[HDOJ4578]Transformation（线段树，多延迟标记）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4578

四种操作：查询、加法、乘法、改数。应该是需要维护三个lazy标记，然后就是套路了。查询是区间内所有的数的p次幂然后再求和，这个p只有三个值（1，2，3），直接维护三棵线段树，分别是1 2 3次幂。

注意延迟标记的时候，如果有改数，那之前的加法和乘法就可以不用做了。在更新乘法的时候，如果有加法存在，那加法的标记应该更新，乘一下乘法的数，因为（a+b）*c = a*c+b*c，父亲是a+b，儿子是a和b。

pushdown的顺序就是：改数、乘法、加法。三种询问好处理，(a+b)^2和(a+b)^3展开就行了。

这是我做过的比较复杂的线段树了。

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 */
 #include <algorithm>
 #include <iostream>
 #include <iomanip>
 #include <cstring>
 #include <climits>
 #include <complex>
 #include <fstream>
 #include <cassert>
 #include <cstdio>
 #include <bitset>
 #include <vector>
 #include <deque>
 #include <queue>
 #include <stack>
 #include <ctime>
 #include <set>
 #include <map>
 #include <cmath>
 using namespace std;
 #define fr first
 #define sc second
 #define cl clear
 #define BUG puts("here!!!")
 #define W(a) while(a--)
 #define pb(a) push_back(a)
 #define Rlf(a) scanf("%lf", &a);
 #define Rint(a) scanf("%d", &a)
 #define Rll(a) scanf("%I64d", &a)
 #define Rs(a) scanf("%s", a)
 #define Cin(a) cin >> a
 #define FRead() freopen("in", "r", stdin)
 #define FWrite() freopen("out", "w", stdout)
 #define Rep(i, len) for(int i = 0; i < (len); i++)
 #define For(i, a, len) for(int i = (a); i < (len); i++)
 #define Cls(a) memset((a), 0, sizeof(a))
 #define Clr(a, x) memset((a), (x), sizeof(a))
 #define Full(a) memset((a), 0x7f7f, sizeof(a))
 #define lrt rt << 1
 #define rrt rt << 1 | 1
 #define pi 3.14159265359
 #define RT return
 #define lowbit(x) x & (-x)
 #define onenum(x) __builtin_popcount(x)
 typedef long long LL;
 typedef long double LD;
 typedef unsigned long long ULL;
 typedef pair<int, int> pii;
 typedef pair<string, int> psi;
 typedef map<string, int> msi;
 typedef vector<int> vi;
 typedef vector<LL> vl;
 typedef vector<vl> vvl;
 typedef vector<bool> vb;

 inline bool scan_d(int &num) {
     char in;bool IsN=false;
     in=getchar();
     if(in==EOF) return false;
     while(in!='-'&&(in<''||in>'')) in=getchar();
     if(in=='-'){ IsN=true;num=;}
     else num=in-'';
     while(in=getchar(),in>=''&&in<=''){
             num*=,num+=in-'';
     }
     if(IsN) num=-num;
     return true;
 }

 const int mod = ;
 const int maxn = ;

 LL add[maxn<<], put[maxn<<], mul[maxn<<];
 LL sum1[maxn<<], sum2[maxn<<], sum3[maxn<<];

 void pushUP(int rt) {
     sum1[rt] = (sum1[lrt] + sum1[rrt]) % mod;
     sum2[rt] = (sum2[lrt] + sum2[rrt]) % mod;
     sum3[rt] = (sum3[lrt] + sum3[rrt]) % mod;
 }

