,n+1) cin>>l[i]>>r[i];
  FOR(i,1,n+1) l[i]=n-l[i];
  segtree stl, str;
  stl.init(n+1,l); str.init(n+1,r);
  vi d1(n+1,n+2); queue<int> bfs; 
  d1[1]=0; stl.rem(1); str.rem(1); bfs.push(1);
  while (!bfs.empty()){
    int u = bfs.front(); bfs.pop();
    int val = str.qry(1,u);
    while (val != -1 && r[val] >= u){
      stl.rem(val); str.rem(val); bfs.push(val); d1[val]=d1[u]+1;
      //cout<<u<<" "<<d1[u]<<" "<<val<<" "<<d1[val]<<"\n";
      val=str.qry(1,u);
    }
    val = stl.qry(u,n);
    while (val!=-1 && l[val] >= n-u){
      stl.rem(val); str.rem(val); bfs.push(val); d1[val]=d1[u]+1;
      //cout<<u<<" "<<d1[u]<<" "<<val<<" "<<d1[val]<<"\n";
      val=stl.qry(u,n);
    }
  }
  //FOR(i,1,n+1) cout<<d1[i]<<" "; cout<<"\n";

  vi dn(n+1,n+2);
  stl.init(n+1,l); str.init(n+1,r);
  dn[n]=0; stl.rem(n); str.rem(n); bfs.push(n);
  while (!bfs.empty()){
    int u = bfs.front(); bfs.pop();
    int val = str.qry(1,u);
    while (val != -1 && r[val] >= u){
      stl.rem(val); str.rem(val); bfs.push(val); dn[val]=dn[u]+1;
      val=str.qry(1,u);
    }
    val = stl.qry(u,n);
    while (val!=-1 && l[val] >= n-u){
      stl.rem(val); str.rem(val); bfs.push(val); dn[val]=dn[u]+1;
      val=stl.qry(u,n);
    }
  }
  //FOR(i,1,n+1) cout<<dn[i]<<" "; cout<<"\n";
  
  vi ans(n+1); FOR(i,1,n+1) ans[i]=d1[i]+dn[i]-1; ans[1]++; ans[n]++;
  int mn=ans[1]; FOR(i,2,n+1) mn=min(mn,ans[1]);
  stl.init(n+1,l); str.init(n+1,r);
  priority_queue<ii,vii,greater<ii>> pq;
  FOR(i,1,n+1){
    if (ans[i]<=n) pq.push({ans[i],i});
  }
  while (!pq.empty()){
    ii node = pq.top(); pq.pop();
    int u = node.se;
    if (ans[u] != node.fi) continue;
    int val = str.qry(1,u);
    while (val != -1 && r[val] >= u){
      stl.rem(val); str.rem(val); bfs.push(val);
      if (ans[val] > ans[u]+1){
        ans[val]=ans[u]+1; pq.push({ans[val],val});
      }
      val=str.qry(1,u);
    }
    val = stl.qry(u,n);
    while (val!=-1 && l[val] >= n-u){
      stl.rem(val); str.rem(val); bfs.push(val);
      if (ans[val] > ans[u]+1){
        ans[val]=ans[u]+1; pq.push({ans[val],val});
      }
      val=stl.qry(u,n);
    }
  }
  
  int q; cin>>q;
  while(q--){
    int x; cin>>x; 
    if (ans[x]>n) ans[x]=-1;
    cout<<ans[x]<<"\n";
  }
  
}

int main(){
	//MOD=MOD1;
    ios::sync_with_stdio(false);
    if (fopen("input.txt", "r")) {
		  freopen("input.txt", "r", stdin);
    	freopen("output.txt", "w", stdout);
	  }
    int TC = 1;
    //cin >> TC; 
    FOR(i, 1, TC+1){
        //cout << "Case #" << i << ": ";
        solve();
    }
	
	return 0;
}

Compilation message

passport.cpp: In function 'int main()':
passport.cpp:166:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  166 |     freopen("input.txt", "r", stdin);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
passport.cpp:167:13: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  167 |      freopen("output.txt", "w", stdout);
      |      ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 549 ms 15308 KB Output is correct
5 Correct 479 ms 14916 KB Output is correct
6 Correct 409 ms 15124 KB Output is correct
7 Correct 316 ms 15412 KB Output is correct
8 Correct 101 ms 10468 KB Output is correct

Subtask #2
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 336 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct

Subtask #3
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 336 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 5 ms 592 KB Output is correct
17 Correct 5 ms 468 KB Output is correct
18 Correct 5 ms 468 KB Output is correct
19 Correct 4 ms 468 KB Output is correct
20 Correct 4 ms 468 KB Output is correct
21 Correct 4 ms 468 KB Output is correct
22 Correct 2 ms 468 KB Output is correct
23 Correct 4 ms 468 KB Output is correct
24 Correct 3 ms 468 KB Output is correct

Subtask #4
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 336 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 5 ms 592 KB Output is correct
17 Correct 5 ms 468 KB Output is correct
18 Correct 5 ms 468 KB Output is correct
19 Correct 4 ms 468 KB Output is correct
20 Correct 4 ms 468 KB Output is correct
21 Correct 4 ms 468 KB Output is correct
22 Correct 2 ms 468 KB Output is correct
23 Correct 4 ms 468 KB Output is correct
24 Correct 3 ms 468 KB Output is correct
25 Correct 1 ms 212 KB Output is correct
26 Correct 0 ms 212 KB Output is correct
27 Correct 7 ms 468 KB Output is correct
28 Correct 7 ms 468 KB Output is correct
29 Correct 7 ms 468 KB Output is correct
30 Correct 6 ms 468 KB Output is correct
31 Correct 7 ms 468 KB Output is correct

Subtask #5
46.0 / 46.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 549 ms 15308 KB Output is correct
5 Correct 479 ms 14916 KB Output is correct
6 Correct 409 ms 15124 KB Output is correct
7 Correct 316 ms 15412 KB Output is correct
8 Correct 101 ms 10468 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 336 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 0 ms 212 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 5 ms 592 KB Output is correct
25 Correct 5 ms 468 KB Output is correct
26 Correct 5 ms 468 KB Output is correct
27 Correct 4 ms 468 KB Output is correct
28 Correct 4 ms 468 KB Output is correct
29 Correct 4 ms 468 KB Output is correct
30 Correct 2 ms 468 KB Output is correct
31 Correct 4 ms 468 KB Output is correct
32 Correct 3 ms 468 KB Output is correct
33 Correct 1 ms 212 KB Output is correct
34 Correct 0 ms 212 KB Output is correct
35 Correct 7 ms 468 KB Output is correct
36 Correct 7 ms 468 KB Output is correct
37 Correct 7 ms 468 KB Output is correct
38 Correct 6 ms 468 KB Output is correct
39 Correct 7 ms 468 KB Output is correct
40 Correct 808 ms 15712 KB Output is correct
41 Correct 724 ms 15872 KB Output is correct
42 Correct 672 ms 15676 KB Output is correct
43 Correct 644 ms 15488 KB Output is correct
44 Correct 638 ms 16056 KB Output is correct
45 Correct 532 ms 14080 KB Output is correct
46 Correct 228 ms 6184 KB Output is correct
47 Correct 629 ms 15204 KB Output is correct
48 Correct 526 ms 14536 KB Output is correct