Submission #599776

#	Time	Username	Problem	Language	Result	Execution time	Memory
599776		slime	The Xana coup (BOI21_xanadu)	C++14	100 / 100	102 ms	40008 KiB

xanadu

#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 / 5
• Subtask 2: 15 / 15
• Subtask 3: 10 / 10
• Subtask 4: 40 / 40
• Subtask 5: 30 / 30