3797714 2014 - 10 - 12 21:58 : 19
Accepted 3820 C++
1350 70240
zz_1215
比較麻烦的一道题吧，開始的时候不停的段异常，后面知道是爆栈了，然后用数组模拟递归，才ac了
思路挺简单的，先找到这个树的直径，单独拿出来，能够证明最后选的两个点一定是在直径上的。我就不证了
然后求出这条直径上的每一个点向外延伸的最远距离
对这个距离做两次RMQ，第一次是对于往左边计算最大距离，所以要这个距离的序列要依次+1，+2，+3.......+n-1，+n
第二次是对于往右边计算最大距离。所以序列要+n，+n-1........+3，+2，+1
然后确定一个左起点。二分右起点
最后的复杂度是O（n*log（n））
实现起来还是挺复杂的，吐槽下这样的考代码能力的题
最后有一点提醒下，向外延伸的时候不要忘了向父节点的方向延伸。由于这个我又wa了一次
#pragma comment(linker, "/STACK:102400000,102400000")
#include<iostream>
#include<vector>
#include<algorithm>
#include<cstdio>
#include<queue>
#include<stack>
#include<string>
#include<map>
#include<set>
#include<cmath>
#include<cassert>
#include<cstring>
#include<iomanip>
using namespace std;
#ifdef _WIN32
#define i64 __int64
#define out64 "%I64d
"
#define in64 "%I64d"
#else
#define i64 long long
#define out64 "%lld
"
#define in64 "%lld"
#endif
/************ for topcoder by zz1215 *******************/
#define foreach(c,itr) for(__typeof((c).begin()) itr=(c).begin();itr!=(c).end();itr++)
#define FOR(i,a,b) for( int i = (a) ; i <= (b) ; i ++)
#define FF(i,a) for( int i = 0 ; i < (a) ; i ++)
#define FFD(i,a,b) for( int i = (a) ; i >= (b) ; i --)
#define S64(a) scanf(in64,&a)
#define SS(a) scanf("%d",&a)
#define LL(a) ((a)<<1)
#define RR(a) (((a)<<1)+1)
#define pb push_back
#define pf push_front
#define X first
#define Y second
#define CL(Q) while(!Q.empty())Q.pop()
#define MM(name,what) memset(name,what,sizeof(name))
#define MC(a,b) memcpy(a,b,sizeof(b))
#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define read freopen("out.txt","r",stdin)
#define write freopen("out2.txt","w",stdout)
const int inf = 0x3f3f3f3f;
const i64 inf64 = 0x3f3f3f3f3f3f3f3fLL;
const double oo = 10e9;
const double eps = 10e-9;
const double pi = acos(-1.0);
const int maxn = 211111;
struct Node{
int now;
int to;
int h;
bool operator < (const Node & cmp) const{
return h>cmp.h;
}
}node;
int n;
vector<Node>g[maxn];
int dfv[maxn];
int dfn[maxn];
int t[maxn];
int h[maxn];
int df;
vector<int>s;
vector<int>si;
bool vis[maxn];
vector<int>line;
int a[maxn];
int ax[maxn][20];
int dx[maxn][20];
int lg2[maxn];
bool isline[maxn];
void dfs(){
for (int i = 1; i <= n; i++){
vis[i] = false;
}
df = 1;
s.clear();
si.clear();
s.push_back(1);
si.push_back(0);
vis[1] = true;
int now, to, id;
while (!s.empty()){
now = s.back();
id = si.back();
if (id < g[now].size()){
to = g[now][id].to;
si.back()++;
if (!vis[to]){
vis[to] = true;
t[to] = now;
s.push_back(to);
si.push_back(0);
}
}
else{
dfv[df] = s.back();
dfn[s.back()] = df++;
s.pop_back();
si.pop_back();
}
}
}
int find_len(int now){
if (g[now].size() >= 2){
return g[now][0].h + g[now][1].h;
}
else if (g[now].size() == 1){
return g[now][0].h;
}
else{
return 0;
}
}
void get_line(int now){
if (g[now].size() >= 2){
int t1 = g[now][0].to;
int t2 = g[now][1].to;
isline[now] = true;
while (true){
isline[t1] = true;
line.push_back(t1);
if (g[t1].size() > 0){
t1 = g[t1][0].to;
}
else{
break;
}
}
reverse(line.begin(), line.end());
line.push_back(now);
while (true){
isline[t2] = true;
line.push_back(t2);
if (g[t2].size() > 0){
t2 = g[t2][0].to;
}
else{
break;
}
}
}
else if(g[now].size() ==1){
while (true){
isline[now] = true;
line.push_back(now);
if (g[now].size() > 0){
now = g[now][0].to;
}
else{
break;
}
}
}
}
int max_way(int now){
int to;
