hdu 4578 Transformation 线段树

题意：有4种操作，1 x y c 给从x到y的所有数加上c，2 x y c 给从x到y的所有数乘上c，3 x y c把从x到y的所有数变成c，4 x y p，计算从x到y的p次方的和,x^p + (x+1)^p + … + y^p (p = 1 2 3)

思路：sum1,sum2,sum3代表p=1,p=2,p=3,时候区间的值，这三个值是可以直接推出来的。关于加和乘的问题，如果直接搞是有问题的，所以变成区间内的和先乘以一个数，再加上一个数的形式，注意，在乘的时候要对加数的lazy进行处理。在第三种操作的时候要取消前两种操作的之前留下的影响。

坑点:wa了之后百思不得其解，直到心一横，所有的都改为long long类型，才过。

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

#include <cstdio>
#include <cmath>
#include <iostream>

#define dist(rt) (t[rt].y - t[rt].x + 1)

using namespace std;

typedef long long LL;

const int MAXN = 1e6+5;
LL MOD = 10007;

struct Node {
    LL x,y;
    LL add,mul,set;
    LL sum1,sum2,sum3;
}t[MAXN<<2];

LL n,m;
LL tmp_sum1,tmp_sum2;

void Push_Up(LL rt) {
    t[rt].sum1 = (t[rt<<1].sum1 + t[rt<<1|1].sum1)%MOD;
    t[rt].sum2 = (t[rt<<1].sum2 + t[rt<<1|1].sum2)%MOD;
    t[rt].sum3 = (t[rt<<1].sum3 + t[rt<<1|1].sum3)%MOD;
}

void Push_Down(LL rt) {
    if(t[rt].set) {
        LL u = t[rt].set;

        t[rt<<1].sum1 = (dist(rt<<1) * u) % MOD; 
        t[rt<<1].sum2 = (dist(rt<<1) * u * u) % MOD; 
        t[rt<<1].sum3 = (dist(rt<<1) * u * u * u) % MOD;

        t[rt<<1|1].sum1 = (dist(rt<<1|1) * u) % MOD;
        t[rt<<1|1].sum2 = (dist(rt<<1|1) * u * u) % MOD;
        t[rt<<1|1].sum3 = (dist(rt<<1|1) * u * u * u) % MOD;

        t[rt<<1].set = t[rt<<1|1].set = t[rt].set;
        t[rt<<1].add = t[rt<<1|1].add = 0;
        t[rt<<1].mul = t[rt<<1|1].mul = 1;

        t[rt].set = 0;
    }
    if(t[rt].mul > 1) {
        LL u = t[rt].mul;

        t[rt<<1].sum1 = (t[rt<<1].sum1 * u) % MOD;
        t[rt<<1].sum2 = (t[rt<<1].sum2 * u * u) % MOD;
        t[rt<<1].sum3 = (t[rt<<1].sum3 * u * u * u) % MOD;

        t[rt<<1|1].sum1 = (t[rt<<1|1].sum1 * u) % MOD;
        t[rt<<1|1].sum2 = (t[rt<<1|1].sum2 * u * u) % MOD;
        t[rt<<1|1].sum3 = (t[rt<<1|1].sum3 * u * u * u) % MOD;

        t[rt<<1].mul = (t[rt<<1].mul * u)%MOD; 
        t[rt<<1|1].mul = (t[rt<<1|1].mul * u)%MOD;
        t[rt<<1].add = (t[rt<<1].add * u)%MOD;
        t[rt<<1|1].add = (t[rt<<1|1].add * u)%MOD;

        t[rt].mul = 1;
    }
    if(t[rt].add) {
        LL u = t[rt].add;

        tmp_sum1 = t[rt<<1].sum1;
        tmp_sum2 = t[rt<<1].sum2;

        t[rt<<1].sum1 = (t[rt<<1].sum1 + dist(rt<<1) * u)%MOD;
        t[rt<<1].sum2 = (t[rt<<1].sum2 + 2*u*tmp_sum1 + u*u*dist(rt<<1))%MOD;
        t[rt<<1].sum3 = (t[rt<<1].sum3 + 3*u*tmp_sum2 + 3*u*u*tmp_sum1 + u*u*u*dist(rt<<1)) % MOD;

        tmp_sum1 = t[rt<<1|1].sum1;
        tmp_sum2 = t[rt<<1|1].sum2;
        t[rt<<1|1].sum1 = (t[rt<<1|1].sum1 + dist(rt<<1|1) * u)%MOD;
        t[rt<<1|1].sum2 = (t[rt<<1|1].sum2 + 2*u*tmp_sum1 + u*u*dist(rt<<1|1))%MOD;
        t[rt<<1|1].sum3 = (t[rt<<1|1].sum3 + 3*u*tmp_sum2 + 3*u*u*tmp_sum1 + u*u*u*dist(rt<<1|1)) % MOD;

