1112练习赛
T2 最大公约数
1<=k<=n<=2000
多手 玩一下啊！！！
会发现，最终的答案肯定是所有数之和的因数，所以就很好做了！
#include<stdio.h> #include<map> #include<algorithm> #define re register int #define LL long long inline LL max(LL x,LL y){return x>y?x:y;} std::map<LL,int>mp; int cnt, n; LL sum[8005], p[8005], ans[8005]; inline void work(const LL x) { mp.clear(); int ret=0; for(re i=1;i<=n;++i) { LL y=sum[i]%x; mp[y]++; ret=max(ret, mp[y]); } ans[ret]=max(ans[ret],x); } inline void div(const LL x) { for(register LL i=1;i*i<=x;++i) if(x%i==0) { p[++cnt]=i; if(i!=x/i)p[++cnt]=x/i; } std::sort(p+1,p+1+cnt); } signed main() { scanf("%d",&n); for(re i=1;i<=n;++i) { int x; scanf("%d",&x); sum[i]=sum[i-1]+x; } div(sum[n]); for(re i=1;i<=cnt;++i)work(p[i]); for(re i=n;i;--i)ans[i]=max(ans[i],ans[i+1]); for(re i=1;i<=n;++i)printf("%I64d\n",ans[i]); return 0; }
T3 直径
1<=n,q<=10^5,sigma(k)<=10^5
有一个小结论！
两个联通块合并，最长链是原本两种最长链的四个端点构成！
又因为它跟子树有关，可以转化为区间问题。
所以，就可以用线段树来维护。
#include<bits/stdc++.h> using namespace std; #define re register int #define LL long long const int N=2e5+5; int tt, las[N], ed[N<<1], nt[N<<1], len[N<<1]; void add(int x, int y, int z){ ed[++tt]=y;nt[tt]=las[x];las[x]=tt;len[tt]=z; } int fa[N],dep[N],sz[N],son[N],top[N],in[N],ou[N],label,dfn[N]; LL val[N]; void hvedge(int x, int f) { fa[x]=f;dep[x]=dep[f]+1;sz[x]=1; for(re i=las[x];i;i=nt[i]) { int v=ed[i]; if(v==f)continue; val[v]=val[x]+len[i]; hvedge(v, x); sz[x]+=sz[v]; if(sz[v]>sz[son[x]])son[x]=v; } } void hvline(int x,int ance) { top[x]=ance;in[x]=++label; dfn[label]=x; if(son[x])hvline(son[x],ance); for(re i=las[x];i;i=nt[i]) { int v=ed[i]; if(v==fa[x]||v==son[x])continue; hvline(v,v); } ou[x]=label; } int lca(int x,int y) { while(top[x]^top[y]) { if(dep[top[x]]<dep[top[y]])swap(x,y); x=fa[top[x]]; } return dep[x]<dep[y]?x:y; } LL gtlen(int x,int y) { if(!x||!y)return 0; int ca=lca(x,y); return val[x]+val[y]-2LL*val[ca]; } struct node{ int x, y; LL d; void init(){x=0;y=0;d=0;} }tr[N<<2],A[N]; node operator+(node p, node q) { int x=p.x,y=p.y; int a=q.x,b=q.y; node z=(p.d>q.d?p:q); if(!z.d)z=(p.x?p:q); LL len; len=gtlen(x,a); if(len>z.d)z=(node){x,a,len}; len=gtlen(x,b); if(len>z.d)z=(node){x,b,len}; len=gtlen(y,a); if(len>z.d)z=(node){y,a,len}; len=gtlen(y,b); if(len>z.d)z=(node){y,b,len}; return z; } void build(int p,int l,int r) { if(l==r) { tr[p]=(node){dfn[l],dfn[l],0}; return; } int mid=(l+r)>>1; build(p<<1, l, mid); build(p<<1|1, mid+1, r); tr[p]=tr[p<<1]+tr[p<<1|1]; } node ask(int p, int l, int r, int x, int y) { if(x<=l&&r<=y)return tr[p]; int mid=(l+r)>>1; if(x<=mid&&y<=mid)return ask(p<<1,l,mid,x,y); if(x>=mid+1&&y>=mid+1)return ask(p<<1|1,mid+1,r,x,y); return ask(p<<1,l,mid,x,y)+ask(p<<1|1,mid+1,r,x,y); } int n,T,fr[N],to[N],p[N],q[N]; bool cmp(int x,int y){return in[x]<in[y];} vector<int>G[N]; void solve(int x) { A[x].init(); int nw=in[x]; for(re v:G[x]) { solve(v); if(nw<=in[v]-1)A[x]=A[x]+ask(1, 1, n, nw, in[v]-1); nw=ou[v]+1; } if(nw<=ou[x])A[x]=A[x]+ask(1,1,n,nw,ou[x]); G[x].clear(); } void work(int k) { sort(p+1,p+1+k,cmp); int h=0; for(re i=1;i<=k;++i) { while(h&&!