 void pushDOWN(int rt, int m) {
     if(put[rt]) {
         put[lrt] = put[rrt] = put[rt];
         add[lrt] = add[rrt] = ;
         mul[lrt] = mul[rrt] = ;
         sum1[lrt] = (m - (m >> )) % mod * put[rt] % mod;
         sum1[rrt] = (m >> ) % mod * put[rt] % mod;
         sum2[lrt] = (m - (m >> )) % mod * put[rt] % mod * put[rt] % mod;
         sum2[rrt] = (m >> ) % mod * put[rt] % mod * put[rt] % mod;
         sum3[lrt] = (m - (m >> ) % mod) * (put[rt] * put[rt]) % mod * put[rt] % mod % mod;
         sum3[rrt] = (m >> ) % mod * put[rt] * put[rt] % mod * put[rt] % mod % mod;
         put[rt] = ;
     }
     if(mul[rt] != ) {
         mul[lrt] = mul[lrt] * mul[rt] % mod;
         mul[rrt] = mul[rrt] * mul[rt] % mod;
         if(add[lrt]) add[lrt] = (add[lrt] * mul[rt]) % mod;
         if(add[rrt]) add[rrt] = (add[rrt] * mul[rt]) % mod;
         sum1[lrt] = (sum1[lrt] * mul[rt]) % mod;
         sum1[rrt] = (sum1[rrt] * mul[rt]) % mod;
         sum2[lrt] = (sum2[lrt] * mul[rt]) % mod * mul[rt] % mod;
         sum2[rrt] = (sum2[rrt] * mul[rt]) % mod * mul[rt] % mod;
         sum3[lrt] = (sum3[lrt] * mul[rt]) % mod * mul[rt] % mod * mul[rt] % mod;
         sum3[rrt] = (sum3[rrt] * mul[rt]) % mod * mul[rt] % mod * mul[rt] % mod;
         mul[rt] = ;
     }
     if(add[rt]) {
         add[lrt] = (add[lrt] + add[rt]) % mod;
         add[rrt] = (add[rrt] + add[rt]) % mod;
         sum3[lrt] = (sum3[lrt] + ((add[rt] * add[rt] % mod) * add[rt] % mod * (m - (m >> )) % mod) +  * add[rt] * ((sum2[lrt] + sum1[lrt] * add[rt]) % mod)) % mod;
         sum3[rrt] = (sum3[rrt] + ((add[rt] * add[rt] % mod) * add[rt] % mod * (m >> ) % mod) +  * add[rt] * ((sum2[rrt] + sum1[rrt] * add[rt]) % mod)) % mod;
         sum2[lrt] = (sum2[lrt] + ((add[rt] * add[rt] % mod) * (m - (m >> )) % mod) + ( * sum1[lrt] * add[rt] % mod)) % mod;
         sum2[rrt] = (sum2[rrt] + (((add[rt] * add[rt] % mod) * (m >> )) % mod) + ( * sum1[rrt] * add[rt] % mod)) % mod;
         sum1[lrt] = (sum1[lrt] + (m - (m >> )) * add[rt]) % mod;
         sum1[rrt] = (sum1[rrt] + (m >> ) * add[rt]) % mod;
         add[rt] = ;
     }
 }

 void build(int l, int r, int rt) {
     add[rt] = put[rt] = ; mul[rt] = ;
     sum1[rt] =sum2[rt] = sum3[rt] = ;
     if(l == r) return;
     int m = (l + r) >> ;
     build(l, m, lrt);
     build(m+, r, rrt);
 }

 void update(int L, int R, int c, int ch, int l, int r, int rt) {
     if(L <= l && r <= R) {
         if(ch == ) {
             put[rt] = c;
             add[rt] = ;
             mul[rt] = ;
             sum1[rt] = ((r - l + ) * c) % mod;
             sum2[rt] = (((r - l + ) * c) % mod * c) % mod;
             sum3[rt] = ((((r - l + ) * c) % mod * c) % mod * c) % mod;
         }
         if(ch == ) {
             mul[rt] = (mul[rt] * c) % mod;
             if(add[rt]) add[rt] = (add[rt] * c) % mod;
             sum1[rt] = (sum1[rt] * c) % mod;
             sum2[rt] = ((sum2[rt] * c) % mod * c) % mod;
             sum3[rt] = (((sum3[rt] * c) % mod * c) % mod * c) % mod;
         }
         if(ch == ) {
             add[rt] += c;
             sum3[rt] = (sum3[rt] + (((c * c) % mod * c) % mod * (r - l + )) % mod +  * c * ((sum2[rt] + sum1[rt] * c) % mod)) % mod;
             sum2[rt] = (sum2[rt] + (c * c % mod * (r - l + ) % mod) +  * sum1[rt] * c) % mod;
             sum1[rt] = (sum1[rt] + (r - l + ) * c) % mod;
         }
         return;
     }
     pushDOWN(rt, r-l+);
     int m = (l + r) >> ;
     if(R <= m) update(L, R, c, ch, l, m, lrt);
     else if(L > m) update(L, R, c, ch, m+, r, rrt);
     else {
         update(L, R, c, ch, l, m, lrt);
         update(L, R, c, ch, m+, r, rrt);
     }
     pushUP(rt);
 }

 LL query(int L, int R, int p, int l, int r, int rt) {
     if(L <= l && r <= R) {
         if(p == ) return sum1[rt] % mod;
         if(p == ) return sum2[rt] % mod;
         if(p == ) return sum3[rt] % mod;
     }
     pushDOWN(rt, r-l+);
     int m = (l + r) >> ;
     if(R <= m) return query(L, R, p, l, m, lrt);
     else if(m < L) return query(L, R, p, m+, r, rrt);
     else return (query(L, R, p, l, m, lrt) + query(L, R, p, m+, r, rrt)) % mod;
 }

 int n, m;
 int a, b, c, ch;

 int main() {
     // FRead();
     while(~scan_d(n) && ~scan_d(m) && n + m) {
         build(, n, );
         W(m) {
             scan_d(ch); scan_d(a); scan_d(b); scan_d(c);
             if(ch != ) update(a, b, c, ch, , n, );
             else cout << query(a, b, c, , n, ) << endl;
         }
     }
     RT ;
 }