splay模板三合一 luogu2042 [NOI2005]维护数列/bzoj1500 [NOI2005]维修数列 | poj3580 SuperMemo | luogu3391 【模板】文艺平衡树（Splay）

先是维修数列

题解看这里，但是我写的跑得很慢

#include <iostream>
#include <cstdio>
using namespace std;
int n, m, idx[500005], a[500005], rot=0, uu, vv, sta[500005], din, ww, cnt;
const int oo=0x3f3f3f3f;
char ss[25];
struct Splay{
    int zdz[500005], sum[500005], lma[500005], rma[500005], siz[500005], val[500005];
    int s[500005][2], fa[500005];
    bool tag[500005], rev[500005];
    void clr(int x){
        zdz[x] = sum[x] = lma[x] = rma[x] = siz[x] = val[x] = s[x][0] = s[x][1] = fa[x] = 0;
        tag[x] = rev[x] = 0;
    }
    int gx(int x){
        return s[fa[x]][1]==x;
    }
    void recycle(int x){
        if(s[x][0])	recycle(s[x][0]);
        if(s[x][1])	recycle(s[x][1]);
        sta[++din] = x;
        clr(x);
    }
    void upd(int x){
        int l=s[x][0], r=s[x][1];
        sum[x] = sum[l] + sum[r] + val[x];
        siz[x] = siz[l] + siz[r] + 1;
        zdz[x] = max(max(zdz[l], zdz[r]), lma[r]+val[x]+rma[l]);
        lma[x] = max(lma[l], sum[l]+val[x]+lma[r]);
        rma[x] = max(rma[r], sum[r]+val[x]+rma[l]);
    }
    void build(int l, int r, int f){
        int mid=(l+r)>>1, now=idx[mid], pre=idx[f];
        if(l==r){
            clr(now);
            zdz[now] = sum[now] = a[l];
            lma[now] = rma[now] = max(a[l], 0);
            siz[now] = 1;
        }
        if(l<mid)	build(l, mid-1, mid);
        if(mid<r)	build(mid+1, r, mid);
        val[now] = a[mid]; fa[now] = pre;
        upd(now);
        s[pre][mid>=f] = now;
    }
    void pushDown(int x){
        int l=s[x][0], r=s[x][1];
        if(tag[x]){
            tag[x] = rev[x] = 0;
            if(l)	tag[l] = 1, val[l] = val[x], sum[l] = siz[l] * val[x];
            if(r)	tag[r] = 1, val[r] = val[x], sum[r] = siz[r] * val[x];
            if(val[x]>=0){
                if(l)	lma[l] = rma[l] = zdz[l] = sum[l];
                if(r)	lma[r] = rma[r] = zdz[r] = sum[r];
            }
            else{
                if(l)	lma[l] = rma[l] = 0, zdz[l] = val[x];
                if(r)	lma[r] = rma[r] = 0, zdz[r] = val[x];
            }
        }
        if(rev[x]){
            rev[x] = false; rev[l] ^= 1; rev[r] ^= 1;
            swap(lma[l], rma[l]); swap(lma[r], rma[r]);
            swap(s[l][0], s[l][1]); swap(s[r][0], s[r][1]);
        }
    }
    int queryLoc(int x, int w){
        pushDown(x);
        if(w<=siz[s[x][0]])	return queryLoc(s[x][0], w);
        else if(w>siz[s[x][0]]+1)	return queryLoc(s[x][1], w-siz[s[x][0]]-1);
        else	return x;
    }
    void xf(int x){
        if(fa[x])	xf(fa[x]);
        pushDown(x);
    }
    void rotate(int x){
        int old=fa[x], oldf=fa[old], w=gx(x);
