Submission #1298903

#TimeUsernameProblemLanguageResultExecution timeMemory
1298903kenkunkinThe Xana coup (BOI21_xanadu)C++20
0 / 100
38 ms20812 KiB
#include <bits/stdc++.h>
using namespace std;

void Init()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
}

typedef long long ll;
const int MAXN = 200000 + 5;
const ll INF = (ll)4e18;

int n;
vector<int> g[MAXN];
int initState[MAXN]; // 0 = off, 1 = on
ll dp[MAXN][2][2];   // dp[v][parentPress][pressV]
int parentArr[MAXN];

void Input()
{
    cin >> n;
    for (int i = 1; i <= n; ++i) {
        g[i].clear();
        initState[i] = 0;
    }
    for (int i = 0; i < n - 1; ++i) {
        int u, v;
        cin >> u >> v;
        g[u].push_back(v);
        g[v].push_back(u);
    }
    string token;
    cin >> token;
    if ((int)token.size() == n) {
        for (int i = 1; i <= n; ++i) initState[i] = token[i-1] - '0';
    } else {
        initState[1] = stoi(token);
        for (int i = 2; i <= n; ++i) cin >> initState[i];
    }
}

void dfs(int v, int p)
{
    parentArr[v] = p;
    for (int to : g[v]) if (to != p) dfs(to, v);

    // initialize dp[v] with INF
    for (int i = 0; i <= 1; ++i)
        for (int j = 0; j <= 1; ++j)
            dp[v][i][j] = INF;

    // tmp[first][second] as in editorial:
    // first = whether v is pressed (0/1)
    // second = parity of number of children pressed (0 = even, 1 = odd)
    ll tmp[2][2];
    tmp[0][0] = 0; tmp[0][1] = INF;
    tmp[1][0] = 0; tmp[1][1] = INF;

    for (int to : g[v]) {
        if (to == p) continue;
        ll newTmp[2][2];
        newTmp[0][0] = newTmp[0][1] = newTmp[1][0] = newTmp[1][1] = INF;

        // apply editorial merge formulas exactly
        // newTmp[0][0] = min(tmp[1][0] + dp[to][0][1], tmp[0][0] + dp[to][0][0])
        if (tmp[1][0] < INF && dp[to][0][1] < INF) newTmp[0][0] = min(newTmp[0][0], tmp[1][0] + dp[to][0][1]);
        if (tmp[0][0] < INF && dp[to][0][0] < INF) newTmp[0][0] = min(newTmp[0][0], tmp[0][0] + dp[to][0][0]);

        // newTmp[0][1] = min(tmp[1][1] + dp[to][1][1], tmp[0][1] + dp[to][1][0])
        if (tmp[1][1] < INF && dp[to][1][1] < INF) newTmp[0][1] = min(newTmp[0][1], tmp[1][1] + dp[to][1][1]);
        if (tmp[0][1] < INF && dp[to][1][0] < INF) newTmp[0][1] = min(newTmp[0][1], tmp[0][1] + dp[to][1][0]);

        // newTmp[1][0] = min(tmp[0][0] + dp[to][0][1], tmp[1][0] + dp[to][0][0])
        if (tmp[0][0] < INF && dp[to][0][1] < INF) newTmp[1][0] = min(newTmp[1][0], tmp[0][0] + dp[to][0][1]);
        if (tmp[1][0] < INF && dp[to][0][0] < INF) newTmp[1][0] = min(newTmp[1][0], tmp[1][0] + dp[to][0][0]);

        // newTmp[1][1] = min(tmp[0][1] + dp[to][1][1], tmp[1][1] + dp[to][1][0])
        if (tmp[0][1] < INF && dp[to][1][1] < INF) newTmp[1][1] = min(newTmp[1][1], tmp[0][1] + dp[to][1][1]);
        if (tmp[1][1] < INF && dp[to][1][0] < INF) newTmp[1][1] = min(newTmp[1][1], tmp[1][1] + dp[to][1][0]);

        // move newTmp -> tmp
        tmp[0][0] = newTmp[0][0];
        tmp[0][1] = newTmp[0][1];
        tmp[1][0] = newTmp[1][0];
        tmp[1][1] = newTmp[1][1];
    }

    // now compute dp[v][i][j] for all i (parentPress) and j (pressV)
    for (int i = 0; i <= 1; ++i) {
        for (int j = 0; j <= 1; ++j) {
            int toggles = (i + j) & 1;
            // after toggles parentPress+pressV, v's state = initState[v] ^ toggles
            // if that equals 1 (ON) -> need odd number of children pressed -> use tmp[j][1]
            // else need even -> use tmp[j][0]
            if ((initState[v] ^ toggles) == 1) {
                if (tmp[j][1] < INF) dp[v][i][j] = (ll)j + tmp[j][1];
            } else {
                if (tmp[j][0] < INF) dp[v][i][j] = (ll)j + tmp[j][0];
            }
            if (dp[v][i][j] > INF) dp[v][i][j] = INF;
        }
    }
}

void Bai()
{
    // choose root = 1 (any root works)
    dfs(1, 0);
    ll ans = min(dp[1][0][0], dp[1][0][1]);
    if (ans >= INF/2) cout << -1 << '\n';
    else cout << ans << '\n';
}

int main()
{
    Init();
    Input();
    Bai();
    return 0;
}
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