連結：Splay 的簡介和相關題目

錯誤記錄（除錯用）

inline int find(int k) {
	int p = root;
	while (1) {
		pushdown(p);//Attention!!
		if (k <= siz[son[p][0]]) {
			//WA : p = siz[son[p][0]]; continue; 
			p = son[p][0]; continue;
		}
		int tmp = siz[son[p][0]] + 1;
		if (k <= tmp)	break;
		k -= tmp;
		p = son[p][1];
	}
	return p;
}
 

//printf("%d\n", sum[son[son[root][0]][1]]);
printf("%d\n", sum[son[son[root][1]][0]]);

inline void Swap(int x, int y) {//y is next to x(..., x, y, ...)
	splay(x, 0); splay(y, x);
	int rt1 = son[x][0], rt2 = son[y][1];
	son[x][0] = 0, son[y][1] = x;
	son[x][1] = rt2, son[y][0] = rt1;
	fa[x] = y, fa[y] = 0;
	fa[rt1] = y, fa[rt2] = x;
	pushup(x); pushup(y);
	root = y;//Attention!
}
 

int build(int L, int R, int faa) {
	if (L > R)	return 0;
	int mid = (L + R) >> 1;
	int cur = num[mid];
	fa[cur] = faa;//Attention!!
	son[cur][0] = build(L, mid - 1, cur);
	son[cur][1] = build(mid + 1, R, cur);
	pushup(cur);
	return cur;
}

void print(int cur) {
	if (!cur)	return ;
	pushdown(cur);//Attention!
	print(son[cur][0]);
	if (cur <= n)	printf("%d\n", cur);//注意順序：先左，再中（本身），再右
	print(son[cur][1]);
}
 

inline void Cut(int cur) {
	int faa = fa[cur]; printf("Cut : faa = %d\n", faa);
	son[faa][get_which(cur)] = 0;
	fa[cur] = 0;
	//pushup(faa);
	//splay(faa, 0);（與main函式中的語句衝突）
}

inline int find(int k) {
	//k++;	不能加此語句，因為我設定哨兵節點的 siz 為0
	int p = rt[nwid];//維護多棵Splay
	while (1) {
		if (k <= siz[son[p][0]]) {
			p = son[p][0];
			continue;
		}
		int tmp = siz[son[p][0]];
		k -= tmp;
		if (k <= (r[p] - l[p] + 1)) {
			split(p, l[p] + k - 1);//拆點，非提取區間
			break;
		}
		k -= (r[p] - l[p] + 1);
		p = son[p][1];
	}
	return p;
}

inline void splay(int cur, int goal) {
	for (register int faa = fa[cur]; faa != goal; rotate(cur), faa = fa[cur])
		if (fa[faa] != goal)	rotate(get_which(cur) == get_which(faa) ? faa : cur);
        //"fa[faa] != goal" !!! not "fa[faa]"!!
	pushup(cur);
	if (!goal)	rt[nwid] = cur;
}

inline int get_pre(int cur) {
	splay(cur, 0);//Attention!!（或者在主函式裡完成這一步）
	int p = son[cur][0];
	while (son[p][1])	p = son[p][1];
	return p;
}

inline void rotate(int cur) {
	int faa = fa[cur], fafa = fa[faa];
	bool flag = get_which(cur);//Bug
	fa[cur] = fafa; if (fafa)	son[fafa][get_which(faa)] = cur;
	son[faa][flag] = son[cur][flag ^ 1]; if (son[cur][flag ^ 1]) fa[son[cur][flag ^ 1]] = faa;//bug
	son[cur][flag ^ 1] = faa; fa[faa] = cur;
	pushup(faa);
}

模板（以區間翻轉，區間推平，區間求和，區間查詢最大子段和，單點查詢，插入一段序列，刪除一段序列為例，含回收廢點）（除錯用）

int n, m;
int son[N][2], fa[N], root, ttot, val[N];
int sum[N], lmx[N], rmx[N], mx[N], siz[N];
bool tag_sam[N], tag_rev[N];
int bin[N], btot;
inline int get_new() {
	int cur = btot ? bin[btot--] : ++ttot;
	son[cur][0] = son[cur][1] = fa[cur] = val[cur] = 0;
	sum[cur] = lmx[cur] = rmx[cur] = mx[cur] = siz[cur] = 0;
	tag_sam[cur] = 0, tag_rev[cur] = 0;
	return cur;
}
inline bool get_which(int cur) {
	return son[fa[cur]][1] == cur;
}
inline void pushup(int cur) {
	//mx[cur]：必須非空 
	//lmx[cur], rmx[cur]：可以為空(=0) 
	int ls = son[cur][0], rs = son[cur][1];
	siz[cur] = siz[ls] + siz[rs] + 1;
	sum[cur] = val[cur] + sum[ls] + sum[rs];
	mx[cur] = max(max(mx[ls], mx[rs]), rmx[ls] + val[cur] + lmx[rs]);
	lmx[cur] = max(lmx[ls], sum[ls] + val[cur] + lmx[rs]);
	rmx[cur] = max(rmx[rs], sum[rs] + val[cur] + rmx[ls]);
}
inline void push_rev(int cur) {
	if (!cur)	return ;
	tag_rev[cur] ^= 1;
	swap(son[cur][0], son[cur][1]);
	swap(lmx[cur], rmx[cur]);
}
inline void push_sam(int cur, int vall) {
	if (!cur)	return ;
	tag_sam[cur] = true;
	val[cur] = vall;
	sum[cur] = siz[cur] * vall;
	if (vall <= 0)	lmx[cur] = rmx[cur] = 0, mx[cur] = vall;
	else	mx[cur] = lmx[cur] = rmx[cur] = sum[cur];
}
inline void pushdown(int cur) {
	if (tag_sam[cur])
		push_sam(son[cur][0], val[cur]), push_sam(son[cur][1], val[cur]), tag_sam[cur] = 0;
	if (tag_rev[cur])
		push_rev(son[cur][0]), push_rev(son[cur][1]), tag_rev[cur] = 0;
}
inline void rotate(int cur) {
	int faa = fa[cur], fafa = fa[faa];
	bool flag = get_which(cur);
	fa[cur] = fafa; if (fafa)	son[fafa][get_which(faa)] = cur;
	son[faa][flag] = son[cur][flag ^ 1]; if (son[cur][flag ^ 1])	fa[son[cur][flag ^ 1]] = faa;
	son[cur][flag ^ 1] = faa; fa[faa] = cur;
	pushup(faa);
}
int stk[N], stop;
inline void splay(int cur, int goal) {
	int p = cur;
	while (p != goal)	stk[++stop] = p, p = fa[p];
	if (goal)	pushdown(goal);
	while (stop)	pushdown(stk[stop--]);
	