(in[q[h]]<=in[p[i]]&&in[p[i]]<=ou[q[h]])) h--; if(h&&in[q[h]]<=in[p[i]]&&in[p[i]]<=ou[q[h]]) G[q[h]].push_back(p[i]); q[++h]=p[i]; } solve(1); } signed main() { scanf("%d",&n); for(re i=1;i<n;++i) { int x,y,z; scanf("%d%d%d",&x,&y,&z); fr[i]=x;to[i]=y; add(x,y,z); add(y,x,z); } hvedge(1,0); hvline(1,1); build(1,1,n); for(re i=1;i<n;++i)if(dep[to[i]]>dep[fr[i]])fr[i]=to[i]; scanf("%d",&T); while(T--) { int k, id; LL ret=0; scanf("%d",&k); for(re i=1;i<=k;++i) { scanf("%d",&id); p[i]=fr[id]; } p[++k]=1; work(k); for(re i=1;i<=k;++i) ret+=A[p[i]].d; printf("%lld\n",ret); } return 0; }
T4 最低位
0<=l,r<=2^31-1
这道题可以打表，“分块”打表，很好做。
当然也可以分析性质，把f的变换规律发现，可得每次[L,R]都会减少一半，很优秀
#include<stdio.h> #include<unordered_map> #include<algorithm> #define re register int #define int long long const int mo=998244353, inv=499122177; std::unordered_map<int,int>mp; inline int lowbit(const int x){return x&-x;} inline int fid1(int x){ re ret=0;while(x)x-=lowbit(x),ret++; return ret; } inline int dfs(const int i) { if(mp.count(i))return mp[i]; int t=fid1(i); if(t==1)return mp[i]=2; if(t==0)return mp[i]=0; return mp[i]=(dfs(i-lowbit(i))*inv%mo+dfs(i+lowbit(i))*inv%mo+1)%mo; } int 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int b[40000], cnt; signed main() { int l, r, ret=0; scanf("%I64d%I64d",&l,&r); if(r<=1000000||l==r) { for(re i=l;i<=r;++i)(ret+=dfs(i))%=mo; printf("%I64d\n",ret); return 0; } ret=0; int lim=(1LL<<31)-1; for(re i=1000000;i<=lim;i+=1000000)b[++cnt]=i; int x=std::lower_bound(b+1,b+1+cnt,l)-b; int y=std::upper_bound(b+1,b+1+cnt,r)-b-1; if(y>=x) { ret=(ans[y]-ans[x]+mo)%mo; for(re i=l,bur=b[x];i<=bur;++i)(ret+=dfs(i))%=mo; for(re i=b[y]+1;i<=r;++i)(ret+=dfs(i))%=mo; printf("%I64d\n",ret); } else { for(re i=l;i<=r;++i)(ret+=dfs(i))%=mo; printf("%I64d\n",ret); } return 0; }
#include<stdio.h> #include<map> #define re register int const int inv=499122177,mo=998244353; std::map<int,int>mp; int dp(int x) { if(mp.count(x))return mp[x]; if(x==1)return 2; if(x&1)return mp[x]=(1LL*inv*dp(x/2)%mo+1LL*inv*dp(x/2+1)%mo+1)%mo; return mp[x]=dp(x>>1); } int dfs(int l,int r) { if(l==r)return dp(l); int ret=0; if(l&1)(ret+=dp(l))%=mo,l++; if(r&1)(ret+=dp(r))%=mo,r--; (ret+=(r-l)/2+2*dfs(l/2,r/2)%mo-1LL*inv*(dp(l)+dp(r))%mo)%=mo; (ret+=mo)%=mo; return ret; } signed main() { int l,r; scanf("%d%d",&l,&r); if(!r)return puts("0"),0; printf("%d",dfs(l,r)); return 0; }
