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Submission #444024

# Submission time Handle Problem Language Result Execution time Memory
444024 2021-07-13T02:49:17 Z yungyao The Xana coup (BOI21_xanadu) C++17
55 / 100
 278 ms 20036 KB 
using namespace std;
#include <iostream>
#include <algorithm>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <utility>
#include <vector>
#include <memory.h>

typedef long long LL;
typedef pair<int,int> pii;
#define F first
#define S second
#define mkp make_pair
#define iter(x) x.begin(),x.end()
#define MEM(s,e) memset(s,e,sizeof(s))

const int maxn = 1e5+100,inf = 1e9;


int dp[maxn][2][2]; //index, t/f, on/off
bool status[maxn];

vector <int> adj[maxn];

void dfs(int x,int fr){
    int ldp[2][2][2],c=0;
    for (auto s:adj[x]) if (s != fr){
        dfs(s,x);
        for (int i=0;i<2;++i) for (int j=0;j<2;++j){
            ldp[c][i][j] = dp[s][i][j];
        }
        ++c;
    }
    if (!c){
        if (status[x]){
            dp[x][1][0] = 0;
            dp[x][0][1] = 1;
            dp[x][0][0] = inf;
            dp[x][1][1] = inf;
        }
        else{
            dp[x][0][0] = 0;
            dp[x][1][1] = 1;
            dp[x][1][0] = inf;
            dp[x][0][1] = inf;
        }
    }
    else if (c == 1){
        if (status[x]){
            dp[x][0][0] = ldp[0][0][1];
            dp[x][0][1] = ldp[0][1][0] + 1;
            dp[x][1][0] = ldp[0][0][0];
            dp[x][1][1] = ldp[0][1][1] + 1;
        }
        else{
            dp[x][0][0] = ldp[0][0][0];
            dp[x][0][1] = ldp[0][1][1] + 1;
            dp[x][1][0] = ldp[0][0][1];
            dp[x][1][1] = ldp[0][1][0] + 1;
        }
    }
    else{
        if (status[x]){
            dp[x][0][0] = min(inf,min(ldp[0][0][1] + ldp[1][0][0],ldp[0][0][0] + ldp[1][0][1]));
            dp[x][0][1] = min(inf,min(ldp[0][1][0] + ldp[1][1][0],ldp[0][1][1] + ldp[1][1][1]) + 1);
            dp[x][1][0] = min(inf,min(ldp[0][0][0] + ldp[1][0][0],ldp[0][0][1] + ldp[1][0][1]));
            dp[x][1][1] = min(inf,min(ldp[0][1][1] + ldp[1][1][0],ldp[0][1][0] + ldp[1][1][1]) + 1);
        }
        else{
            dp[x][0][0] = min(inf,min(ldp[0][0][0] + ldp[1][0][0],ldp[0][0][1] + ldp[1][0][1]));
            dp[x][0][1] = min(inf,min(ldp[0][1][1] + ldp[1][1][0],ldp[0][1][0] + ldp[1][1][1]) + 1);
            dp[x][1][0] = min(inf,min(ldp[0][0][1] + ldp[1][0][0],ldp[0][0][0] + ldp[1][0][1]));
            dp[x][1][1] = min(inf,min(ldp[0][1][0] + ldp[1][1][0],ldp[0][1][1] + ldp[1][1][1]) + 1);
        }
    }
}

int n,mxsub[maxn];
int findg(int x,int fr){
    int cnt = 1;
    for (auto i:adj[x]) if (i != fr){
        int r = findg(i,x);
        cnt += r;
        mxsub[x] = max(mxsub[x],r);
    }
    mxsub[x] = max(mxsub[x],n - cnt);
    return cnt;
}

vector <int> findans(int g,int op){
    vector <int> hadj[22]; int c=0;
    vector <int> ret(4,inf); //00 for f/off, 01 for f/on, 10 for t/off, 11 for t/on
    bool vis[44]{};
    int trs[44]{},invtrs[22]{};

    queue <int> bfs; bfs.push(g); vis[g] = true;
    while (bfs.size()){
        int x = bfs.front(); bfs.pop();
        invtrs[c] = x; trs[x] = c++;
        for (auto i:adj[x]){
            if (vis[i]){
                hadj[trs[x]].push_back(trs[i]);
                hadj[trs[i]].push_back(trs[x]);
            }
            else if (i != op){
                bfs.push(i);
                vis[i] = true;
            }
        }
    }
    for (int mask=0;mask<(1 << c);++mask){
        bool stat_copy[22];
        for (int i=0;i<c;++i) stat_copy[i] = status[invtrs[i]];

