/*
sin(x + v) = sinx*cosv+sinvcosx
cos(x + v) = cosx*cosv-sinx*sinv
sin(x1 + v) + sin(x2 + v) = cosv*(sinx1+sinx2) + sinv*(cosx1+cosx2)
cos(x1 + v) + cos(x1 + v) = cosv*(cosx1+cosx2) - sinv*(sinx1+sinx2)
*/
#include<iostream>
#include<algorithm>
#include<math.h>
#include<map>
/*
// sin(x + v) = sinx*cosv+sinvcosx
// cos(x + v) = cosx*cosv-sinx*sinv
// sin(x1 + v) + sin(x2 + v) = cosv*(sinx1+sinx2) + sinv*(cosx1+cosx2)
// cos(x1 + v) + cos(x1 + v) = cosv*(cosx1+cosx2) - sinv*(sinx1+sinx2)
*/
using namespace std;
typedef long long ll;
const int maxn=1e6+100;
struct node{
int l,r;
double sinsum,cossum;
double lazy;
}t[maxn];
const double eps=1e-8;
double a[maxn];
void push(int p){
double sinval,cosval,tsin,tcos;
if(fabs(t[p].lazy)>eps){
tsin=sin(t[p].lazy);
tcos=cos(t[p].lazy);
sinval=t[2*p].sinsum;
cosval=t[2*p].cossum;
t[2*p].sinsum=tsin*cosval+tcos*sinval;
t[2*p].cossum=tcos*cosval-tsin*sinval;
t[2*p].lazy+=t[p].lazy;
sinval=t[2*p+1].sinsum;
cosval=t[2*p+1].cossum;
t[2*p+1].sinsum=tsin*cosval+tcos*sinval;
t[2*p+1].cossum=tcos*cosval-tsin*sinval;
t[2*p+1].lazy+=t[p].lazy;
t[p].lazy=0.0;
}
}
void build(int p,int l,int r){
t[p].l=l;
t[p].r=r;
t[p].lazy=0.0;
if(l==r){
t[p].sinsum=1.0*sin(a[l]);
t[p].cossum=1.0*cos(a[l]);
return ;
}
int mid=(t[p].l+t[p].r)/2;
build(2*p,l,mid);
build(2*p+1,mid+1,r);
t[p].sinsum=t[2*p].sinsum+t[2*p+1].sinsum;
t[p].cossum=t[2*p].cossum+t[2*p+1].cossum;
}
void add(int p,int l,int r,double k){
double sinval,cosval,tsin,tcos;
if(l<=t[p].l&&r>=t[p].r){
sinval=sin(k),cosval=cos(k),tsin=t[p].sinsum,tcos=t[p].cossum;
t[p].lazy+=k;
t[p].sinsum=tsin*cosval+tcos*sinval;
t[p].cossum=tcos*cosval-tsin*sinval;
return ;
}
int mid=(t[p].l+t[p].r)/2;
push(p);
if(l<=mid){
add(2*p,l,r,k);
}
if(r>mid){
add(2*p+1,l,r,k);
}
t[p].sinsum=t[2*p].sinsum+t[2*p+1].sinsum;
t[p].cossum=t[2*p].cossum+t[2*p+1].cossum;
}
double query(int p,int l,int r){
if(t[p].l>=l&&t[p].r<=r){
return t[p].sinsum;
}
double ans=0.0;
int mid=(t[p].l+t[p].r)/2;
push(p);
if(l<=mid){
ans+=query(2*p,l,r);
}
if(r>mid){
ans+=query(2*p+1,l,r);
}
return ans;
}
int main(){
int n,m;
cin>>n;
for(int i=1;i<=n;i++){
scanf("%lf",&a[i]);
}
build(1,1,n);
cin>>m;
int op,x,y;
double c;
for(int i=1;i<=m;i++){
scanf("%d%d%d",&op,&x,&y);
if(op==1){
scanf("%lf",&c);
add(1,x,y,c);
}
else{
double ans=query(1,x,y);
printf("%.1lf\n",ans);
}
}
}
这个题要维护两个值就是区间sin和 和 区间cos和
#include<iostream>#include<algorithm>#include<math.h> #include<map>/*// sin(x + v) = sinx*cosv+sinvcosx// cos(x + v) = cosx*cosv-sinx*sinv
// sin(x1 + v) + sin(x2 + v) = cosv*(sinx1+sinx2) + sinv*(cosx1+cosx2)// cos(x1 + v) + cos(x1 + v) = cosv*(cosx1+cosx2) - sinv*(sinx1+sinx2)*/using namespace std;typedef long long ll;const int maxn=1e6+100;struct node{int l,r;double sinsum,cossum;double lazy;}t[maxn];const double eps=1e-8;double a[maxn];void push(int p){double sinval,cosval,tsin,tcos;if(fabs(t[p].lazy)>eps){tsin=sin(t[p].lazy);tcos=cos(t[p].lazy);sinval=t[2*p].sinsum;cosval=t[2*p].cossum; t[2*p].sinsum=tsin*cosval+tcos*sinval;t[2*p].cossum=tcos*cosval-tsin*sinval;t[2*p].lazy+=t[p].lazy;sinval=t[2*p+1].sinsum;cosval=t[2*p+1].cossum;t[2*p+1].sinsum=tsin*cosval+tcos*sinval;t[2*p+1].cossum=tcos*cosval-tsin*sinval;t[2*p+1].lazy+=t[p].lazy;t[p].lazy=0.0;} }void build(int p,int l,int r){t[p].l=l;t[p].r=r;t[p].lazy=0.0;if(l==r){t[p].sinsum=1.0*sin(a[l]);t[p].cossum=1.0*cos(a[l]);return ;}int mid=(t[p].l+t[p].r)/2;build(2*p,l,mid);build(2*p+1,mid+1,r);t[p].sinsum=t[2*p].sinsum+t[2*p+1].sinsum;t[p].cossum=t[2*p].cossum+t[2*p+1].cossum;}void add(int p,int l,int r,double k){double sinval,cosval,tsin,tcos;if(l<=t[p].l&&r>=t[p].r){sinval=sin(k),cosval=cos(k),tsin=t[p].sinsum,tcos=t[p].cossum;t[p].lazy+=k;t[p].sinsum=tsin*cosval+tcos*sinval;t[p].cossum=tcos*cosval-tsin*sinval;return ; }int mid=(t[p].l+t[p].r)/2;push(p);if(l<=mid){add(2*p,l,r,k);}if(r>mid){add(2*p+1,l,r,k);}t[p].sinsum=t[2*p].sinsum+t[2*p+1].sinsum;t[p].cossum=t[2*p].cossum+t[2*p+1].cossum;}double query(int p,int l,int r){if(t[p].l>=l&&t[p].r<=r){return t[p].sinsum;}double ans=0.0;int mid=(t[p].l+t[p].r)/2;push(p);if(l<=mid){ans+=query(2*p,l,r);}if(r>mid){ans+=query(2*p+1,l,r);} return ans;} int main(){int n,m;cin>>n;for(int i=1;i<=n;i++){scanf("%lf",&a[i]);}build(1,1,n);cin>>m;int op,x,y;double c;for(int i=1;i<=m;i++){scanf("%d%d%d",&op,&x,&y);if(op==1){scanf("%lf",&c);add(1,x,y,c);}else{double ans=query(1,x,y);printf("%.1lf\n",ans);}}}