        s[old][w] = s[x][w^1]; s[x][w^1] = old;
        fa[s[old][w]] = old; fa[old] = x; fa[x] = oldf;
        if(oldf)	s[oldf][s[oldf][1]==old] = x;
        else	rot = x;
        upd(old); upd(x);
    }
    void splay(int x, int goal){
        xf(x);
        while(fa[x]!=goal){
            int f=fa[x];
            if(fa[f]!=goal)	rotate(gx(f)==gx(x)?f:x);
            rotate(x);
        }
        upd(x);
    }
    void insert(int uu, int vv){
        for(int i=1; i<=vv; i++){
            scanf("%d", &a[i]);
            if(din)	idx[i] = sta[din--];
            else	idx[i] = ++cnt;
        }
        build(1, vv, 0);
        int ww=idx[(vv+1)>>1];
        int tx=queryLoc(rot, uu+1), ty=queryLoc(rot, uu+2);
        splay(tx, 0); splay(ty, rot);
        s[ty][0] = ww; fa[ww] = ty;
        upd(ty); upd(tx);
    }
    int spilt(int uu, int vv){
        int tx=queryLoc(rot, uu), ty=queryLoc(rot, uu+vv+1);
        splay(tx, 0); splay(ty, rot);
        return s[ty][0];
    }
    void shanssu(int uu, int vv){
        int x=spilt(uu, vv), y=fa[x];
        recycle(x); s[y][0] = 0;
        upd(y); upd(fa[y]);
    }
    void modify(int uu, int vv, int ww){
        int x=spilt(uu, vv), f=fa[x];
        val[x] = ww; tag[x] = true; sum[x] = siz[x] * ww;
        if(ww>=0)	lma[x] = rma[x] = zdz[x] = sum[x];
        else	lma[x] = rma[x] = 0, zdz[x] = ww;
        upd(f); upd(fa[f]);
    }
    void reverse(int uu, int vv){
        int x=spilt(uu, vv), f=fa[x];
        if(!tag[x]){
            rev[x] ^= 1;
            swap(s[x][0], s[x][1]);
            swap(lma[x], rma[x]);
            upd(f); upd(fa[f]);
        }
    }
    int getSum(int uu, int vv){
        int x=spilt(uu, vv);
        return sum[x];
    }
}splay;
int main(){
    cin>>n>>m;
    splay.zdz[0] = a[1] = a[n+2] = -oo;
    for(int i=1; i<=n; i++)	scanf("%d", &a[i+1]);
    for(int i=1; i<=n+2; i++)	idx[i] = i;
    splay.build(1, n+2, 0);
    rot = (n + 3) >> 1;
    cnt = n + 2;
    while(m--){
        scanf("%s", ss);
        if(ss[0]=='I'){
            scanf("%d %d", &uu, &vv);
            splay.insert(uu, vv);
        }
        if(ss[0]=='D'){
            scanf("%d %d", &uu, &vv);
            splay.shanssu(uu, vv);
        }
        if(ss[0]=='M' && ss[2]=='K'){
            scanf("%d %d %d", &uu, &vv, &ww);
            splay.modify(uu, vv, ww);
        }
        if(ss[0]=='R'){
            scanf("%d %d", &uu, &vv);
            splay.reverse(uu, vv);
        }
        if(ss[0]=='G'){
            scanf("%d %d", &uu, &vv);
            printf("%d\n", splay.getSum(uu, vv));
        }
        if(ss[0]=='M' && ss[2]=='X')
            printf("%d\n", splay.zdz[rot]);
    }
    return 0;
}

