Submission #1297551

#TimeUsernameProblemLanguageResultExecution timeMemory
1297551SzymonKrzywdaSvjetlo (COCI20_svjetlo)C++20
110 / 110
723 ms150144 KiB
#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <set>

using namespace std;


const int MAXN = 5e5 + 7;
vector<int> graf[MAXN];
int dp[MAXN][2][2]; //zmiana parent, koncze w v
bool color[MAXN];
int xorr[MAXN];
int optsuma[MAXN];

multiset<pair<int, int>> opt1[MAXN];
multiset<pair<int, int>> opt2[MAXN];


void policz(int v) {
    dp[v][0][0] = 1e9;
    dp[v][0][1] = 1e9;
    dp[v][1][0] = 1e9;
    dp[v][1][1] = 1e9;


    // czesc kosztowna

    if (opt1[v].size()) {
        int koszt = (*(opt1[v].begin())).first;
        int koszt2 = (*(opt1[v].begin())).second;
        dp[v][0][0] = min(dp[v][0][0], optsuma[v] + koszt + (xorr[v] ^ 1) * (int)1e7 - 1);
        dp[v][0][0] = min(dp[v][0][0], optsuma[v] + koszt2  + (xorr[v] ) * (int)1e7 - 1);
        dp[v][1][0] = min(dp[v][1][0], optsuma[v] + koszt  + (xorr[v]) * (int)1e7 - 1 + 2);
        dp[v][1][0] = min(dp[v][1][0], optsuma[v] + koszt2 + (xorr[v] ^ 1) * (int)1e7 - 1 + 2);
    }

    if (opt2[v].size()) {
        int koszt = (*(opt2[v].begin())).first;
        int koszt2 = (*(opt2[v].begin())).second;
        dp[v][0][0] = min(dp[v][0][0], optsuma[v] + koszt + (xorr[v]) * (int)1e7 - 1);
        dp[v][0][0] = min(dp[v][0][0], optsuma[v] + koszt2 + (xorr[v] ^ 1) * (int)1e7 - 1);
        dp[v][1][0] = min(dp[v][1][0], optsuma[v] + koszt + (xorr[v] ^ 1) * (int)1e7 - 1 + 2);
        dp[v][1][0] = min(dp[v][1][0], optsuma[v] + koszt2 + (xorr[v]) * (int)1e7 - 1 + 2);
    }

    // for (int s : graf[v]) {
    //     if (s == p) continue;
    //     int oh = dp[s][0][1] > dp[s][1][1];
    //     int optsuma2 = optsuma - min(dp[s][0][1], dp[s][1][1]);
    //     //cout << "O: " << v << ' ' << s << ' ' <<  min(dp[s][0][1], dp[s][1][1]) <<  ' ' << optsuma << ' ' << optsuma2 << ' ' << dp[s][0][0] << ' ' << xorr << ' ' << oh << '\n';
    //     dp[v][0][0] = min(dp[v][0][0], optsuma2 + dp[s][0][0] + (xorr ^ oh) * (int)1e7 - 1);
    //     dp[v][0][0] = min(dp[v][0][0], optsuma2 + dp[s][1][0] + (xorr ^ oh ^ 1) * (int)1e7 - 1);
    //     dp[v][1][0] = min(dp[v][1][0], optsuma2 + dp[s][0][0] + (xorr ^ oh ^ 1) * (int)1e7 - 1 + 2);
    //     dp[v][1][0] = min(dp[v][1][0], optsuma2 + dp[s][1][0] + (xorr ^ oh) * (int)1e7 - 1 + 2);
    // }


    // koniec czesci kosztownej

    
    if (!xorr[v]) dp[v][1][1] = optsuma[v] + 2;
    else dp[v][0][1] = optsuma[v];
    dp[v][0][0] = min(dp[v][0][0], dp[v][0][1]);
    dp[v][1][0] = min(dp[v][1][0], dp[v][1][1]);
}




void change(int v, int v2) {
    xorr[v] ^= 1; //juz nie root
    optsuma[v] --; //juz nie root
    xorr[v2] ^= 1; // tera root
    optsuma[v2] ++; //tera root

