POJ 3468 A Simple Problem with Integers 伸展树splay 区间更新

题目：

http://poj.org/problem?id=3468

题意：

给定一个序列，有两种操作：
1. Q a b询问[a,b]区间内元素和
2. C a b c把区间[a,b]内的元素全部加上c

思路：

线段树区间更新模板题，用splay来找虐了。。。旋转某个节点前，要把它所有的祖先节点都往下更新，旋转节点时也要让节点向下更新。最后，这个题，用单旋过的很愉快，用双旋卡着时间过。。。

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>using namespace std;#define key_val son[son[root][1]][0]typedef long long ll;const int N = 100010, INF = 0x3f3f3f3f, MOD = 1000000;int son[N][2], pre[N], siz[N];ll key[N], val[N], lazy[N];int root, num, cas;int arr[N];int n, m;void new_node(int &x, int fa, int v){    x = ++num;    pre[x] = fa, key[x] = val[x] = v;    siz[x] = 1, lazy[x] = 0;    son[x][0] = son[x][1] = 0;}void push_up(int x){    siz[x] = siz[son[x][0]] + siz[son[x][1]] + 1;    val[x] = key[x] + lazy[x] + val[son[x][0]] + val[son[x][1]];}void push_down(int x){    if(lazy[x])    {        key[x] += lazy[x];        lazy[son[x][0]] += lazy[x], lazy[son[x][1]] += lazy[x];        val[son[x][0]] += siz[son[x][0]] * lazy[x];        val[son[x][1]] += siz[son[x][1]] * lazy[x];        lazy[x] = 0;    }}void _rotate(int x, int dir){    int y = pre[x];    push_down(y), push_down(x);    son[y][!dir] = son[x][dir], pre[son[x][dir]] = y;    if(pre[y]) son[pre[y]][son[pre[y]][1]==y] = x;    pre[x] = pre[y];    son[x][dir] = y, pre[y] = x;    push_up(y);}void splay(int x, int goal){    push_down(x);    while(pre[x] != goal)    {        int y = pre[x];        if(pre[y] == goal) _rotate(x, son[y][0] == x);        else        {            int dir = son[pre[y]][0] == y;            if(son[y][dir] == x) _rotate(x, !dir), _rotate(x, dir);            else _rotate(y, dir), _rotate(x, dir);        }    }    push_up(x);    if(goal == 0) root = x;}//void splay(int x, int goal)//{//    push_down(x);//    while(pre[x] != goal) _rotate(x, son[pre[x]][0] == x);//    push_up(x);//    if(goal == 0) root = x;//}int get_prec(int x){    push_down(x);    int t = son[x][0];    push_down(t);    while(son[t][1]) t = son[t][1], push_down(t);    return t;}int get_subs(int x){    push_down(x);    int t = son[x][1];    push_down(t);    while(son[t][0]) t = son[t][0], push_down(t);    return t;}int _find(int v){    int x = root;    push_down(x);    while(x && key[x] != v) x = son[x][key[x]<v], push_down(x);    return x;}void _delete(int v){    int x = _find(v);    if(!x) return;    splay(x, 0);    if(!son[root][0] || !son[root][1])        root = son[root][0] + son[root][1], pre[root] = 0;    else    {        int t = get_subs(root);        splay(t, root);        son[son[root][1]][0] = son[root][0], root = son[root][1];        pre[son[root][0]] = root, pre[root] = 0;        push_up(root);    }}int get_kth(int k){    int x = root;    push_down(x);    while(siz[son[x][0]] + 1 != k)    {        if(siz[son[x][0]] + 1 > k) x = son[x][0];        else k -= (siz[son[x][0]] + 1), x = son[x][1];        push_down(x);    }    return x;}bool _insert(int v){    if(!root) new_node(root, 0, v);    else    {        int x = root;        while(son[x][key[x]<v])        {            if(key[x] == v)            {                splay(x, 0);                return false;            }            x = son[x][key[x]<v];        }        new_node(son[x][key[x]<v], x, v);        splay(son[x][key[x]<v], 0);    }    return true;}void build(int &x, int l, int r, int fa){    if(l > r) return;    int mid = (l + r) >> 1;    new_node(x, fa, arr[mid]);    build(son[x][0], l, mid-1, x);    build(son[x][1], mid+1, r, x);    push_up(x);}ll query(int l, int r){    splay(get_kth(l), 0);    splay(get_kth(r+2), root);    return val[key_val];}void update(int l, int r, int v){    splay(get_kth(l), 0);    splay(get_kth(r+2), root);    lazy[key_val] += v;    val[key_val] += v * siz[key_val];}void init(){    root = num = 0;    son[root][0] = son[root][1] = siz[root] = pre[root] = 0;    key[root] = val[root] = lazy[root] = 0;    new_node(root, 0, 0);    new_node(son[root][1], root, 0);    build(key_val, 1, n, son[root][1]);    push_up(son[root][1]), push_up(root);}int main(){    while(~ scanf("%d%d", &n, &m))    {        for(int i = 1; i <= n; i++) scanf("%d", &arr[i]);        init();        char ch;        int a, b, c;        for(int i = 1; i <= m; i++)        {            scanf(" %c%d%d", &ch, &a, &b);            if(ch == 'Q') printf("%lld\n", query(a, b));            else scanf("%d", &c), update(a, b, c);        }    }    return 0;}