首页 > 代码库 > 【SPOJ1297】Palindrome (SA+RMQ)
【SPOJ1297】Palindrome (SA+RMQ)
求最长回文串。把原串翻转后,加在原串后面,中间插入一个辨别字符。然后求SA,Height。然后枚举每个字母作为回文串中心,分长度为奇数和偶数去讨论:奇数求 suffix(i)和suffix(n-i+1)的最长公共前缀,偶数则求suffix(i)和suffix(n-i+2)(当然,i=1时不成立) 。然后问题就是求最长公共前缀了,转换为RMQ问题,O(nlogn)预处理,O(1)询问即可.
1 const maxn=2419; 2 3 var 4 x,y,rank,sa,h,c:array[0..maxn] of longint; 5 s:ansistring; 6 f:array[0..maxn,0..15] of longint; 7 t,q,n:longint; 8 9 function max(x,y:longint):longint; begin if x>y then exit(x) else exit(y); end; 10 function min(x,y:longint):longint; begin if x<y then exit(x) else exit(y); end; 11 procedure swap(var x,y:longint);var tmp:longint; begin tmp:=x; x:=y;y:=tmp; end; 12 procedure make; 13 var i,j,p,tot:longint; 14 begin 15 p:=1; 16 while p<n do 17 begin 18 fillchar(c,sizeof(c),0); 19 for i:= 1 to n-p do y[i]:=rank[i+p]; 20 for i:= n-p+1 to n do y[i]:=0; 21 for i:= 1 to n do inc(c[y[i]]); 22 for i:= 1 to n do inc(c[i],c[i-1]); 23 for i:= 1 to n do 24 begin 25 sa[c[y[i]]]:=i; 26 dec(c[y[i]]); 27 end; 28 fillchar(c,sizeof(c),0); 29 for i:= 1 to n do x[i]:=rank[i]; 30 for i:= 1 to n do inc(c[x[i]]); 31 for i:= 1 to n do inc(c[i],c[i-1]); 32 for i:= n downto 1 do 33 begin 34 y[sa[i]]:=c[x[sa[i]]]; 35 dec(c[x[sa[i]]]); 36 end; 37 for i:= 1 to n do sa[y[i]]:=i; 38 tot:=1; 39 rank[sa[1]]:=1; 40 for i:= 2 to n do 41 begin 42 if (x[sa[i]]<>x[sa[i-1]]) or (x[sa[i]+p]<>x[sa[i-1]+p]) then inc(tot); 43 rank[sa[i]]:=tot; 44 end; 45 p:=p<<1; 46 end; 47 end; 48 49 procedure makeh; 50 var i,j,p:longint; 51 begin 52 h[1]:=0; p:=0; 53 for i:= 1 to n do 54 begin 55 p:=max(p-1,0); 56 if rank[i]=1 then continue; 57 j:=sa[rank[i]-1]; 58 while (i+p<=n) and (j+p<=n) and (s[i+p]=s[j+p]) do inc(p); 59 h[rank[i]]:=p; 60 end; 61 // for i:= 1 to n do write(h[i],‘ ‘); 62 // writeln; 63 end; 64 65 procedure rmq; 66 var i,j:longint; 67 begin 68 fillchar(f,sizeof(f),$7f); 69 for i:= 1 to n do f[i,0]:=h[i]; 70 for i:= 1 to trunc(ln(n)/ln(2)) do 71 for j:= 1 to n-1<<i+1 do 72 f[j,i]:=min(f[j,i-1],f[j+1<<(i-1),i-1]); 73 end; 74 75 function lcp(x,y:longint):longint; 76 var t:longint; 77 begin 78 x:=rank[x]; y:=rank[y]; 79 if x>y then swap(x,y); 80 if x<y then x:=x+1; 81 t:=trunc(ln(y-x+1)/ln(2)); 82 exit(min(f[x,t],f[y-1<<t+1,t])); 83 end; 84 85 procedure init; 86 var i,j,tot:longint; 87 ch:char; 88 begin 89 readln(s); 90 s:=s+‘#‘; 91 for i:= length(s)-1 downto 1 do s:=s+s[i]; 92 n:=length(s); 93 for i:= 1 to n do x[i]:=ord(s[i]); 94 fillchar(c,sizeof(c),0); 95 for i:= 1 to n do inc(c[x[i]]); 96 for i:= 1 to 180 do inc(c[i],c[i-1]); 97 for i:= 1 to n do 98 begin 99 sa[c[x[i]]]:=i;100 dec(c[x[i]]);101 end;102 rank[sa[1]]:=1;103 tot:=1;104 for i:= 2 to n do105 begin106 if x[sa[i]]<>x[sa[i-1]] then inc(tot);107 rank[sa[i]]:=tot;108 end;109 make;110 makeh;111 rmq;112 end;113 114 procedure solve;115 var ans,st,i,k:longint;116 begin117 ans:=0;st:=0;118 for i:= 1 to n do119 begin120 k:=lcp(i,n-i+1);121 if k*2-1>ans then122 begin123 st:=i-k+1;124 ans:=k*2-1;125 end;126 if i>1 then127 begin128 k:=lcp(i,n-i+2);129 if k*2>ans then130 begin131 st:=i-k;132 ans:=k*2;133 end;134 end;135 end;136 for i:= st to st+ans-1 do write(s[i]);137 end;138 139 Begin140 init;141 solve;142 End.
【SPOJ1297】Palindrome (SA+RMQ)
声明:以上内容来自用户投稿及互联网公开渠道收集整理发布,本网站不拥有所有权,未作人工编辑处理,也不承担相关法律责任,若内容有误或涉及侵权可进行投诉: 投诉/举报 工作人员会在5个工作日内联系你,一经查实,本站将立刻删除涉嫌侵权内容。