叶子的染色(Coloring Leaves) 题解

思路分析

按题目要求使用对应数据结构与算法模拟/递推求解，注意数据范围边界与时间复杂度。

参考代码

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

const int INF = 100000000;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int m, n;
    if (!(cin >> m >> n)) return 0;
    vector<int> c(n + 1, 0);
    for (int i = 1; i <= n; ++i) cin >> c[i];
    vector<vector<int>> adj(m + 1);
    for (int i = 1; i < m; ++i) {
        int u, v;
        cin >> u >> v;
        adj[u].push_back(v);
        adj[v].push_back(u);
    }
    int root = n + 1;
    vector<int> par(m + 1, 0), order;
    vector<bool> vis(m + 1, false);
    vis[root] = true;
    order.push_back(root);
    for (int idx = 0; idx < (int)order.size(); ++idx) {
        int u = order[idx];
        for (int v : adj[u]) {
            if (!vis[v]) {
                vis[v] = true;
                par[v] = u;
                order.push_back(v);
            }
        }
    }
    vector<int> dp0(m + 1, 1), dp1(m + 1, 1);
    for (int i = 1; i <= n; ++i) {
        if (c[i] == 0) dp1[i] = INF;
        else dp0[i] = INF;
    }
    for (int i = m - 1; i >= 0; --i) {
        int u = order[i];
        int p = par[u];
        if (p) {
            dp0[p] += min(dp0[u] - 1, dp1[u]);
            dp1[p] += min(dp1[u] - 1, dp0[u]);
        }
    }
    cout << min(dp0[root], dp1[root]) << "\n";
    return 0;
}