    //pierwsze roota, potem nowy
    if (dp[v2][0][1] > dp[v2][1][1]) {
        opt1[v].extract({dp[v2][0][0] - dp[v2][1][1], dp[v2][1][0] - dp[v2][1][1]});
        xorr[v] ^= 1;
    }
    else {
        opt2[v].extract({dp[v2][0][0] - dp[v2][0][1], dp[v2][1][0] - dp[v2][0][1]});
    }
    optsuma[v] -= min(dp[v2][0][1], dp[v2][1][1]);


    if (graf[v].size() == 1) {
        dp[v][0][0] = 1;
        dp[v][0][1] = 1;
        dp[v][1][1] = 5;
        dp[v][1][0] = 5;
    }
    else policz(v);

    

    if (dp[v][0][1] > dp[v][1][1]) {
        opt1[v2].insert({dp[v][0][0] - dp[v][1][1], dp[v][1][0] - dp[v][1][1]});
        xorr[v2] ^= 1;
    }
    else {
        opt2[v2].insert({dp[v][0][0] - dp[v][0][1], dp[v][1][0] - dp[v][0][1]});
    }
    optsuma[v2] += min(dp[v][0][1], dp[v][1][1]);
    policz(v2);



    
} //do napisania


void dfs(int v, int p) {
    opt1[v].clear();
    opt2[v].clear();

    xorr[v] = (graf[v].size()) % 2;
    optsuma[v] = graf[v].size() + (v == p);
    if (v == p) xorr[v] ^= 1;
    xorr[v] ^= color[v]; 



    if (v != p && graf[v].size() == 1) {
        dp[v][0][0] = 1;
        dp[v][0][1] = 1;
        dp[v][1][1] = 5;
        dp[v][1][0] = 5;
        return;
    }

  


    for (int s : graf[v]) {
        if (s != p) {
            dfs(s, v);
            if (dp[s][0][1] > dp[s][1][1]) {
                xorr[v] ^= 1;
                opt1[v].insert({dp[s][0][0] - dp[s][1][1], dp[s][1][0] - dp[s][1][1]});
            }
            else {
                opt2[v].insert({dp[s][0][0] - dp[s][0][1], dp[s][1][0] - dp[s][0][1]});
            }
            optsuma[v] += min(dp[s][0][1], dp[s][1][1]);
        }
    }

   policz(v);

    // cout << v << ": " << dp[v][0][0] << ' ' << dp[v][0][1] << ' ' << dp[v][1][0] << ' ' << dp[v][1][1] << ' ' << optsuma << ' ' << xorr << '\n';

}


int ans = 1e9;


void dfs2(int v, int p) {
    ans = min({ans, dp[v][0][0], dp[v][0][1], dp[v][1][1]});
    for (int s : graf[v]) {
        if (s != p) {
            change(v, s);
            dfs2(s, v);
            change(s, v);
        }
    }
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int n, a, b;
    cin >> n;

    vector<bool> blocked(n + 1, 0);
    vector<int> indegree(n + 1, 0);

    char c;
    for (int i = 1; i <= n; i++) {
        cin >> c;
        color[i] = c - '0';
    }

    for (int i = 0; i < n - 1; i++) {
        cin >> a >> b;
        graf[a].push_back(b);
        graf[b].push_back(a);
        indegree[a]++;
        indegree[b]++;
    }

    vector<int> kolejka;
    for (int i = 1; i <= n; i++) {
        if (indegree[i] == 1 && color[i]) kolejka.push_back(i);
    }

    while (kolejka.size()) {
        int v = kolejka.back();
        blocked[v] = 1;
        kolejka.pop_back();
        for (int s : graf[v]) {
            indegree[s] --;
            if (indegree[s] == 1 && color[s]) kolejka.push_back(s);
        }
    }

    for (int i = 1; i <= n; i++) {
        if (blocked[i]) {
            graf[i].clear();
            continue;
        }

        vector<int> s2;
        for (int s : graf[i]) {
            if (!blocked[s]) s2.push_back(s);
        }
        graf[i] = s2;
    }

    
    for (int i = 1; i <= n; i++) {
        if (!blocked[i]) {
            dfs(i, i);
            dfs2(i, i);
            break;
        }
    }
    // for (int i = 1; i <= n; i++) {
    //     if (blocked[i]) continue;
    //     dfs(i, i);
    //     //cout << dp[i][0][0] << ' ' << dp[i][0][1] << ' ' << dp[i][1][1] << '\n';
    //     ans = min({ans, dp[i][0][0], dp[i][0][1], dp[i][1][1]});
    // } 


    cout << ans << '\n';



    return 0;
}
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