題面
題解
這道題由於是求字典序最小的,所以要貪心地枚舉數字,然後找可以走到的編號最小的點,處理這條路徑。
這條路徑有一些特性。
以下是特別精煉的結論:
所以一旦選好了路徑,這些邊的先後順序就被定死了,後面的路徑肯定不能與他衝突
於是我們只要記錄邊的先後關係,然後進行非常嚴密的邏輯判斷選擇一條不衝突的路徑。
複雜度O(n^2)
Code
你們看不懂的
#include<cstdio>
#include<iostream>
#include<cstring>
#include<vector>
#include<stack>
#include<algorithm>
#define LL long long
using namespace std;
int read() {
int f = 1,x = 0;char s = getchar();
while(s < '0' || s > '9') {if(s == '-')f = -1;s = getchar();}
while(s >= '0' && s <= '9') {x = x * 10 + s - '0';s = getchar();}
return x * f;
}
struct ed{
int v,id;
ed(){}
ed(int V,int I){v = V;id = I;}
};
vector<ed> g[2005];
int id[2005];
int pre[8005],suf[8005];
int fa[8005];
int le[8005];
int minn;
int find(int x) {
if(fa[x] != x) fa[x] = find(fa[x]);
return fa[x];
}
void unionSet(int a,int b) {
int u = find(a),v = find(b);
if(u < v) le[u] += le[v],fa[v] = u;
else le[v] += le[u],fa[u] = v;
}
int n,m,i,j,s,o,k;
void dfs(int x,int fat,int fai) {
if(fai != 0 && (((find(fai) > n || le[find(fai)] == g[x].size()) && !suf[fai] && !pre[x + n]) || g[x].size() == 1)) minn = min(minn,x);
// printf("minn:%d x:%d find[%d]:%d\n",minn,x,fai,find(fai));
for(int i = 0;i < g[x].size();i ++) {
int y = g[x][i].v,z = g[x][i].id;
if((fai == 0 && (((find(z) > 2*n || le[find(z)] == g[x].size()) && !pre[z] && !suf[x]) || g[x].size() == 1)) || (y != fat && !pre[z] && !suf[fai] && find(fai) != find(z) && !(find(fai) <= n && find(z) <= 2*n && le[find(fai)] + le[find(z)] != g[x].size()))) {
int zi = z;
if(zi <= 3 * n) zi += n;
else zi -= n;
dfs(g[x][i].v,x,zi);
}
}
return ;
}
bool dfs2(int x,int fat,int mini,int fai) {
if(x == mini) {
suf[fai] = x + n;
pre[x + n] = fai;
unionSet(x + n,fai);
return 1;
}
bool ff = 0;
for(int i = 0;i < g[x].size();i ++) {
if(g[x][i].v != fat) {
int z = g[x][i].id,zi = g[x][i].id;
if(z <= 3*n) z += n;
else z -= n;
bool fff = ff;
ff |= dfs2(g[x][i].v,x,mini,z);
if(!fff && ff) {
if(fai == 0) {
pre[zi] = x;
suf[x] = zi;
unionSet(x,zi);
}
else {
pre[zi] = fai;
suf[fai] = zi;
unionSet(fai,zi);
}
}
}
}
return ff;
}
int main() {
// freopen("tree.in","r",stdin);
// freopen("tree.out","w",stdout);
int T;
scanf("%d",&T);
while(T --) {
scanf("%d",&n);
memset(pre,0,sizeof(pre));
memset(suf,0,sizeof(suf));
memset(le,0,sizeof(le));
for(int i = 1;i < n;i ++) {
id[i] = read();
g[i].clear();
fa[i] = i;
fa[i + n] = i + n;
fa[i + 2*n] = i + n*2;
fa[i + 3*n] = i + n*3;
}
scanf("%d",&id[n]);
g[n].clear();
fa[n] = n;
fa[2*n] = 2*n;
fa[3*n] = 3*n;
fa[4*n] = 4*n;
for(int i = 1;i < n;i ++) {
s = read();o = read();
g[s].push_back(ed(o,i + n*2));
g[o].push_back(ed(s,i + n*3));
le[i + n*2] = le[i + n * 3] = 1;
}
// for(int i = 1;i <= n;i ++) printf("p:%d size:%d\n",i,g[i].size());
for(int i = 1;i <= n;i ++) {
s = id[i];
minn = 0x7f7f7f7f;
// cout<<"point:"<<i<<"("<<s<<")"<<endl;
dfs(s,0,0);
if(minn <= n) {
id[i] = minn;
dfs2(s,0,minn,0);
}
}
for(int i = 1;i <= n;i ++) {
printf("%d ",id[i]);
}putchar('\n');
}
return 0;
}