int re = 0;
for (int i = 0; i < g[now].size(); i++){
to = g[now][i].to;
if (!isline[to]){
re = max(re, g[now][i].h);
}
}
return re;
}
void sparse_table(){
for (int i = 0; i < line.size(); i++){
ax[i][0] = a[i]+i;
dx[i][0] = a[i]+(int)line.size()-1-i;
}
for (int step = 1; (1 << step) < line.size(); step++){
for (int i = 0; i < line.size(); i++){
ax[i][step] = ax[i][step - 1];
dx[i][step] = dx[i][step - 1];
if (i + (1 << (step - 1)) < line.size()){
ax[i][step] = max(ax[i][step], ax[i + (1 << (step - 1))][step - 1]);
dx[i][step] = max(dx[i][step], dx[i + (1 << (step - 1))][step - 1]);
}
}
}
}
int max_a(int l, int r){
return max(ax[l][lg2[r - l + 1]], ax[r - (1 << lg2[r - l + 1]) + 1][lg2[r - l + 1]]);
}
int max_d(int l, int r){
return max(dx[l][lg2[r - l + 1]], dx[r - (1 << lg2[r - l + 1]) + 1][lg2[r - l + 1]]);
}
int find(int l, int r){
int mid = (r + l) / 2;
return max(max_a(l, mid) - l, max_d(mid+1,r)-( (int)line.size()-1-r ) );
}
int back[maxn];
void find_back(){
for (int i = 1; i <= n; i++){
back[i] = 0;
}
queue<int>q;
q.push(1);
int now, to,fa,temp;
while (!q.empty()){
now = q.front();
q.pop();
if (t[now]){
fa = t[now];
back[now] = 1 + back[fa];
temp = 0;
if (g[fa][0].to == now){
if (g[fa].size() >= 2){
temp = g[fa][1].h+1;
}
}
else{
temp = g[fa][0].h;
}
back[now] = max(back[now], temp);
}
for (int i = 0; i < g[now].size(); i++){
q.push(g[now][i].to);
}
}
}
void start(){
dfs();
for (int i = 1; i <= n; i++){
h[i] = 0;
}
vector<Node>gg;
int now, to;
for (now = 1; now <= n; now++){
gg.clear();
for (int i = 0; i < g[now].size(); i++){
to = g[now][i].to;
if (to != t[now]){
gg.push_back(g[now][i]);
}
}
g[now] = gg;
}
for (int x = 1; x < df; x++){
now = dfv[x];
for (int i = 0; i < g[now].size(); i++){
to = g[now][i].to;
h[now] = max(h[now], h[to] + 1);
}
}
for (now = 1; now <= n; now++){
for (int i = 0; i < g[now].size(); i++){
to = g[now][i].to;
g[now][i].h = h[to] + 1;
}
}
for (now = 1; now <= n; now++){
sort(g[now].begin(), g[now].end());
}
int id;
int len = -1;
int temp;
for (now = 1; now <= n; now++){
temp = find_len(now);
if (temp > len){
len = temp;
id = now;
}
}
for (int i = 1; i <= n; i++){
isline[i] = false;
}
line.clear();
get_line(id);
find_back();
for (int i = 0; i < line.size(); i++){
a[i] = max_way(line[i]);
if (line[i] == id){
a[i] = max(a[i], back[id]);
}
}
sparse_table();
int ans=inf;
int left;
int right;
int l, r;
for (int lend = 0; lend < line.size(); lend++){
l = lend;
r = line.size() - 1;
while (l + 2 < r){
int mid = (l + r) / 2;
if (find(lend, mid) > (int)line.size() - 1 - mid){
r = mid;
}
else{
l = mid;
}
}
for (int x = l; x <= r; x++){
temp = max(find(lend, x), (int)line.size() - 1 - x);
temp = max(temp, lend);
if (temp < ans){
ans = temp;
left = lend;
right = x;
}
}
}
cout << ans << " " << line[left] << " " << line[right] << endl;
}
int main(){
for (int i = 0; i < 20; i++){
if ((1 << i) < maxn){
lg2[1 << i] = i;
}
}
for (int i = 3; i < maxn; i++){
if (!lg2[i]){
lg2[i] = lg2[i - 1];
}
}
int T;
cin >> T;
while (T--){
cin >> n;
for (int i = 1; i <= n; i++){
g[i].clear();
}
node.h = 0;
for (int i = 1; i <= n - 1; i++){
// cin >> node.now >> node.to;
SS(node.now); SS(node.to);
g[node.now].push_back(node);
swap(node.now, node.to);
g[node.now].push_back(node);
}
start();
}
return 0;
}
版权声明：本文博客原创文章，博客，未经同意，不得转载。