        for (int i=0;i<c;++i) if (mask & (1 << i)){
            stat_copy[i] ^= 1;
            for (auto cn:hadj[i]) stat_copy[cn] ^= 1;
        }
        bool ok = true;
        for (int i=1;i<c;++i) if (stat_copy[i]){ok = false; break;}

        if (ok){
            if (stat_copy[0] and (mask & 1)) ret[3] = min(ret[3],__builtin_popcount(mask));
            else if (stat_copy[0] and !(mask & 1)) ret[2] = min(ret[2],__builtin_popcount(mask));
            else if (!stat_copy[0] and (mask & 1)) ret[1] = min(ret[1],__builtin_popcount(mask));
            else if (!stat_copy[0] and !(mask & 1)) ret[0] = min(ret[0],__builtin_popcount(mask));
        }
    }

    return ret;
}

void brutesolve(){
    findg(1,0);
    int g[2],c = 0;
    for (int i=1;i<=n;++i) if (mxsub[i] <= n/2) g[c++] = i;
    if (c == 1) g[1] = adj[g[0]][0];

    vector <int> v1 = findans(g[0],g[1]), v2 = findans(g[1],g[0]);
    int ans = min(min(v1[0]+v2[0],v1[3]+v2[3]),min(v1[1]+v2[2],v1[2]+v2[1]));
    
    if (ans >= inf) cout << "impossible\n";
    else cout << ans << '\n';
}

int main(){
    cin >> n;
    for (int _=n-1;_--;){
        int u,v;

        cin >> u >> v;
        adj[u].push_back(v);
        adj[v].push_back(u);
    }
    for (int i=1;i<=n;++i) cin >> status[i];
    if (n <= 40) {brutesolve(); return 0;}

    for (int i=1;i<=n;++i) if (adj[i].size() == 1){
        dfs(i,0);
        int ans = min(dp[i][0][0],dp[i][0][1]);
        if (ans >= inf) cout << "impossible\n";
        else cout << ans << '\n';
        break;
    }
    return 0;
}

Compilation message

xanadu.cpp: In function 'void brutesolve()':
xanadu.cpp:142:40: warning: 'g[1]' may be used uninitialized in this function [-Wmaybe-uninitialized]
  142 |     vector <int> v1 = findans(g[0],g[1]), v2 = findans(g[1],g[0]);
      |                                        ^
xanadu.cpp:142:40: warning: 'g[0]' may be used uninitialized in this function [-Wmaybe-uninitialized]

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 69 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 78 ms 2636 KB Output is correct

Subtask #2
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 69 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 78 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 2 ms 2636 KB Output is correct
8 Correct 70 ms 2636 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 67 ms 2640 KB Output is correct
11 Correct 138 ms 2636 KB Output is correct
12 Correct 208 ms 2636 KB Output is correct
13 Correct 278 ms 2640 KB Output is correct
14 Runtime error 5 ms 5196 KB Execution killed with signal 11
15 Halted 0 ms 0 KB -

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 117 ms 19928 KB Output is correct
2 Correct 162 ms 19672 KB Output is correct
3 Correct 124 ms 20036 KB Output is correct

Subtask #4
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 116 ms 19892 KB Output is correct
2 Correct 115 ms 19736 KB Output is correct
3 Correct 151 ms 19960 KB Output is correct
4 Correct 115 ms 7092 KB Output is correct
5 Correct 124 ms 7540 KB Output is correct
6 Correct 125 ms 7700 KB Output is correct
7 Correct 2 ms 2636 KB Output is correct
8 Correct 39 ms 4600 KB Output is correct
9 Correct 127 ms 7712 KB Output is correct
10 Correct 129 ms 7764 KB Output is correct
11 Correct 130 ms 8516 KB Output is correct
12 Correct 125 ms 8852 KB Output is correct
13 Correct 117 ms 7368 KB Output is correct
14 Correct 120 ms 7628 KB Output is correct

Subtask #5
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 69 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 78 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 2 ms 2636 KB Output is correct
8 Correct 70 ms 2636 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 67 ms 2640 KB Output is correct
11 Correct 138 ms 2636 KB Output is correct
12 Correct 208 ms 2636 KB Output is correct
13 Correct 278 ms 2640 KB Output is correct
14 Runtime error 5 ms 5196 KB Execution killed with signal 11
15 Halted 0 ms 0 KB -