oj.uz

Submission #599776

# Submission time Handle Problem Language Result Execution time Memory
599776 2022-07-19T21:05:59 Z slime The Xana coup (BOI21_xanadu) C++14
100 / 100
 102 ms 40008 KB 
#include "bits/stdc++.h"
using namespace std;
#define int long long
const int MAXN = 3e5 + 10;
const int MOD = 1e9 + 7;
#define ll __int128
mt19937_64 rng((int)std::chrono::steady_clock::now().time_since_epoch().count());
int rnd(int x, int y) {
  int u = uniform_int_distribution<int>(x, y)(rng); return u;
}
ll read() { int x; cin >> x; return (ll)x; }
long long bm(long long b, long long p) {
  if(p==0) return 1 % MOD;
  long long r = bm(b, p >> 1);
  if(p&1) return (((r*r) % MOD) * b) % MOD;
  return (r*r) % MOD;
}
long long inv(long long b) { 
  return bm(b, MOD-2);
}
long long f[MAXN];
long long nCr(int n, int r) { 
  long long ans = f[n]; ans *= inv(f[r]); ans %= MOD;
  ans *= inv(f[n-r]); ans %= MOD; return ans;
}
long long fib[MAXN], lucas[MAXN];
void precomp() { 
  for(int i=0; i<MAXN; i++) f[i] = (i == 0 ? 1 % MOD : (f[i-1] * i) % MOD); 
  lucas[0] = 2;
  lucas[1] = 1;
  for(int i=2; i<MAXN; i++) lucas[i] = (lucas[i-2] + lucas[i-1]) % MOD;
  fib[0] = 0;
  fib[1] = 1;
  for(int i=2; i<MAXN; i++) fib[i] = (fib[i-2] + fib[i-1]) % MOD;
}
int fastlog(int x) {
  return (x == 0 ? -1 : 64 - __builtin_clzll(x) - 1);
}
void gay(int i) { cout << "Case #" << i << ": "; }
int csb(int l, int r, int k) { // count number of [l, r] such that i & 2^k > 0
  if(l > r) return 0;
  if(l == 0) {
    int s = r / (1ll << (k+1)); // number of complete cycles
    int t = r % (1ll << (k+1));
    int ans = s * (1ll << k);
    ans += (t >= (1ll << k) ? t - (1ll << k) + 1 : 0);
    return ans;
  }
  else return csb(0, r, k) - csb(0, l - 1, k);
}
int lis(vector<int> a) {
  int n = a.size();
  int bucket[n+1];
  for(int i=1; i<=n; i++) bucket[i] = 1e18;
  int ans = 1;
  for(int x: a) {
    auto it = lower_bound(bucket + 1, bucket +n +1, x);
    int d = distance(bucket, it);
    ans = max(ans, d);
    bucket[d] = min(bucket[d], x);
  }
  return ans;
}

int n;
vector<int> adj[MAXN];
int ogname[MAXN];

int dp[MAXN][2][2];
void dfs(int node, int prv) {
  vector<int> vt;
  for(int x: adj[node]) {
    if(x != prv) {
      dfs(x, node);
      vt.push_back(x);
    }
  }
  int m = vt.size();

  if(m == 0) {
    dp[node][ogname[node]][0] = 0;
    dp[node][(1 ^ ogname[node])][1] = 1;
    return;
  }

  int sub0[m][2], sub1[m][2];
  for(int i=0; i<m; i++) for(int j=0; j<2; j++) sub0[i][j] = sub1[i][j] = 1e9;  
  
  sub0[0][0] = dp[vt[0]][0][0];
  sub0[0][1] = dp[vt[0]][0][1];

  sub1[0][0] = dp[vt[0]][1][0];
  sub1[0][1] = dp[vt[0]][1][1];

  for(int i=1; i<m; i++) {
    sub0[i][0] = min(sub0[i-1][0] + dp[vt[i]][0][0], sub0[i-1][1] + dp[vt[i]][0][1]);
    sub0[i][1] = min(sub0[i-1][0] + dp[vt[i]][0][1], sub0[i-1][1] + dp[vt[i]][0][0]);

    sub1[i][0] = min(sub1[i-1][0] + dp[vt[i]][1][0], sub1[i-1][1] + dp[vt[i]][1][1]);
    sub1[i][1] = min(sub1[i-1][0] + dp[vt[i]][1][1], sub1[i-1][1] + dp[vt[i]][1][0]);
  }
  
