[CF 718C] Sasha and Array

传送门

Solution

用线段树维护矩阵

第一个操作相当于区间乘

第二个操作相当于区间求和

Code 

#include<bits/stdc++.h>
#define ll long long
#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))
inline int read()
{
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+ch-'0';ch=getchar();}
	return x*f;
}
#define mod 1000000007
#define MN 100005
#define mid ((l+r)>>1)
int n,m;
struct matrix
{
	ll a[2][2];
    matrix(){memset(a,0,sizeof a);}
    matrix operator *(const matrix &b) const
    {
        register matrix c;register int i,j,k;
        for(i=0;i<2;++i)for(j=0;j<2;j++)for(k=0;k<2;++k)
        (c.a[i][j]+=b.a[i][k]*a[k][j]%mod)%=mod;
        return c;
    }
    matrix operator +(const matrix &b) const
    {
    	register matrix c;register int i,j;
    	for(i=0;i<2;++i)for(j=0;j<2;++j) c.a[i][j]=(b.a[i][j]+a[i][j])%mod;
    	return c;
	}
    
}tmp,xxx,t[MN<<2],lazy[MN<<2],orig,pro,unit;
void fpow(int x)
{
	for(tmp=unit,xxx=pro;x;x>>=1,xxx=xxx*xxx) if(x&1) tmp=tmp*xxx;
}
void print(matrix x)
{
	for(int i=0;i<2;++i)
	{
		for(int j=0;j<2;++j) printf("%d ",x.a[i][j]);
		puts("");
	}
	puts("");
}
inline void pushdown(int x)
{
	t[x<<1]=t[x<<1]*lazy[x];t[x<<1|1]=t[x<<1|1]*lazy[x];
	lazy[x<<1]=lazy[x<<1]*lazy[x];lazy[x<<1|1]=lazy[x<<1|1]*lazy[x];
	lazy[x]=unit;
}
void build(int x,int l,int r)
{
	if(l==r){fpow(read()-1),t[x]=orig*tmp,lazy[x]=unit;return;}
	build(x<<1,l,mid);build(x<<1|1,mid+1,r);
	t[x]=t[x<<1]+t[x<<1|1];lazy[x]=unit;
}
matrix query(int x,int l,int r,int a,int b)
{
	if(a==l&&r==b) return t[x];
	pushdown(x);
	if(b<=mid) return query(x<<1,l,mid,a,b);
	if(a>mid) return query(x<<1|1,mid+1,r,a,b);
	return query(x<<1,l,mid,a,mid)+query(x<<1|1,mid+1,r,mid+1,b);
}
void Modify(int x,int l,int r,int a,int b)
{
	if(a==l&&b==r){lazy[x]=lazy[x]*tmp,t[x]=t[x]*tmp;return;}
	pushdown(x);
	if(b<=mid) Modify(x<<1,l,mid,a,b);
	else if(a>mid) Modify(x<<1|1,mid+1,r,a,b);
	else Modify(x<<1,l,mid,a,mid),Modify(x<<1|1,mid+1,r,mid+1,b);
	t[x]=t[x<<1]+t[x<<1|1];
}
int main()
{
	unit.a[0][0]=unit.a[1][1]=1;
	orig.a[0][0]=1;
	pro.a[0][0]=pro.a[0][1]=pro.a[1][0]=1;
	n=read(),m=read();
	build(1,1,n);
	register int type,l,r;
	while(m--)
	{
		type=read();l=read();r=read();
		if(type==1) fpow(read()),Modify(1,1,n,l,r);
		else printf("%lld\n",query(1,1,n,l,r).a[0][0]);
	}
	return 0;
}

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