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BZOJ 1798 维护序列（多校连萌，对线段树进行加乘混合操作）

2022-08-04 13:15:00 【51CTO】

题目地址：http://www.lydsy.com/JudgeOnline/problem.php?id=1798

思路：对一段区间的数进行加乘混合操作，思路还是挺巧的，举个例子

sum[rt]为一段区间的和，对区间+x再乘以p(sum[rt]+x)*p=sum[rt]*p+x*p可以写成对这个区间乘以p，每次乘的时候对a[rt]乘p，这个思路很巧

AC代码：

       
       #include <iostream>
       
       #include <cstdio>
       
       #include <cstdlib>
       
       #include <algorithm>
       
       #include <queue>
       
       #include <stack>
       
       #include <map>
       
       #include <cstring>
       
       #include <climits>
       
       #include <cmath>
       
       #include <cctype>
       
       const 
       
       int 
       
       inf 
       
       = 
       
       0x3f3f3f3f;
       
       //1061109567
       
       typedef 
       
       long 
       
       long 
       
       LL;
       
       #define lson l,m,rt<<1
       
       #define rson m+1,r,rt<<1|1
       
       using 
       
       namespace 
       
       std;
       
       const 
       
       int 
       
       maxn 
       
       = 
       
       100010;
       
       LL 
       
       add[
       
       maxn
       
       <<
       
       2],
       
       mul[
       
       maxn
       
       <<
       
       2],
       
       sum[
       
       maxn
       
       <<
       
       2];
       
       LL 
       
       p;
       
       void 
       
       pushup(
       
       int 
       
       rt)
       
{
       
       sum[
       
       rt] 
       
       = (
       
       sum[
       
       rt
       
       <<
       
       1] 
       
       + 
       
       sum[
       
       rt
       
       <<
       
       1
       
       |
       
       1]) 
       
       % 
       
       p;
       
}
       
       void 
       
       pushdown(
       
       int 
       
       rt,
       
       int 
       
       m)
       
{
       
       if(
       
       add[
       
       rt] 
       
       == 
       
       0 
       
       && 
       
       mul[
       
       rt] 
       
       == 
       
       1)
       
       return;
       
       add[
       
       rt
       
       <<
       
       1] 
       
       = (
       
       add[
       
       rt
       
       <<
       
       1]
       
       *
       
       mul[
       
       rt] 
       
       + 
       
       add[
       
       rt]) 
       
       % 
       
       p;
       
       //前面包括的是乘，后面包括的是加和先加后乘的
       
       //假设sum[rt]为一段和，(sum[rt]+x)*p,最后的结果只是这一段的和乘以p加上x*p
       
       add[
       
       rt
       
       <<
       
       1
       
       |
       
       1] 
       
       = (
       
       add[
       
       rt
       
       <<
       
       1
       
       |
       
       1]
       
       *
       
       mul[
       
       rt] 
       
       + 
       
       add[
       
       rt]) 
       
       % 
       
       p;
       
       mul[
       
       rt
       
       <<
       
       1] 
       
       = (
       
       mul[
       
       rt
       
       <<
       
       1] 
       
       * 
       
       mul[
       
       rt]) 
       
       % 
       
       p;
       
       mul[
       
       rt
       
       <<
       
       1
       
       |
       
       1] 
       
       = (
       
       mul[
       
       rt
       
       <<
       
       1
       
       |
       
       1]
       
       *
       
       mul[
       
       rt]) 
       
       % 
       
       p;
       
       sum[
       
       rt
       
       <<
       
       1] 
       
       = (
       
       sum[
       
       rt
       
       <<
       
       1] 
       
       * 
       
       mul[
       
       rt] 
       
       + (
       
       m 
       
       - (
       
       m
       
       >>
       
       1)) 
       
       * 
       
       add[
       
       rt]) 
       
       % 
       
       p;
       
       //注意里面的参数
       
       sum[
       
       rt
       
       <<
       
       1
       
       |
       
       1] 
       
       = (
       
       sum[
       
       rt
       
       <<
       
       1
       
       |
       
       1] 
       
       * 
       
       mul[
       
       rt] 
       
       + (
       
       m
       
       >>
       
       1) 
       
       * 
       
       add[
       
       rt]) 
       
       % 
       
       p;
       
       add[
       
       rt] 
       
       = 
       
       0,
       
       mul[
       
       rt] 
       
       = 
       
       1;
       
}
       
       void 
       
       updata(
       
       int 
       
       L,
       
       int 
       
       R,
       
       int 
       
       value,
       
       int 
       
       l,
       
       int 
       
       r,
       
       int 
       
       rt,
       
       int 
       
       op)
       
{
       
       if(
       
       l 
       
       >= 
       
       L 
       
       && 
       
       r 
       
       <= 
       
       R)
       