  // Compute dp[node][0][1]: dp[vt[j]][1][x], sum of x mod 2 = (1 ^ ogname)

  dp[node][0][1] = sub1[m-1][(1 ^ ogname[node])] + 1;
  dp[node][1][0] = sub0[m-1][(1 ^ ogname[node])];

  dp[node][0][0] = sub0[m-1][ogname[node]];
  dp[node][1][1] = sub1[m-1][ogname[node]] + 1;
  
  /*
  for(int i=0; i<(1<<m); i++) {
    int st = ogname[node];
    for(int j=0; j<m; j++) {
      int bit = (i & (1<<j));
      if(bit > 0) st ^= 1;
    }
    // st = current state
    if(st) { // cur state = 1
      // if final state = 0 (Toggle node)
      int sm = 0;
      for(int j=0; j<m; j++) {
        if(i & (1<<j)) sm += dp[vt[j]][1][1];
        else sm += dp[vt[j]][1][0];
      }
      dp[node][0][1] = min(dp[node][0][1], sm + 1); 
      // if final state = 1 (Don't toggle node)
      sm = 0;
      for(int j=0; j<m; j++) {
        if(i & (1<<j)) sm += dp[vt[j]][0][1];
        else sm += dp[vt[j]][0][0];
      }
      dp[node][1][0] = min(dp[node][1][0], sm); 

    }
    else { // cur state = 0

      // if final state = 0 (Don't toggle node)
      int sm = 0;
      for(int j=0; j<m; j++) {
        if(i & (1<<j)) sm += dp[vt[j]][0][1];
        else sm += dp[vt[j]][0][0];
      }
      dp[node][0][0] = min(dp[node][0][0], sm); 
      // if final state = 1 (Toggle node)
      sm = 0;
      for(int j=0; j<m; j++) {
        if(i & (1<<j)) sm += dp[vt[j]][1][1];
        else sm += dp[vt[j]][1][0];
      }
      dp[node][1][1] = min(dp[node][1][1], sm + 1); 
      
    }

  }
  */
}
void solve(int tc) {
  cin >> n;
  for(int i=2; i<=n; i++) {
    int a, b;
    cin >> a >> b;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }

  for(int i=1; i<=n; i++) {
    for(int j=0; j<2; j++) {
      for(int k=0; k<2; k++) {
        dp[i][j][k] = 1e9;
      }
    }
  }

  for(int i=1; i<=n; i++) {
    cin >> ogname[i];
  }

  dfs(1, -1);

  cout << (min(dp[1][0][0], dp[1][0][1]) >= 1e8 ? "impossible" : to_string(min(dp[1][0][0], dp[1][0][1]))) << "\n";

  //cout << dp[4]

}
int32_t main() {
  precomp();
  ios::sync_with_stdio(0); cin.tie(0);
  int t = 1; //cin >> t;
  for(int i=1; i<=t; i++) solve(i);
}
// I don't know geometry.
// Teaming is unfair.

/*
4
1 2
2 3
1 4
1 0 0 0
*/

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 14420 KB Output is correct
2 Correct 12 ms 14428 KB Output is correct
3 Correct 13 ms 14352 KB Output is correct
4 Correct 12 ms 14420 KB Output is correct
5 Correct 11 ms 14420 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 14420 KB Output is correct
2 Correct 12 ms 14428 KB Output is correct
3 Correct 13 ms 14352 KB Output is correct
4 Correct 12 ms 14420 KB Output is correct
5 Correct 11 ms 14420 KB Output is correct
6 Correct 13 ms 14388 KB Output is correct
7 Correct 11 ms 14396 KB Output is correct
8 Correct 11 ms 14420 KB Output is correct
9 Correct 11 ms 14420 KB Output is correct
10 Correct 11 ms 14292 KB Output is correct
11 Correct 12 ms 14420 KB Output is correct
12 Correct 11 ms 14424 KB Output is correct
13 Correct 11 ms 14336 KB Output is correct
14 Correct 14 ms 14308 KB Output is correct
15 Correct 11 ms 14420 KB Output is correct
16 Correct 12 ms 14396 KB Output is correct

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 64 ms 38580 KB Output is correct
2 Correct 64 ms 38284 KB Output is correct
3 Correct 62 ms 38760 KB Output is correct

