2018 icpc徐州站网络赛 H Ryuji doesn't want to study

xiaoxiao2021-03-01  12

题目:点击打开链接

题意:给定一个数列,1操作求一个这样的区间[ L , R ]和:a[ R ]+a[ R-1 ]*2+a[ R-2 ]*3+...+a[ L ]*( R - L +1  ),2操作修改一个a[ i ]的值。

分析:借助两颗线段树,线段树s1维护正常区间和,线段树s2维护数列:a[ n ],a[ n-1 ]*2,a[ n-2 ]*3,,,,a[ 1 ]*n 的区间和,假如题目求区间[  l ,r ]的的和,先算出 r 到 n 的差 len ,那么s2[ l , r] - s1[ l , r ]*len就是答案。

代码:

#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #pragma comment(linker, "/STACK:102400000,102400000") #include<unordered_map> #include<unordered_set> #include<algorithm> #include<iostream> #include<fstream> #include<complex> #include<cstdlib> #include<cstring> #include<cassert> #include<iomanip> #include<string> #include<cstdio> #include<bitset> #include<vector> #include<cctype> #include<cmath> #include<ctime> #include<stack> #include<queue> #include<deque> #include<list> #include<set> #include<map> using namespace std; #define pt(a) cout<<a<<endl #define debug test #define mst(ss,b) memset((ss),(b),sizeof(ss)) #define rep(i,a,n) for (ll i=a;i<=n;i++) #define per(i,a,n) for (ll i=n-1;i>=a;i--) #define all(x) (x).begin(),(x).end() #define fi first #define se second #define SZ(x) ((ll)(x).size()) #define ll long long #define ull unsigned long long #define pb push_back #define mp make_pair #define inf 0x3f3f3f3f #define eps 1e-10 #define PI acos(-1.0) typedef pair<ll,ll> PII; const ll mod = 1e9+7; const ll N = 1e5+10; ll gcd(ll p,ll q){return q==0?p:gcd(q,p%q);} ll qp(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;} ll to[4][2]={{-1,0},{1,0},{0,-1},{0,1}}; ll n,q,a[N],b[N],s1[4*N],s2[4*N]; void bd(ll l,ll r,ll id) { if(l==r) { s1[id]=a[l],s2[id]=b[l]; return ; } ll m=(l+r)/2; bd(l,m,2*id); bd(m+1,r,2*id+1); s1[id]=s1[id*2]+s1[id*2+1]; s2[id]=s2[id*2]+s2[id*2+1]; } ll res=0; void qy(ll l,ll r,ll ql,ll qr,ll id,ll tp[]) { if(ql<=l&&qr>=r) { res+=tp[id]; return ; } ll m=(l+r)/2; if(ql<=m) qy(l,m,ql,qr,2*id,tp); if(qr>m) qy(m+1,r,ql,qr,2*id+1,tp); } void up(ll l,ll r,ll id,ll x,ll val,ll tp[]) { if(l==r) { tp[id]=val; return ; } ll m=(l+r)/2; if(x<=m) up(l,m,2*id,x,val,tp); else up(m+1,r,2*id+1,x,val,tp); tp[id]=tp[id*2]+tp[2*id+1]; } int main() { ios::sync_with_stdio(0),cin.tie(0),cout.tie(0); while(cin>>n>>q) { rep(i,1,n) cin>>a[i],b[i]=(n-i+1)*a[i]; bd(1,n,1); rep(i,1,q) { ll op,id,val,l,r; cin>>op; if(op==1) { res=0; cin>>l>>r; qy(1,n,l,r,1,s2); ll tp=res; res=0; qy(1,n,l,r,1,s1); cout<<tp-res*(n-r)<<endl; }else { cin>>id>>val; up(1,n,1,id,val,s1); up(1,n,1,id,id*val,s2); } } } return 0; }

 

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