        t[rt<<1].add = (t[rt<<1].add + u)%MOD; 
        t[rt<<1|1].add = (t[rt<<1|1].add + u)%MOD;

        t[rt].add = 0;
    }
}

void Build(LL x,LL y,LL rt) {
    t[rt].x = (LL)x; t[rt].y = (LL)y;
    t[rt].add = t[rt].set = 0;
    t[rt].mul = 1;
    if(x == y) {
        t[rt].sum1 = t[rt].sum2 = t[rt].sum3 = 0;
        return ;
    }
    LL mid = (x + y) >> 1;
    Build(x,mid,rt<<1);
    Build(mid+1,y,rt<<1|1);
    Push_Up(rt);
}

void Update(LL rt,LL left,LL right,LL u,LL flag) {
    if(t[rt].x >= left && t[rt].y <= right) {
        if(flag == 1) {
            t[rt].add = (t[rt].add + u)%MOD;

            tmp_sum1 = t[rt].sum1;
            tmp_sum2 = t[rt].sum2;

            t[rt].sum1 = (t[rt].sum1 + dist(rt) * u)%MOD;
            t[rt].sum2 = (t[rt].sum2 + 2*u*tmp_sum1 + u*u*dist(rt))%MOD;
            t[rt].sum3 = (t[rt].sum3 + 3*u*tmp_sum2 + 3*u*u*tmp_sum1 + u*u*u*dist(rt)) % MOD;
        }
        else if(flag == 2) {
            t[rt].mul = (t[rt].mul * u) % MOD;
            t[rt].add = (t[rt].add * u) % MOD;
            t[rt].sum1 = (t[rt].sum1 * u) % MOD;
            t[rt].sum2 = (t[rt].sum2 * u * u) % MOD;
            t[rt].sum3 = (t[rt].sum3 * u * u * u) % MOD;
        }
        else {
            t[rt].mul = 1;
            t[rt].add = 0;
            t[rt].set = u;
            t[rt].sum1 = (dist(rt) * u)%MOD;
            t[rt].sum2 = (dist(rt) * u * u)%MOD;
            t[rt].sum3 = (dist(rt) * u * u * u)%MOD;
        }
        return ;
    }
    LL mid = (t[rt].x + t[rt].y) >> 1;
    Push_Down(rt);
    if(mid >= left) Update(rt<<1,left,right,u,flag);
    if(mid < right) Update(rt<<1|1,left,right,u,flag);
    Push_Up(rt);
}

LL sum1,sum2,sum3;

void Query(LL rt,LL left,LL right) {
    if(t[rt].x >= (LL)left && t[rt].y <= (LL)right) {
        sum1 = (sum1 + t[rt].sum1)%MOD;
        sum2 = (sum2 + t[rt].sum2)%MOD;
        sum3 = (sum3 + t[rt].sum3)%MOD;
        return ;
    }
    LL mid = (t[rt].x + t[rt].y) >> 1;
    Push_Down(rt);
    if(mid >= left) Query(rt<<1,left,right);
    if(mid < right) Query(rt<<1|1,left,right);
    Push_Up(rt);
}

void Print_Tree(LL rt) {
    printf("%I64d %I64d %I64d\n",t[rt].x,t[rt].y,t[rt].sum2);
    if(t[rt].x == t[rt].y) {
        //printf("%d ",t[rt].sum2);
        return ;
    }
    Push_Down(rt);
    Print_Tree(rt<<1);
    Print_Tree(rt<<1|1);
}

void input() {
    Build(1,n,1);
    LL x,y,u,ok;
    for(LL i = 1 ; i <= n ; i ++) {
        // Print_Tree(1);
        // puts("");
        scanf("%I64d %I64d %I64d %I64d",&ok,&x,&y,&u);
        if(ok <= 3) {
            Update(1,x,y,u,ok);
        }
        else {
            sum1 = sum2 = sum3 = 0;
            Query(1,x,y);
            if(u == 1) printf("%I64d\n",sum1);
            else if(u == 2) printf("%I64d\n",sum2);
            else printf("%I64d\n",sum3);
        }
    }
}

void solve() {

}

int main(void) {
    //freopen("a.in","r",stdin);
    while(scanf("%I64d %I64d",&n,&m),n+m) {
        input();
        solve();
    }
}