| 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 |
显示代码纯文本
#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;
}