bzoj 1267 Kth Number I (点分治,堆)
超级钢琴的树上版本, 类似做法即可, 只不过区间转为dfs序了, 用点分求一下, 复杂度$O(nlog^2n)$
#include <iostream> #include <algorithm> #include <cstdio> #include <math.h> #include <set> #include <map> #include <queue> #include <string> #include <string.h> #include <bitset> #define REP(i,a,n) for(int i=a;i<=n;++i) #define PER(i,a,n) for(int i=n;i>=a;--i) #define hr putchar(10) #define pb push_back #define lc (o<<1) #define rc (lc|1) #define mid ((l+r)>>1) #define ls lc,l,mid #define rs rc,mid+1,r #define x first #define y second #define io std::ios::sync_with_stdio(false) #define endl '\n' using namespace std; typedef long long ll; typedef pair<int,int> pii; const int P = 1e9+7, INF = 0x3f3f3f3f; ll gcd(ll a,ll b) {return b?gcd(b,a%b):a;} ll qpow(ll a,ll n) {ll r=1%P;for (a%=P;n;a=a*a%P,n>>=1)if(n&1)r=r*a%P;return r;} ll inv(ll x){return x<=1?1:inv(P%x)*(P-P/x)%P;} //head const int N = 1e6+10; int n, m, sum, rt; struct _ {int to,w;}; vector<_> g[N]; int mx[N], sz[N], vis[N]; #define go for (int i=0,y,w; i<g[x].size()?w=g[x][i].w,y=g[x][i].to:0; ++i) void getrt(int x, int fa) { mx[x]=0,sz[x]=1; go if (!vis[y]&&y!=fa) { getrt(y,x),sz[x]+=sz[y]; mx[x]=max(mx[x],sz[y]); } mx[x]=max(mx[x],sum-sz[x]); if (mx[rt]>mx[x]) rt=x; } int s[N], L, R; pii a[N]; void dfs(int x, int f, int d, int rt) { s[++*s]=d, a[*s]=pii(L,R); go if (!vis[y]&&y!=f) dfs(y,x,d+w,rt); } void solve(int x) { vis[x]=1,s[++*s]=0,L=R=*s; go if (!vis[y]) dfs(y,x,w,x),R=*s; go if (!vis[y]) { mx[rt=0]=n,sum=sz[y]; getrt(y,0),solve(rt); } } int Log[N], f[N][20]; void init(int n) { Log[0]=-1; REP(i,1,n) f[i][0]=i,Log[i]=Log[i>>1]+1; for (int j=1; (1<<j)<=n; ++j) { for (int i=0; i+(1<<j)-1<=n; ++i) { int x=f[i][j-1], y=f[i+(1<<(j-1))][j-1]; f[i][j]=s[x]>s[y]?x:y; } } } int RMQ(int l, int r) { int k=Log[r-l+1]; int x=f[l][k],y=f[r-(1<<k)+1][k]; return s[x]>s[y]?x:y; } struct node { int l,r,pos,opt,v; node () {} node (int l, int r, int pos) : l(l),r(r),pos(pos) { opt = RMQ(l,r); v = s[pos]+s[opt]; } bool operator < (const node & rhs) const { return v < rhs.v; } }; priority_queue<node> q; int main() { scanf("%d%d", &n, &m); REP(i,2,n) { int u, v, w; scanf("%d%d%d", &u, &v, &w); g[u].pb({v,w}),g[v].pb({u,w}); } sum=mx[0]=n,getrt(1,0),solve(rt); init(*s); REP(i,1,*s) if (a[i].x) q.push(node(a[i].x,a[i].y,i)); REP(i,1,m) { node t = q.top(); printf("%d\n", t.v);q.pop(); if (t.opt!=t.l) q.push(node(t.l,t.opt-1,t.pos)); if (t.opt!=t.r) q.push(node(t.opt+1,t.r,t.pos)); } }