Subtask #4
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 61 ms 38564 KB Output is correct
2 Correct 71 ms 38368 KB Output is correct
3 Correct 76 ms 38676 KB Output is correct
4 Correct 69 ms 21616 KB Output is correct
5 Correct 66 ms 22220 KB Output is correct
6 Correct 66 ms 22468 KB Output is correct
7 Correct 12 ms 14420 KB Output is correct
8 Correct 26 ms 17108 KB Output is correct
9 Correct 80 ms 22092 KB Output is correct
10 Correct 68 ms 22300 KB Output is correct
11 Correct 66 ms 23312 KB Output is correct
12 Correct 67 ms 23596 KB Output is correct
13 Correct 63 ms 22248 KB Output is correct
14 Correct 67 ms 22632 KB Output is correct

Subtask #5
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 14420 KB Output is correct
2 Correct 12 ms 14428 KB Output is correct
3 Correct 13 ms 14352 KB Output is correct
4 Correct 12 ms 14420 KB Output is correct
5 Correct 11 ms 14420 KB Output is correct
6 Correct 13 ms 14388 KB Output is correct
7 Correct 11 ms 14396 KB Output is correct
8 Correct 11 ms 14420 KB Output is correct
9 Correct 11 ms 14420 KB Output is correct
10 Correct 11 ms 14292 KB Output is correct
11 Correct 12 ms 14420 KB Output is correct
12 Correct 11 ms 14424 KB Output is correct
13 Correct 11 ms 14336 KB Output is correct
14 Correct 14 ms 14308 KB Output is correct
15 Correct 11 ms 14420 KB Output is correct
16 Correct 12 ms 14396 KB Output is correct
17 Correct 64 ms 38580 KB Output is correct
18 Correct 64 ms 38284 KB Output is correct
19 Correct 62 ms 38760 KB Output is correct
20 Correct 61 ms 38564 KB Output is correct
21 Correct 71 ms 38368 KB Output is correct
22 Correct 76 ms 38676 KB Output is correct
23 Correct 69 ms 21616 KB Output is correct
24 Correct 66 ms 22220 KB Output is correct
25 Correct 66 ms 22468 KB Output is correct
26 Correct 12 ms 14420 KB Output is correct
27 Correct 26 ms 17108 KB Output is correct
28 Correct 80 ms 22092 KB Output is correct
29 Correct 68 ms 22300 KB Output is correct
30 Correct 66 ms 23312 KB Output is correct
31 Correct 67 ms 23596 KB Output is correct
32 Correct 63 ms 22248 KB Output is correct
33 Correct 67 ms 22632 KB Output is correct
34 Correct 11 ms 14420 KB Output is correct
35 Correct 13 ms 14372 KB Output is correct
36 Correct 11 ms 14356 KB Output is correct
37 Correct 11 ms 14420 KB Output is correct
38 Correct 11 ms 14328 KB Output is correct
39 Correct 11 ms 14420 KB Output is correct
40 Correct 12 ms 14356 KB Output is correct
41 Correct 11 ms 14420 KB Output is correct
42 Correct 13 ms 14420 KB Output is correct
43 Correct 11 ms 14420 KB Output is correct
44 Correct 11 ms 14424 KB Output is correct
45 Correct 73 ms 39888 KB Output is correct
46 Correct 63 ms 39480 KB Output is correct
47 Correct 62 ms 40008 KB Output is correct
48 Correct 61 ms 22628 KB Output is correct
49 Correct 72 ms 23488 KB Output is correct
50 Correct 98 ms 23588 KB Output is correct
51 Correct 11 ms 14384 KB Output is correct
52 Correct 24 ms 17420 KB Output is correct
53 Correct 70 ms 23308 KB Output is correct
54 Correct 74 ms 23500 KB Output is correct
55 Correct 71 ms 24496 KB Output is correct
56 Correct 81 ms 24792 KB Output is correct
57 Correct 76 ms 23356 KB Output is correct
58 Correct 83 ms 23904 KB Output is correct
59 Correct 26 ms 17360 KB Output is correct
60 Correct 64 ms 22428 KB Output is correct
61 Correct 64 ms 23252 KB Output is correct
62 Correct 102 ms 23464 KB Output is correct
63 Correct 68 ms 23460 KB Output is correct
64 Correct 64 ms 23440 KB Output is correct
65 Correct 53 ms 23824 KB Output is correct
66 Correct 53 ms 23756 KB Output is correct
67 Correct 51 ms 27628 KB Output is correct
68 Correct 49 ms 27624 KB Output is correct
69 Correct 51 ms 27636 KB Output is correct
70 Correct 58 ms 27588 KB Output is correct