---

下面是poj的，稍加改动即可ac洛谷。

如果想看题意分析及讲解请看这里，讲得很好，一下就让我明白splay维护区间了。

splay的价值在于维护区间，如果只是维护点的话完全可以用treap等平衡树代替

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
int n, m, uu, vv, ww, rot, sze;
const int oo=0x3f3f3f3f;
char ss[15];
struct Splay{
	int s[200005][2], zxz[200005], val[200005], fa[200005], siz[200005];
	int rev[200005], tag[200005];
	void clr(int x){
		s[x][0] = s[x][1] = zxz[x] = val[x] = fa[x] = siz[x] = rev[x] = tag[x] = 0;
	}
	int gx(int x){
		return s[fa[x]][1]==x;
	}
	int newNode(int x){
		clr(++sze); siz[sze] = 1;
		val[sze] = zxz[sze] = x; return sze;
	}
	void ins(int x){
		newNode(x); s[rot][1] = sze; fa[sze] = rot; splay(sze, 0);
	}
	int queryLoc(int now, int x){
		pushDown(now);
		if(x<=siz[s[now][0]])	return  queryLoc(s[now][0], x);
		else if(x>siz[s[now][0]]+1)	return queryLoc(s[now][1], x-siz[s[now][0]]-1);
		else	return now;
	}
	void upd(int x){
		siz[x] = siz[s[x][0]] + siz[s[x][1]] + 1;
		zxz[x] = val[x];
		if(s[x][0])	zxz[x] = min(zxz[x], zxz[s[x][0]]);
		if(s[x][1])	zxz[x] = min(zxz[x], zxz[s[x][1]]);
	}
	void rotate(int x){
		int old=fa[x], oldf=fa[old], w=gx(x);
		s[old][w] = s[x][w^1]; s[x][w^1] = old;
		fa[s[old][w]] = old; fa[old] = x; fa[x] = oldf;
		if(oldf)	s[oldf][s[oldf][1]==old] = x;
		else	rot = x;
		upd(old); upd(x);
	}
	void pushDown(int x){
		if(tag[x])
			for(int i=0; i<2; i++)
				if(s[x][i]){
					zxz[s[x][i]] += tag[x];
					val[s[x][i]] += tag[x];
					tag[s[x][i]] += tag[x];
				}
		if(rev[x]){
			if(s[x][0])	rev[s[x][0]] ^= 1;
			if(s[x][1])	rev[s[x][1]] ^= 1;
			swap(s[x][0], s[x][1]);
		}
		tag[x] = rev[x] = 0;
	}
	void xf(int x){
		if(fa[x])	xf(fa[x]);
		pushDown(x);
	}
	void splay(int x, int goal){
		xf(x);
		while(fa[x]!=goal){
			int f=fa[x];
			if(fa[f]!=goal)	rotate(gx(x)==gx(f)?f:x);
			rotate(x);
		}
		upd(x);
	}
	void update(int uu, int vv, int ww){
		int tx=queryLoc(rot, uu), ty=queryLoc(rot, vv+2);
		splay(tx, 0); splay(ty, rot);
		val[s[ty][0]] += ww; zxz[s[ty][0]] += ww; tag[s[ty][0]] += ww;
	}
	void reverse(int uu, int vv){
		int tx=queryLoc(rot, uu), ty=queryLoc(rot, vv+2);
		splay(tx, 0); splay(ty, rot);
		rev[s[ty][0]] ^= 1;
	}
	void revolve(int uu, int vv, int ww){
		int len=vv-uu+1;
		ww = (ww%len+len)%len;
		int tx=queryLoc(rot, vv-ww+1), ty=queryLoc(rot, vv+2);
		int x=queryLoc(rot, uu), y=queryLoc(rot, uu+1);
		splay(tx, 0); splay(ty, rot);
		int tmp=s[ty][0]; s[ty][0] = 0;
		splay(x, 0); splay(y, rot);
		s[y][0] = tmp; fa[s[y][0]] = y;
	}
	void insert(int uu, int vv){
		int tx=queryLoc(rot, uu+1), ty=queryLoc(rot, uu+2);
		splay(tx, 0); splay(ty, rot);
		s[ty][0] = newNode(vv); fa[s[ty][0]] = ty;
	}
	void shanchu(int uu){
		int tx=queryLoc(rot, uu), ty=queryLoc(rot, uu+2);
		splay(tx, 0); splay(ty, rot);
		s[ty][0] = 0;
	}
	int queryMin(int uu, int vv){
		int tx=queryLoc(rot, uu), ty=queryLoc(rot, vv+2);
		splay(tx, 0); splay(ty, rot);
		return zxz[s[ty][0]];
	}
}splay;
int main(){
	cin>>n;
	rot = splay.newNode(oo);
	for(int i=1; i<=n; i++){
		scanf("%d", &uu);
		splay.ins(uu);
	}
	splay.ins(oo);
	cin>>m;
	while(m--){
		scanf("%s", ss);
		if(ss[0]=='A'){
			scanf("%d %d %d", &uu, &vv, &ww);
			splay.update(uu, vv, ww);
		}
		if(ss[0]=='R' && ss[3]=='E'){
			scanf("%d %d", &uu, &vv);
			splay.reverse(uu, vv);
		}
		if(ss[0]=='R' && ss[3]=='O'){
			scanf("%d %d %d", &uu, &vv, &ww);
			splay.revolve(uu, vv, ww);
		}
		if(ss[0]=='I'){
			scanf("%d %d", &uu, &vv);
			splay.insert(uu, vv);
		}
		if(ss[0]=='D'){
			scanf("%d", &uu);
			splay.shanchu(uu);
		}
		if(ss[0]=='M'){
			scanf("%d %d", &uu, &vv);
			printf("%d\n", splay.queryMin(uu, vv));
		}
	}
	return 0;
}