	for (register int faa = fa[cur]; faa != goal; rotate(cur), faa = fa[cur])
		if (fa[faa] != goal)	rotate(get_which(cur) == get_which(faa) ? faa : cur);
	pushup(cur);
	if (goal == 0)	root = cur;
}
inline int find(int k) {
	k++;
	int p = root;
	while (1) {
		pushdown(p);
		if (k <= siz[son[p][0]]) {
			p = son[p][0];
			continue;
		}
		int tmp = siz[son[p][0]] + 1;
		if (k <= tmp)	break;
		k -= tmp;
		p = son[p][1];
	}
	return p;
}
inline void split(int x, int y) {
	splay(x, 0);
	splay(y, x);
}

int num[N];
int build(int L, int R, int faa) {
	if (L > R)	return 0;
	int mid = (L + R) >> 1;
	int cur = get_new();
	fa[cur] = faa;
	sum[cur] = mx[cur] = val[cur] = num[mid];//必須非空 
	lmx[cur] = rmx[cur] = max(0, val[cur]);//可以為空 
	son[cur][0] = build(L, mid - 1, cur);
	son[cur][1] = build(mid + 1, R, cur);
	pushup(cur);
	return cur;
}

inline void clear_tre(int cur) {
	if (!cur)	return;
	bin[++btot] = cur;
	clear_tre(son[cur][0]); clear_tre(son[cur][1]);
}

int main() {
	read(n); read(m);
	mx[0] = -inf;
	num[1] = -inf;
	for (register int i = 1; i <= n; ++i)	read(num[i + 1]);
	num[n + 2] = -inf;
	root = build(1, n + 2, 0);
	char opt[10];
	for (register int i = 1; i <= m; ++i) {
		scanf("%s", opt);
		if (opt[0] == 'G' && opt[3] == '-') {//GET-SUM
			register int x, nn;
			read(x); read(nn);
			if (!nn) {
				printf("0\n");
				continue;
			}
			nn = find(x + nn); x = find(x - 1);
			split(x, nn);
			printf("%d\n", sum[son[son[root][1]][0]]);
		} else if (opt[0] == 'G') {//GET
			register int x;
			read(x);
			x = find(x);
			printf("%d\n", val[x]);
		} else if (opt[0] == 'M' && opt[2] == 'X') {//MAX-SUM
			register int x, nn;
			read(x); read(nn);
			nn = find(x + nn); x = find(x - 1);
			split(x, nn);
			printf("%d\n", mx[son[son[root][1]][0]]);
		} else if (opt[0] == 'R') {//REVERSE
			register int x, nn;
			read(x); read(nn);
			nn = find(x + nn); x = find(x - 1);
			split(x, nn);
			push_rev(son[son[root][1]][0]);
			pushup(son[root][1]); pushup(root);
		} else if (opt[0] == 'M') {//MAKE-SAME
			register int x, nn, t;
			read(x); read(nn); read(t);
			nn = find(x + nn); x = find(x - 1);
			split(x, nn);
			push_sam(son[son[root][1]][0], t);
			pushup(son[root][1]); pushup(root);
		} else if (opt[0] == 'D') {//DELETE
			register int x, nn;
			read(x); read(nn);
			nn = find(x + nn); x = find(x - 1);
			split(x, nn);
			clear_tre(son[son[root][1]][0]);
			son[son[root][1]][0] = 0;
			pushup(son[root][1]); pushup(root);
		} else if (opt[0] == 'I') {//INSERT
			register int x, nn, nxt;
			read(x); read(nn);
			for (register int i = 1; i <= nn; ++i)	read(num[i]);
			nxt = find(x + 1); x = find(x);
			split(x, nxt);
			int rt = build(1, nn, nxt);
			son[nxt][0] = rt;
			pushup(nxt); pushup(root);
		}
	}
	return 0;
}

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