线段树の二 区间乘+区间加

Posted 2020-10-02 Wider Gao

具体就不解释了，看上一篇文章

放代码

注意点：！！！！

注意运算符优先级

比如：

a*=b%p 是b先mod p再与a相乘

参见：https://baike.baidu.com/item/%E8%BF%90%E7%AE%97%E7%AC%A6%E4%BC%98%E5%85%88%E7%BA%A7/4752611?fr=aladdin

/*******************************
线段树V2.0
支持区间加、区间乘、区间和查询
********************************/
#include<iostream>
#include<cstdio>
#include<cstring>
#define N 1000010
using namespace std;
struct node
{
	int left;//节点所代表区间左端
	int right;//节点所代表区间右端
	long long sum;//区间和
	long long add;//区间加Lazy标记
	long long mult;//区间乘Lazy标记 
	node(){mult=1;}
} tree[N];
long long a[N];
int n,m,p;//n:区间大小 m:操作次数 p:取模 

//left:当前区间左端 right:当前区间右端 node:当前节点
void Build_Tree(int left,int right,int node)
{
	tree[node].left=left;
	tree[node].right=right;
	if(left==right) tree[node].sum=a[left];
	else
	{
		int mid=(left+right)>>1;
		Build_Tree(left,mid,node<<1);
		Build_Tree(mid+1,right,node<<1|1);
		tree[node].sum=(tree[node<<1].sum+tree[node<<1|1].sum)%p;
	}
}

//标记下放 node:当前节点
void Push_Down(int node)
{
	if(tree[node].add==0&&tree[node].mult==1) return;
	tree[node<<1].mult=tree[node<<1].mult*tree[node].mult%p;
	tree[node<<1|1].mult=tree[node<<1|1].mult*tree[node].mult%p;
	tree[node<<1].add=tree[node<<1].add*tree[node].mult%p;
	tree[node<<1|1].add=tree[node<<1|1].add*tree[node].mult%p;
	tree[node<<1].sum=tree[node<<1].sum*tree[node].mult%p;
	tree[node<<1|1].sum=tree[node<<1|1].sum*tree[node].mult%p;
	tree[node].mult=1;
	tree[node<<1].add=(tree[node<<1].add+tree[node].add)%p;
	tree[node<<1|1].add=(tree[node<<1|1].add+tree[node].add)%p;
	tree[node<<1].sum=(tree[node<<1].sum+tree[node].add*(tree[node<<1].right-tree[node<<1].left+1))%p;
	tree[node<<1|1].sum=(tree[node<<1|1].sum+tree[node].add*(tree[node<<1|1].right-tree[node<<1|1].left+1))%p;
	tree[node].add=0;
}

//上推 node:当前节点
void Push_Up(int node)
{
	tree[node].sum=(tree[node<<1].sum+tree[node<<1|1].sum)%p;
}

//区间加操作 left:操作区间左端点 right:操作区间右端点 node:当前节点 value:操作值
void Add_Range(int left,int right,int node,long long value)
{
	if(tree[node].left>=left&&tree[node].right<=right)
	{
		tree[node].add+=value%p;
		tree[node].sum+=value*(tree[node].right-tree[node].left+1)%p;
		return;
	}
	Push_Down(node);
	int mid=(tree[node].left+tree[node].right)>>1;
	if(left<=mid) Add_Range(left,right,node<<1,value);
	if(right>mid) Add_Range(left,right,node<<1|1,value);
	Push_Up(node);
}

//区间乘操作 left:操作区间左端点 right:操作区间右端点 node:当前节点 value:操作值
void Mult_Range(int left,int right,int node,long long value)
{
	if(tree[node].left>=left&&tree[node].right<=right)
	{
		tree[node].mult=tree[node].mult*value%p;
		tree[node].add=tree[node].add*value%p;
		tree[node].sum=tree[node].sum*value%p;
		return;
	}
	Push_Down(node);
	int mid=(tree[node].left+tree[node].right)>>1;
	if(left<=mid) Mult_Range(left,right,node<<1,value);
	if(right>mid) Mult_Range(left,right,node<<1|1,value);
	Push_Up(node);
}

//区间和查询 left:查询区间左端点 right:查询区间右端点 node:当前节点
long long Query_Sum(int left,int right,int node)
{
	if(tree[node].left>right||tree[node].right<left) 
	return 0;
	Push_Down(node);
	if(tree[node].left>=left&&tree[node].right<=right) 
	return tree[node].sum%p;
	return (Query_Sum(left,right,node*2)+Query_Sum(left,right,node*2+1))%p;
}

int main()
{

	cin>>n>>m>>p;
	for(int i=1; i<=n; i++) cin>>a[i];
	Build_Tree(1,n,1);
	while(m--)
	{
		int x,y,c;
		cin>>c>>x>>y;
		if(c==1)//区间乘操作 
		{
			long long v;
			cin>>v;
			Mult_Range(x,y,1,v);
		}
		if(c==2)//区间加操作
		{
			long long v;
			cin>>v;
			Add_Range(x,y,1,v);
		}
		if(c==3)//查询
		cout<<Query_Sum(x,y,1)<<endl;
	}
	return 0;
}