查找所有树的直径都经过的边的数量
P3304
此题思路上跟 https://www.cnblogs.com/kingbuffalo/p/17027323.html 上的思路差不多。
大体思路
- 第一遍 dfs 找到最远点
- 第二遍 dfs 找到直径，及直径的中点。
- 分情况讨论，
3.1. 当直径中点在一条边时，分裂成两树：对边的两点进行dfs找到 maxdeep
3.2. 当直径中点在一个点时，对点的child找到maxdeep最长的两个，然后分裂成2棵树
3.3. 被分裂的树中，如果树的root的maxdeep的child只有一个，那么共直径的边数量就+1
code
#include <iostream>
#include <cassert>
#include <iomanip>
#include <vector>
#include <queue>
#include <string>
#include <cstring>
#include <cmath>
#include <climits>
#include <functional>
#include <list>
#include <cstdlib>
#include <set>
#include <stack>
#include <sstream>
#include <numeric>
#include <map>
#include <algorithm>
#include <bitset>
#define endl "\n"
#define i64 long long
#define ui64 unsigned long long
#define INF 0x3f3f3f3f
#define MZ(arr) memset(arr,0,sizeof(arr))
#define MS(arr,val) memset(arr,val,sizeof(arr))
//浮点数输出保留小数点多少位
//cout << setiosflags(ios::fixed) << setprecision(2);
using namespace std;
namespace Buffalo{
struct HeadNxtG{
vector<int> head;
vector<int> ver;
vector<int> nxt;
vector<int> wi;
int tot;
HeadNxtG(int nodeLen,int edgeLen){
head.resize(nodeLen);
ver.resize(edgeLen<<1);
nxt.resize(edgeLen<<1);
wi.resize(edgeLen<<1);
deep.resize(nodeLen);
maxDeep.resize(nodeLen);
parents.resize(nodeLen);
parentswi.resize(nodeLen);
tot=0;
}
void add(int u,int v,int w){
ver[++tot] = v;
nxt[tot] = head[u];
head[u] = tot;
wi[tot] = w;
}
void addE(int u,int v,int w){
add(u,v,w);
add(v,u,w);
}
i64 maxLen;
int q;
vector<i64> deep;
vector<i64> maxDeep;
vector<int> parents;
vector<i64> parentswi;
void findMaxLen() {
maxLen = 0; q = 0;
dfs(1, 0);
deep[q] = 0;
maxLen = 0;
dfs2(q, 0);
i64 midLen = maxLen / 2;
i64 findParentLen = 0;
int preq;
while (findParentLen < midLen) {
findParentLen += parentswi[q];
preq = q;
q = parents[q];
}
deep.assign(head.size(), 0);
//一个点分成两棵树
if (findParentLen == midLen) {
dfs3(q, 0);
i64 maxV = 0;
int maxVcnt = 1;
for (int e = head[q]; e > 0; e = nxt[e]) {
if (maxV <= maxDeep[ver[e]]) {
if (maxV < maxDeep[ver[e]]) maxV = maxDeep[ver[e]];
else maxVcnt++;
}
}
if (maxVcnt != 2) {
cout << maxLen << endl << 0 << endl;
return;
}
int twochild1=0;
int twochild2=0;
for (int e = head[q]; e > 0; e = nxt[e]) {
if (maxV == maxDeep[ver[e]]) {
if (twochild1 == 0) twochild1 = ver[e];
else twochild2 = ver[e];
}
}
int ret = findCnt(twochild1, q);
ret += findCnt(twochild2, q);
cout << maxLen << endl << ret << endl;
} else {
dfs3(q, preq);
dfs3(preq,q);
int ret = findCnt(q, preq) + 1;
ret += findCnt(preq, q);
cout << maxLen << endl << ret << endl;
}
}
//查找直径未分裂的数量
int findCnt(int u, int fa) {
i64 maxCDeep = 0;
int cnt = 0;
int maxV = 0;
for (int e = head[u]; e > 0; e = nxt[e]) {
int v = ver[e];
if (v != fa) {
if (maxDeep[v] > maxCDeep) {
maxCDeep = maxDeep[v];
maxV = v;
}
}
}
for (int e = head[u]; e > 0; e = nxt[e]) {
int v = ver[e];
if (v != fa) {
if (maxDeep[v] == maxCDeep) {
cnt++;
}
}
}
if (cnt == 1 && maxV > 0) {
return 1 + findCnt(maxV, u);
}
return 0;
}
//求maxdeep
void dfs3(int u, int fa) {
maxDeep[u] = deep[u];
for (int e = head[u]; e > 0; e = nxt[e]) {
int v = ver[e];
int w = wi[e];
if (v != fa) {
deep[v] = deep[u] + w;
dfs3(v, u);
maxDeep[u] = max(maxDeep[u], maxDeep[v]);
}
}
}
//最远点查找最远点,并求出直径长度及路径
void dfs2(int u, int fa) {
for (int e = head[u]; e > 0; e = nxt[e]) {
int v = ver[e];
int w = wi[e];
if (v != fa) {
deep[v] = deep[u] + w;
parents[v] = u;
parentswi[v] = w;
if (maxLen < deep[v]) {
maxLen = deep[v];
q = v;
}
dfs2(v, u);
}
}
}
//任一点查找最远点
void dfs(int u, int fa) {
for (int e = head[u]; e > 0; e = nxt[e]) {
int v = ver[e];
int w = wi[e];
if (v != fa) {
deep[v] = deep[u] + w;
if (maxLen < deep[v]) {
maxLen = deep[v];
q = v;
}
dfs(v, u);
}
}
}
};
}
namespace SLOVER {
#define NMAX 100005
void slove() {
i64 maxLen = 0;
int q;
int n;
cin >> n;
Buffalo::HeadNxtG hng(n + 1, n + 1);
int u, v, w;
for (int i = 1; i < n; ++i) {
cin >> u >> v >> w;
hng.addE(u, v, w);
}
hng.findMaxLen();
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int t = 1;
while (t--) { SLOVER::slove(); }
return 0;
}