    {
       
       if(
       
       op 
       
       == 
       
       1)
       
        {
       
       add[
       
       rt] 
       
       = 
       
       add[
       
       rt] 
       
       * 
       
       value 
       
       % 
       
       p;
       
       mul[
       
       rt] 
       
       = 
       
       mul[
       
       rt] 
       
       * 
       
       value 
       
       % 
       
       p;
       
       sum[
       
       rt] 
       
       = 
       
       sum[
       
       rt] 
       
       * 
       
       value 
       
       % 
       
       p;
       
        }
       
       else
       
        {
       
       add[
       
       rt] 
       
       = (
       
       add[
       
       rt] 
       
       + 
       
       value) 
       
       % 
       
       p;
       
       sum[
       
       rt] 
       
       = (
       
       sum[
       
       rt] 
       
       + (
       
       r 
       
       - 
       
       l 
       
       + 
       
       1) 
       
       * (
       
       LL)
       
       value) 
       
       % 
       
       p;
       
        }
       
       return;
       
    }
       
       pushdown(
       
       rt,
       
       r
       
       -
       
       l
       
       +
       
       1);
       
       int 
       
       m 
       
       = (
       
       l 
       
       + 
       
       r)
       
       >>
       
       1;
       
       if(
       
       L 
       
       <= 
       
       m) 
       
       updata(
       
       L,
       
       R,
       
       value,
       
       lson,
       
       op);
       
       if(
       
       R 
       
       > 
       
       m) 
       
       updata(
       
       L,
       
       R,
       
       value,
       
       rson,
       
       op);
       
       pushup(
       
       rt);
       
}
       
       void 
       
       build(
       
       int 
       
       l,
       
       int 
       
       r,
       
       int 
       
       rt)
       
{
       
       add[
       
       rt] 
       
       = 
       
       0,
       
       mul[
       
       rt] 
       
       = 
       
       1;
       
       if(
       
       l 
       
       == 
       
       r)
       
    {
       
       scanf(
       
       "%lld",
       
       &
       
       sum[
       
       rt]);
       
       return;
       
    }
       
       int 
       
       m 
       
       = (
       
       l 
       
       + 
       
       r) 
       
       >> 
       
       1;
       
       build(
       
       lson);
       
       build(
       
       rson);
       
       pushup(
       
       rt);
       
}
       
       LL 
       
       query(
       
       int 
       
       L,
       
       int 
       
       R,
       
       int 
       
       l,
       
       int 
       
       r,
       
       int 
       
       rt)
       
{
       
       if(
       
       l 
       
       >= 
       
       L 
       
       && 
       
       r 
       
       <= 
       
       R)
       
       return 
       
       sum[
       
       rt];
       
       pushdown(
       
       rt,
       
       r
       
       -
       
       l
       
       +
       
       1);
       
       int 
       
       m 
       
       = (
       
       l 
       
       + 
       
       r)
       
       >>
       
       1;
       
       LL 
       
       ans 
       
       = 
       
       0;
       
       if(
       
       L 
       
       <= 
       
       m) 
       
       ans 
       
       += 
       
       query(
       
       L,
       
       R,
       
       lson);
       
       if(
       
       R 
       
       > 
       
       m) 
       
       ans 
       
       += 
       
       query(
       
       L,
       
       R,
       
       rson);
       
       return 
       
       ans 
       
       % 
       
       p;
       
}
       
       int 
       
       main()
       
{
       
       int 
       
       n;
       
       while(
       
       scanf(
       
       "%d%lld",
       
       &
       
       n,
       
       &
       
       p) 
       
       != 
       
       EOF)
       
    {
       
       build(
       
       1,
       
       n,
       
       1);
       
       int 
       
       m;
       
       scanf(
       
       "%d",
       
       &
       
       m);
       
       for(
       
       int 
       
       i
       
       =
       
       0; 
       
       i
       
       <
       
       m; 
       
       i
       
       ++)
       
        {
       
       int 
       
       x,
       
       left,
       
       right,
       
       value;
       
       scanf(
       
       "%d",
       
       &
       
       x);
       
       if(
       
       x 
       
       < 
       
       3)
       
            {
       
       scanf(
       
       "%d%d%d",
       
       &
       
       left,
       
       &
       
       right,
       
       &
       
       value);
       
       updata(
       
       left,
       
       right,
       
       value,
       
       1,
       
       n,
       
       1,
       
       x);
       
            }
       
       else
       
            {
       
       scanf(
       
       "%d%d",
       
       &
       
       left,
       
       &
       
       right);
       
       printf(
       
       "%lld\n",
       
       query(
       
       left,
       
       right,
       
       1,
       
       n,
       
       1));
       
            }
       
        }
       
    }
       
       return 
       
       0;
       
}
      
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