BZOJ2119:股市的预测 分治+后缀数组
思路:
一种分治的神做法.建议去看原论文[2011年集训队作业]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 | #include<map>#include<cstdio>#include<cctype>#include<cstring>#include<iostream>#include<algorithm>using namespace std; #define INF 0x3f3f3f3f #define N 50010 int n,lim; int len[N];inline void pre(int n){ for(int i=2;i<=n;++i)len[i]=len[i>>1]+1;} int Read[N],s[N],ss[N],v[N],nv[N],q[N],c[N];inline bool cmp(int x,int y,int hl,int n){ return v[x]==v[y]&&((x+hl>n&&y+hl>n)||(x+hl<=n&&y+hl<=n&&v[x+hl]==v[y+hl]));}struct SuffixArray{ int rk[N],h[N],sa[N],rmqh[N][16]; inline void Init(int s[],int n,int m){ int i,j,k,hl,id; for(i=1;i<=m;++i)c[i]=0; for(i=1;i<=n;++i)++c[v[i]=s[i]]; for(i=2;i<=m;++i)c[i]+=c[i-1]; for(i=n;i>=1;--i)sa[c[v[i]]--]=i; for(int d=1;;++d){ for(hl=1<<(d-1),id=0,i=n-hl+1;i<=n;++i)q[++id]=i; for(i=1;i<=n;++i)if(sa[i]>hl)q[++id]=sa[i]-hl; for(i=1;i<=m;++i)c[i]=0; for(i=1;i<=n;++i)++c[v[q[i]]]; for(i=2;i<=m;++i)c[i]+=c[i-1]; for(i=n;i>=1;--i)sa[c[v[q[i]]]--]=q[i]; for(i=m=1;i<=n;++m,i=j+1){ for(j=i;j!=n&&cmp(sa[j],sa[j+1],hl,n);++j); for(k=i;k<=j;++k)nv[sa[k]]=m; } if(--m==n)break; for(i=1;i<=n;++i)v[i]=nv[i]; } for(i=1;i<=n;++i)rk[sa[i]]=i; for(i=1;i<=n;++i){ if(rk[i]==1)continue; j=max(0,h[rk[i-1]]-1); while(i+j<=n&&sa[rk[i]-1]+j<=n&&s[i+j]==s[sa[rk[i]-1]+j])++j; h[rk[i]]=j; } for(i=1;i<=n;++i)rmqh[i][0]=h[i]; for(j=1;j<=15;++j)for(i=1;i+(1<<j)-1<=n;++i)rmqh[i][j]=min(rmqh[i][j-1],rmqh[i+(1<<(j-1))][j-1]); } inline int askrmq(int l,int r){ return min(rmqh[l][len[r-l+1]],rmqh[r-(1<<len[r-l+1])+1][len[r-l+1]]); } inline int getlcp(int x,int y){ int lins=min(rk[x],rk[y]),rins=max(rk[x],rk[y]); if(lins==rins)return n-x+1; else return askrmq(lins+1,rins); }}Steins,revSteins; inline int lcp(int x,int y){ return Steins.getlcp(x,y);}inline int lcs(int x,int y){ return revSteins.getlcp(n-x+1,n-y+1);}inline bool same(int l1,int l2,int len){ return lcp(l1,l2)>=len;} map<int,int>M;int sav[N]; long long res;inline void SteinsGate(int l,int r){ if(r-l+1<lim+2)return; int mid=(l+r)>>1; SteinsGate(l,mid),SteinsGate(mid+1,r); int prelen,suflen,insl,insr,nowlen; for(prelen=0;prelen<lim;++prelen){ suflen=lim-1-prelen; insl=mid-prelen,insr=mid+suflen; if(insl>=l&&insr<=r) for(nowlen=1;insl-nowlen>=l&&insr+nowlen<=r;++nowlen)if(same(insl-nowlen,insr+1,nowlen))++res; } int lins,rins,anotherins,Lcp,Lcs,up,down; for(anotherins=l;anotherins<=r;++anotherins){ if((anotherins>mid&&anotherins-mid-1>=lim)||(mid>anotherins&&mid-anotherins-1>=lim)){ lins=min(mid,anotherins),rins=max(mid,anotherins); Lcp=lcp(lins,rins),Lcs=lcs(lins,rins); down=-INF,up=INF; down=max(down,rins-Lcs-lim+1);//rins-(x+m-1)<=lcs up=min(up,lins+Lcp);//x-lins<=lcp down=max(down,l-lim+rins-lins);//lins-(rins-(x+m-1))+1>=l up=min(up,r+1+lins-rins);//rins+(x-lins)-1<=r down=max(down,lins+1),up=min(up,rins-1);//lins<=x<=rins down=max(down,lins+2-lim),up=min(up,rins-lim);//lins<=x+m-1<=rins if(down<=up){ res+=up-down+1; if(anotherins<mid&&down==anotherins+1)--res; } } }} int main(){ #ifndef ONLINE_JUDGE freopen("tt.in","r",stdin); #endif scanf("%d%d",&n,&lim);register int i; for(i=0;i<n;++i)scanf("%d",&Read[i]); for(--n,i=1;i<=n;++i)s[i]=Read[i]-Read[i-1]; for(i=1;i<=n;++i)sav[i]=s[i];sort(sav+1,sav+n+1); int id=0;for(sav[0]=-INF,i=1;i<=n;++i)if(sav[i]!=sav[i-1])M[sav[i]]=++id; for(i=1;i<=n;++i)s[i]=M[s[i]]; for(i=n;i>=1;--i)ss[i]=s[n+1-i]; pre(n),Steins.Init(s,n,id),revSteins.Init(ss,n,id); SteinsGate(1,n); cout<<res<<endl; return 0;} |
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