# CF719E. Sasha and Array

1. a[l..r] 每一项都加一个常数 C, 其中 0 ≤ C ≤ 10^9
2. 求 F[a[l]]+F[a[l+1]]+...F[a[r]] mod 1e9+7 的余数

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long ll;
#define lc x<<1
#define rc x<<1|1
#define mid ((l+r)>>1)
#define lson lc, l, mid
#define rson rc, mid+1, r
const int N = 1e5+5, P = 1e9+7;

int n, m;
struct Matrix {
ll a[2][2];
ll* operator [](int x) {return a[x];}
Matrix(int p=0) {
if(!p) a[0][0] = a[0][1] = a[1][0] = a[1][1] = 0;
else a[0][0] = a[1][1] = 1, a[0][1] = a[1][0] = 0;
}
} B;

Matrix operator + (Matrix a, Matrix b) {
Matrix c;
for(int i=0; i<2; i++)
for(int j=0; j<2; j++)
c[i][j] = (a[i][j] + b[i][j]) %P;
return c;
}

Matrix operator * (Matrix a, Matrix b) {
Matrix c;
for(int i=0; i<2; i++)
for(int j=0; j<2; j++) {
ll &x = c[i][j];
for(int k=0; k<2; k++)
x = (x + a[i][k] * b[k][j] %P) %P;
}
return c;
}

Matrix operator ^ (Matrix a, int b) {
Matrix ans(1);
ans[0][0] = ans[1][1] = 1;
for(; b; b>>=1, a=a*a)
if(b & 1) ans = ans*a;
return ans;
}

struct meow {
Matrix f;
Matrix v;
int c;
meow() {f[0][0] = 1; v[0][0] = v[1][1] = 1;}
} t[N<<2];

void paint(int x, int l, int r, int d, Matrix &v) {
t[x].c += d;
t[x].v = v * t[x].v;
t[x].f = v * t[x].f;
}
void push_down(int x, int l, int r) {
if(t[x].c) {
paint(lson, t[x].c, t[x].v);
paint(rson, t[x].c, t[x].v);
t[x].c = 0;
t[x].v = Matrix(1);
}
}
void merge(int x) {
t[x].f = t[lc].f + t[rc].f;
}

void build(int x, int l, int r) {
if(l == r) {
cin >> t[x].c;
if(t[x].c > 1) t[x].f = (B ^ (t[x].c - 1)) * t[x].f;
} else {
build(lson);
build(rson);
merge(x);
}
}

void Add(int x, int l, int r, int ql, int qr, int d, Matrix &v) {
if(ql <= l && r <= qr) paint(x, l, r, d, v);
else {
push_down(x, l, r);
if(ql <= mid) Add(lson, ql, qr, d, v);
if(mid < qr)  Add(rson, ql, qr, d,v );
merge(x);
}
}

ll Que(int x, int l, int r, int ql, int qr) {
if(ql <= l && r <= qr) return t[x].f[0][0];
else {
push_down(x, l, r);
ll ans = 0;
if(ql <= mid) ans = (ans + Que(lson, ql, qr)) %P;
if(mid < qr)  ans = (ans + Que(rson, ql, qr)) %P;
return ans;
}
}

int main() {
//freopen("in", "r", stdin);
ios::sync_with_stdio(false); cin.tie(); cout.tie();

B[0][0] = B[0][1] = B[1][0] = 1;
cin >> n >> m;
build(1, 1, n);

for(int i=1; i<=m; i++) {
int tp, l, r, x;
cin >> tp >> l >> r;
if(tp == 1) {
cin >> x;
Matrix t = B^x;
Add(1, 1, n, l, r, x, t);
} else cout << Que(1, 1, n, l, r) << '\n';
}

posted @ 2018-07-16 20:16  Candy?  阅读(263)  评论(0编辑  收藏