USACO 2.3.1 Longest Prefix
2014-07-20 17:32
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基本的动态规划吧。。想到方法了其实很简单(苯渣用暴搜做了2个小时,优化无数都TLE我会说)
还有人用TRIE做的- -
这个程序的几个优化:
一、将元素排序
二、二分搜索。这两个是为了加快查找速度。O(n)=>O(logn)
三、找出元素中最长串的长度MAX_SIZE。这是为了减少动态规划时J循环的不必要的循环量。
DP原理:长为N的前缀存在,当且仅当GOAL串中自N-J+1至N的字符串属于集合,且长为N-J的前缀存在,此处1<=J<=MIN(N,MAX_SIZE)。
/*
ID:szwjcch971
LANG:C++
TASK:prefix
*/
#include "stdio.h"
#include "string.h"
#include "stdlib.h"
char arr[205][11],goal[200005];
int max=0,arrtop;
unsigned char visited[205];
int min_size;int st[27],en[27];
int min(int a,int b){
return a<b?a:b;
}
int DoubleFind(char arr[205][11],char s[11],int left,int right){
int p,t,mid=(left+right)/2,len=strlen(s);
char temp[11];
t=strcmp(arr[mid],s);
if(!t)return 1;
if(left==right)return 0;
if(t>0)return DoubleFind(arr,s,left,mid);
if(t<0)return DoubleFind(arr,s,mid+1,right);
}
int main(){
int i,j,k,l;
char temp[200005],is_visited[200005],tmp[11];
int max_size=-1345;
FILE *fin=fopen("prefix.in","r");
FILE *fout=fopen("prefix.out","w");
i=1;
memset(goal,0,sizeof(goal));
memset(temp,0,sizeof(temp));
memset(is_visited,0,sizeof(is_visited));
//Now input the strings.
while(1){
fscanf(fin,"%s",&arr[i]);
if(arr[i][0]=='.')break;
l=strlen(arr[i]);
if(l>max_size)max_size=l;
i++;
}
arrtop=i-1;arr[0][0]='.';
while(fscanf(fin,"%s",&temp)!=EOF){
strcat(goal,temp);
}
//Now sort the strings.
for(i=1;i<=arrtop-1;i++){
for(j=i+1;j<=arrtop;j++){
if(strcmp(arr[i],arr[j])>0){
strcpy(temp,arr[i]);
strcpy(arr[i],arr[j]);
strcpy(arr[j],temp);
}
}
}
st[1]=en[1]=1;k=1;
for(i=1;i<=arrtop;i++){
if(arr[i][0]==k+64)en[k]=i;
else{
k++;
st[k]=en[k]=i;
}
}
//Now search.
is_visited[0]=1;
l=strlen(goal);
for(i=1;i<=l;i++){
for(j=1;j<=max_size;j++){
if(i-j<0)break;
memset(tmp,0,sizeof(tmp));
strncpy(tmp,goal+i-j,j);
if((is_visited[i-j])&&DoubleFind(arr,tmp,st[tmp[0]-64],en[tmp[0]-64])){
is_visited[i]=1;
break;
}
}
}
for(i=l;i>=1;i--){if(is_visited[i])break;}
fprintf(fout,"%d\n",i);
return 0;
}
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