HDU2586(LCA)解题报告
2019/3/18 xzc
题目链接：
How far away ？
- 这道题我寒假打牛客的时候学了一下LCA的倍增算法，当时找了HDU上的这道题，AC了。31ms,用得是最朴素的倍增，两个人先到同一个高度，然后两个人一起一步一往上移动直到相遇
/*
HDU 2586 LCA(最朴素的倍增，一步一步往上挑，数据太水)
Author:xzc
2019-01-28 23:54:52 Accepted 2586 31MS
4396K 1282 B G++ apareHDU
*/
#include <bits/stdc++.h>
using namespace std;
const int maxn = 4e4+20;
struct Graph{
int head[maxn],deep[maxn],fa[maxn],dis[maxn],tot,n;
struct Edge{
int to,next;
long long d;
}edge[maxn<<1];
void init(int nn)
{
n = nn;
tot = 0;
memset(head,0,sizeof(head));
memset(deep,0,sizeof(deep));
deep[1] = 1; fa[1] = 0;dis[1] = 0;
}
void addedge(int u,int v,long long dd)
{
edge[++tot].to = v;
edge[tot].d = dd;
edge[tot].next = head[u];
head[u] = tot;
}
void dfs(int u)
{
for(int i=head[u];i;i=edge[i].next)
{
int to = edge[i].to;
if(deep[to]) continue;
dis[to] = edge[i].d;
fa[to] = u;
deep[to] = deep[u]+1;
dfs(to);
}
}
void solve(int a,int b)
{
long long ans = 0;
if(deep[a]>deep[b]) swap(a,b);
while(deep[b]>deep[a]) ans+=dis[b],b=fa[b];
while(b!=a) ans+=dis[a]+dis[b],b=fa[b],a=fa[a];
printf("%lld
",ans);
}
}G;
int main()
{
long long dd;
int T,n,m,u,v;cin>>T;
while(T--)
{
scanf("%d%d",&n,&m);
G.init(n);
for(int i=1;i<n;i++)
{
scanf("%d%d%lld",&u,&v,&dd);
G.addedge(u,v,dd);
G.addedge(v,u,dd);
}
G.dfs(1);
while(m--)
{
scanf("%d%d",&u,&v);
G.solve(u,v);
}
}
return 0;
}
- 最近学了主席树求静态区间第K大，老会长推荐去写那个书上第K大，于是我就先来学LCA了
这次学的是nlogn预处理，O(1)查询的(dfs+RMQ)的算法
学习的时候是参考的这篇博客
这个是番茄学长给我推荐的topcoder上的我还没看完就去马鞍山吃烧烤了~
这个也是番茄学长给我推荐的中文写的
/*
HDU2586 LCA(dfs+RMQ)
Author: xzc
2019-03-18 10:36:20 Accepted 2586(HDU)
93MS 15832K 2730 B G++ apareHDU
*/
#include <bits/stdc++.h>
#define For(i,a,b) for(register int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(register int i=(a);i>=(b);--i)
#define Mst(a,b) memset(a,(b),sizeof(a))
#define LL long long
using namespace std;
const int maxn = 1e5+20;
struct Edge{
int to,Next;
LL d;
}edge[maxn];
int head[maxn],tot;
void initG()
{
Mst(head,-1);
tot = 0;
}
void addedge(int from,int to,LL d)
{
edge[tot].to = to;
edge[tot].d = d;
edge[tot].Next = head[from];
head[from] = tot++;
}
bool vis[maxn];
int First[maxn];///First[i]表示节点i在欧拉序中首次出现的位置
int deep[maxn*2],cnt;
int sequence[maxn*2]; ///存欧拉序中节点的编号
void initDFS()
{
Mst(vis,0);
cnt = 0;
}
//int fa[maxn];
LL dis[maxn]; ///记录该节点到根节点的距离
void dfs(int root,int dep) ///Mst(vis),cnt=0; fa[1] = 1;dis[1] = 0;
{
vis[root] = true;
sequence[++cnt] = root;
deep[cnt] = dep;
First[root] = cnt;
for(int i=head[root];i!=-1;i=edge[i].Next)
{
int to = edge[i].to;
if(vis[to]) continue;
//fa[to] = root;
dis[to] = dis[root] + edge[i].d;
dfs(to,dep+1);
sequence[++cnt] = root;
deep[cnt] = dep;
}
}
int Min[maxn*2][20]; ///log2(1e6)==19.9 log2(1e5) = 16.6 log2(8e4) =16.28
int Log2[maxn*2];
void ST(int n) ///这里的n是欧拉序的长度：节点个数*2-1
{///预出理出dfs序中区间里深度的最小值，并记录去到最小值的下标
For(i,2,n) Log2[i] = Log2[i>>1]+1; ///预处理所有log2(x) x=1,2,3,...n
For(i,1,n) Min[i][0] = i;
for(int j=1; (1<<j)<=n; ++j)
{
for(int i=1;i+(1<<j)-1<=n;++i)
{
int a = Min[i][j-1];
int b = Min[i+(1<<(j-1))][j-1];
Min[i][j] = deep[a]>deep[b]?b:a;
}
}
}
int LCA(int x,int y)
{
int left = First[x];
int right = First[y];
if(left>right) swap(left,right),swap(x,y);
int j = Log2[right-left+1];
int a = Min[left][j];
int b = Min[right-(1<<j)+1][j];
return deep[a]>deep[b]?sequence[b]:sequence[a];
}
int main()
{
//freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);
int T,m,n,u,v;
LL d;
scanf("%d",&T);
while(T--)
{
scanf("%d%d",&n,&m);
initG();
For(i,1,n-1)
{
scanf("%d%d%lld",&u,&v,&d);
addedge(u,v,d);
addedge(v,u,d);
}
initDFS();
dis[1] = 0;
dfs(1,1);
ST(2*n-1);
while(m--)
{
scanf("%d%d",&u,&v);
int lca = LCA(u,v);
int ans = 1ll*dis[u]+dis[v]-2*dis[lca];
printf("%d
",ans);
}
}
return 0;
}