比赛 NOIP2025模拟赛1 评测结果 C
题目名称 路径覆盖 最终得分 0
用户昵称 淮淮清子 运行时间 0.000 s
代码语言 C++ 内存使用 0.00 MiB
提交时间 2025-11-24 12:29:59
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#include<iostream>
#include<vector>
#include<algorithm>
#include<cstring>
using namespace std;

typedef long long ll;
const int MAXN = 20;
const int INF = 0x3f3f3f3f;

struct node{
    int to, nxt, id;
} e[MAXN << 1];

int n, q, E, tot;
int h[MAXN], star[MAXN];
vector<int> E;
int dp[1 << MAXN];
bool flag;

void add(int x, int y, int id){
    e[++ tot] = {y, h[x], id};
    h[x] = tot;
}

void dfs(int u, int v, int fa, int cm){
    if(flag || u == v){
        if(u == v){
            E.push_back(cm);
            flag = true;
        }
        return;
    }
    for(int i = h[u];i;i = e[i].nxt){
        int vv = e[i].to;
        if(vv != fa){
            dfs(vv, v, u, cm | (1 << e[i].id));
        }
    }
}

int main(){

    ios::sync_with_stdio(0);
    cin.tie(0);
    cin >> n >> q;
    for(int i = 0;i < n - 1;++ i){
        int u, v; cin >> u >> v;
        add(u, v, i); add(v, u, i);
    }
    for(int u = 1;u <= n;++ u){
        int m = 0;
        for(int i = h[u];i;i = e[i].nxt){
            m |= (1 << e[i].id);
        }
        star[u] = m;
    }
    for(int i = 1;i <= n;++ i){
        for(int j = i + 1;j <= n;++ j){
            flag = false;
            dfs(i, j, 0, 0);
        }
    }
    sort(E.begin(), E.end());
    E.erase(unique(E.begin(), E.end()), E.end());
    int FULL = (1 << (n - 1)) - 1;
    while(q --){
        int x; cin >> x;
        memset(dp, 0x3f, sizeof(dp));
        dp[star[x]] = 1;
        for(int mask = 0;mask < (1 << (n - 1));++ mask){
            if(dp[mask] == INF) continue;
            int uc = FULL ^ mask;
            for(int& pm : E){
                if((pm & uc) == pm){
                    dp[mask | pm] = min(dp[mask | pm], dp[mask] + 1);
                }
            }
            for(int u = 1;u <= n;++ u){
                int now = star[u] & uc;
                if(now){
                    dp[mask | now] = min(dp[mask | now], dp[mask] + 1);
                }
            }
        }
        cout << dp[FULL] << '\n';
    }
    return 0;
}

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

typedef long long ll;
const int MAXN = 20;
const int INF = 0x3f3f3f3f;

struct node{
    int to, nxt, id;
} e[MAXN << 1];

int n, q, tot;
int h[MAXN], star[MAXN], deg[MAXN];
vector<int> paths;
int dp[1 << MAXN];
bool flag;
bool is_chrys, is_chain;
int center;

void add(int x, int y, int id){
    e[++tot] = {y, h[x], id};
    h[x] = tot;
    deg[x]++, deg[y]++;
}

void dfs(int u, int v, int fa, int cm){
    if(flag || u == v){
        if(u == v) paths.push_back(cm), flag = true;
        return;
    }
    for(int i = h[u]; i; i = e[i].nxt){
        int vv = e[i].to;
        if(vv != fa) dfs(vv, v, u, cm | (1 << e[i].id));
    }
}

int main(){
    ios::sync_with_stdio(0);
    cin.tie(0);
    cin >> n >> q;
    memset(h, 0, sizeof(h));
    memset(deg, 0, sizeof(deg));
    for(int i = 0; i < n - 1; ++i){
        int u, v; cin >> u >> v;
        add(u, v, i); add(v, u, i);
    }

    // 判断特殊树:菊花树
    int cnt_max = 0;
    center = -1;
    for(int u = 1; u <= n; ++u){
        if(deg[u] == n - 1) cnt_max++, center = u;
    }
    is_chrys = (cnt_max == 1);

    // 判断特殊树:链状树
    int cnt_deg1 = 0, cnt_deg2 = 0;
    for(int u = 1; u <= n; ++u){
        if(deg[u] == 1) cnt_deg1++;
        else if(deg[u] == 2) cnt_deg2++;
    }
    is_chain = (cnt_deg1 == 2 && cnt_deg1 + cnt_deg2 == n);

    // 非特殊树才预处理
    if(!is_chrys && !is_chain){
        for(int u = 1; u <= n; ++u){
            int m = 0;
            for(int i = h[u]; i; i = e[i].nxt) m |= (1 << e[i].id);
            star[u] = m;
        }
        for(int i = 1; i <= n; ++i){
            for(int j = i + 1; j <= n; ++j){
                flag = false;
                dfs(i, j, 0, 0);
            }
        }
        sort(paths.begin(), paths.end());
        paths.erase(unique(paths.begin(), paths.end()), paths.end());
    }

    int FULL = (1 << (n - 1)) - 1;
    while(q--){
        int x; cin >> x;
        if(is_chrys){
            cout << (x == center ? 1 : 1 + (n - 2)/2) << '\n';
            continue;
        }
        if(is_chain){
            cout << 2 << '\n';
            continue;
        }
        // 原DP逻辑
        memset(dp, 0x3f, sizeof(dp));
        dp[star[x]] = 1;
        for(int mask = 0; mask < (1 << (n - 1)); ++mask){
            if(dp[mask] == INF) continue;
            int uc = FULL ^ mask;
            for(int& pm : paths){
                if((pm & uc) == pm) dp[mask | pm] = min(dp[mask | pm], dp[mask] + 1);
            }
            for(int u = 1; u <= n; ++u){
                int now = star[u] & uc;
                if(now) dp[mask | now] = min(dp[mask | now], dp[mask] + 1);
            }
        }
        cout << dp[FULL] << '\n';
    }
    return 0;
}