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文章目錄

• 題意：
• 思路：

題意：

給你一個長度為$n$的序列$a$，有$m$次操作，每次操作分兩種類型：

$(1)l,r,v$，將$a_l,a_{l+1},...,a_r$分別加上$v$。

$(2)l,r$，詢問${\sum }_{i=l}^r\sin (a_i)$ 。

思路：

閑的沒事來水倆題。

考慮高中的和差公式，$sin(a+b)=sin(a)cos(b)+sin(b)cos(a)$，所以我們可以多維護一個$cos$，讓后$cos(a+b)=cos(a)cos(b)?sin(x)sin(b)$，打個$lazy$，維護的時候注意一下細節(jié)即可。

瞎搞維護一下就好。

// Problem: P6327 區(qū)間加區(qū)間sin和 // Contest: Luogu // URL: https://www.luogu.com.cn/problem/P6327 // Memory Limit: 125 MB // Time Limit: 1000 ms // // Powered by CP Editor (https://cpeditor.org)//#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native") //#pragma GCC optimize(2) #include<cstdio> #include<iostream> #include<string> #include<cstring> #include<map> #include<cmath> #include<cctype> #include<vector> #include<set> #include<queue> #include<algorithm> #include<sstream> #include<ctime> #include<cstdlib> #include<random> #include<cassert> #define X first #define Y second #define L (u<<1) #define R (u<<1|1) #define pb push_back #define mk make_pair #define Mid ((tr[u].l+tr[u].r)>>1) #define Len(u) (tr[u].r-tr[u].l+1) #define random(a,b) ((a)+rand()%((b)-(a)+1)) #define db puts("---") using namespace std;//void rd_cre() { freopen("d://dp//data.txt","w",stdout); srand(time(NULL)); } //void rd_ac() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//AC.txt","w",stdout); } //void rd_wa() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//WA.txt","w",stdout); }typedef long long LL; typedef unsigned long long ULL; typedef pair<int,int> PII;const int N=200010,mod=1e9+7,INF=0x3f3f3f3f; const double eps=1e-6;int n,m; int a[N]; struct Node {int l,r;double sums,sumc;LL lazy; }tr[N<<2];void pushup(int u) {tr[u].sumc=tr[L].sumc+tr[R].sumc;tr[u].sums=tr[L].sums+tr[R].sums; }void pushdown(int u) {LL lazy=tr[u].lazy; tr[u].lazy=0;tr[L].lazy+=lazy; tr[R].lazy+=lazy;double ss=tr[L].sums,sc=tr[L].sumc;tr[L].sums=ss*cos(lazy)+sin(lazy)*sc;tr[L].sumc=sc*cos(lazy)-ss*sin(lazy);ss=tr[R].sums,sc=tr[R].sumc;tr[R].sums=ss*cos(lazy)+sin(lazy)*sc;tr[R].sumc=sc*cos(lazy)-ss*sin(lazy); }void build(int u,int l,int r) {tr[u]={l,r};if(l==r) {tr[u].sums=sin(a[l]);tr[u].sumc=cos(a[l]);return;}build(L,l,Mid); build(R,Mid+1,r);pushup(u); }void change(int u,int l,int r,int x) {if(tr[u].l>=l&&tr[u].r<=r) {tr[u].lazy+=x;double ss=tr[u].sums,sc=tr[u].sumc;tr[u].sums=ss*cos(x)+sin(x)*sc;tr[u].sumc=sc*cos(x)-sin(x)*ss;return;}pushdown(u); if(l<=Mid) change(L,l,r,x);if(r>Mid) change(R,l,r,x);pushup(u); }double query(int u,int l,int r) {if(tr[u].l>=l&&tr[u].r<=r) return tr[u].sums;pushdown(u);double ans=0.0;if(l<=Mid) ans+=query(L,l,r);if(r>Mid) ans+=query(R,l,r);return ans; }int main() { // ios::sync_with_stdio(false); // cin.tie(0);scanf("%d",&n);for(int i=1;i<=n;i++) scanf("%d",&a[i]);build(1,1,n);scanf("%d",&m);while(m--) {int op,l,r; scanf("%d%d%d",&op,&l,&r);if(op==1) {int x; scanf("%d",&x);change(1,l,r,x);} else printf("%.1lf\n",query(1,l,r));}return 0; } /**/ 創(chuàng)作挑戰(zhàn)賽新人創(chuàng)作獎勵來咯，堅持創(chuàng)作打卡瓜分現金大獎

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