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及其简短的Splay代码
#include <stdio.h> #include <queue> #include <algorithm> #include <stdlib.h> #include <math.h> #include <iostream> #define inf 1000000000 using namespace std; #define getch() getchar() inline int F() {register int aa , bb , ch; while(ch = getch() , (ch<‘0‘||ch>‘9‘) && ch != ‘-‘); ch == ‘-‘ ? aa=bb=0 : (aa=ch-‘0‘,bb=1); while(ch = getch() , ch>=‘0‘&&ch<=‘9‘) aa = aa*10 + ch-‘0‘; return bb ? aa : -aa; } const int Maxn = 1000005; queue<int> q; int n , m , root , sz; int fa[Maxn] , c[Maxn][2] , mx[Maxn] , lx[Maxn] , rx[Maxn] , v[Maxn] , size[Maxn] , sum[Maxn] , a[Maxn] , id[Maxn]; bool lazy[Maxn] , rev[Maxn]; void update(int x) { int lc = c[x][0] , rc = c[x][1]; sum[x] = sum[lc] + sum[rc] + v[x]; size[x] = size[lc] + size[rc] + 1; mx[x] = max(mx[lc] , mx[rc]); mx[x] = max(mx[x] , rx[lc]+v[x]+lx[rc]); lx[x] = max(lx[lc] , sum[lc] + v[x] + lx[rc]); rx[x] = max(rx[rc] , sum[rc] + v[x] + rx[lc]); } void downpush(int x) { int lc = c[x][0] , rc = c[x][1]; if(lazy[x]) { rev[x] = lazy[x] = 0; if(lc) lazy[lc] = 1 , v[lc] = v[x] , sum[lc] = v[x]*size[lc]; if(rc) lazy[rc] = 1 , v[rc] = v[x] , sum[rc] = v[x]*size[rc]; if(v[x] >= 0) { if(lc) lx[lc] = rx[lc] = mx[lc] = sum[lc]; if(rc) lx[rc] = rx[rc] = mx[rc] = sum[rc]; } else { if(lc) lx[lc] = rx[lc] = 0 , mx[lc] = v[x]; if(rc) lx[rc] = rx[rc] = 0 , mx[rc] = v[x]; } } if(rev[x]) { rev[x] = 0; rev[lc] ^= 1; rev[rc] ^= 1; swap(lx[lc] , rx[lc]); swap(lx[rc] , rx[rc]); c[x][0] = rc; c[x][1] = lc; swap(lx[x] , rx[x]); } } void rotate(int&root , int x) { int y = fa[x] , z = fa[y] , p , q; if(x == c[y][0]) p = 0; else p = 1; q = p^1; if(y == root) root = x; else { if(c[z][0] == y) c[z][0] = x; else c[z][1] = x; } fa[x] = z; fa[y] = x; fa[c[x][q]] = y; c[y][p] = c[x][q]; c[x][q] = y; update(y); update(x); } void splay(int&root , int x) { int y , z; while(x != root) { y = fa[x] , z = fa[y]; if(y != root) { if((x == c[y][0]) ^ (y == c[z][0])) rotate(root , x); else rotate(root , y); } rotate(root , x); } } int find(int x , int rk) { downpush(x); int lc = c[x][0] , rc = c[x][1]; if(size[lc] + 1 == rk) return x; if(size[lc] >= rk) return find(lc , rk); else return find(rc , rk-size[lc]-1); } void rec(int x) { if(!x) return ; int lc = c[x][0] , rc = c[x][1]; rec(lc);rec(rc);q.push(x); fa[x] = c[x][0] = c[x][1] = lazy[x] = rev[x] = 0; } int split(int k , int tot) { int x = find(root , k); splay(root , x); x = find(root , k+tot+1); splay(c[root][1] , x); return c[ c[root][1] ][0]; } void query(int k , int tot) { int x = split(k , tot); printf("%d\n",sum[x]); } void modify(int k , int tot , int val) { int x = split(k , tot) , y = fa[x]; v[x] = val; lazy[x] = 1; sum[x] = size[x]*val; if(val >= 0) lx[x] = rx[x] = mx[x] = sum[x]; else lx[x] = rx[x] = 0 , mx[x] = val; update(y); update(fa[y]); } void reverse(int k , int tot) { int x = split(k , tot); if(!lazy[x]) { rev[x] ^= 1; downpush(x); update(fa[x]); update(fa[fa[x]]); } } void erase(int k , int tot) { int x = split(k , tot) , y = fa[x]; rec(x); c[y][0] = 0; update(y); update(fa[y]); } void build(int l,int r,int f) { if(l>r)return; int mid=(l+r)>>1,now=id[mid],last=id[f]; if(l==r) { sum[now]=a[l];size[now]=1; lazy[now]=rev[now]=0; if(a[l]>=0)lx[now]=rx[now]=mx[now]=a[l]; else lx[now]=rx[now]=0,mx[now]=a[l]; } else build(l,mid-1,mid),build(mid+1,r,mid); v[now]=a[mid];fa[now]=last;update(now); c[last][mid>=f]=now; } void insert(int k,int tot) { for(int i=1;i<=tot;i++)a[i]=F(); for(int i=1;i<=tot;i++) if(!q.empty())id[i]=q.front(),q.pop(); else id[i]=++sz; build(1,tot,0);int z=id[(1+tot)>>1]; int x=find(root,k+1),y=find(root,k+2); splay(root,x);splay(c[x][1],y); fa[z]=y;c[y][0]=z; update(y);update(x); } int main() { n = F(); m = F(); mx[0] = a[1] = a[n+2] = -inf; for(int i=1; i<=n; ++i) { a[i+1] = F(); } for(int i=1;i<=n+2;i++)id[i]=i; build(1,n+2,0); root = (n+3) >> 1;sz = n + 2; int k , tot , val; char ch[10]; while(m--) { scanf("%s",ch); if(ch[0]!=‘M‘ || ch[2] != ‘X‘) k = F() , tot = F(); if(ch[0] == ‘I‘) insert(k , tot); if(ch[0] == ‘D‘) erase(k , tot); if(ch[0] == ‘M‘) { if(ch[2] == ‘X‘) printf("%d\n",mx[root]); else val = F() , modify(k , tot , val); } if(ch[0] == ‘R‘) reverse(k , tot); if(ch[0] == ‘G‘) query(k , tot); } }
Splay的核心操作
void rotate(int&root , int x) { int y = fa[x] , z = fa[y] , p , q; if(x == c[y][0]) p = 0; else p = 1; q = p^1; if(y == root) root = x; else { if(c[z][0] == y) c[z][0] = x; else c[z][1] = x; } fa[x] = z; fa[y] = x; fa[c[x][q]] = y; c[y][p] = c[x][q]; c[x][q] = y; update(y); update(x); } void splay(int&root , int x) { int y , z; while(x != root) { y = fa[x] , z = fa[y]; if(y != root) { if((x == c[y][0]) ^ (y == c[z][0])) rotate(root , x); else rotate(root , y); } rotate(root , x); } }
及其简短的Splay代码
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