本文主要是介绍POJ - 3294 Life Forms，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
1.题面
http://poj.org/problem?id=3294
2.题意
给你n个字符串，希望你求出一个长度最长的子串s,s在至少n/2个字符串中出现过，
3.思路
将所有的数字连在一起后使用后缀数组，二分答案
第二种方法也是先用后缀数组处理，后面使用一个尺取法
二分 ８００＋ms
尺取法 １２00+ms
我觉得set的常数产生了很大的影响
4.代码
二分代码
/*****************************************************************> File Name: Cpp_Acm.cpp> Author: Uncle_Sugar> Mail: uncle_sugar@qq.com> Created Time: 2016年08月01日 星期一 18时50分27秒
*****************************************************************/
# include <cstdio>
# include <cstring>
# include <cctype>
# include <cmath>
# include <cstdlib>
# include <climits>
# include <iostream>
# include <iomanip>
# include <set>
# include <map>
# include <vector>
# include <stack>
# include <queue>
# include <algorithm>
using namespace std;# define rep(i,a,b) for (i=a;i<=b;i++)
# define rrep(i,a,b) for (i=b;i>=a;i--)template<class T>void PrintArray(T* first,T* last,char delim=' '){ for (;first!=last;first++) cout << *first << (first+1==last?'\n':delim);
}const int debug = 1;
const int size = 1000 + 300000 ;
const int INF = INT_MAX>>1;
typedef long long ll;const int MAXN = 500000 + 1000;
#define F(x) ((x)/3+((x)%3==1?0:tb))
#define G(x) ((x)<tb?(x)*3+1:((x)-tb)*3+2)
int wa[MAXN*3],wb[MAXN*3],wv[MAXN*3],wss[MAXN*3];
int c0(int *r,int a,int b)
{ return r[a] == r[b] && r[a+1] == r[b+1] && r[a+2] == r[b+2];
}
int c12(int k,int *r,int a,int b)
{ if(k == 2) return r[a] < r[b] || ( r[a] == r[b] && c12(1,r,a+1,b+1) ); else return r[a] < r[b] || ( r[a] == r[b] && wv[a+1] < wv[b+1] );
}
void sort(int *r,int *a,int *b,int n,int m)
{ int i; for(i = 0;i < n;i++)wv[i] = r[a[i]]; for(i = 0;i < m;i++)wss[i] = 0; for(i = 0;i < n;i++)wss[wv[i]]++; for(i = 1;i < m;i++)wss[i] += wss[i-1]; for(i = n-1;i >= 0;i--) b[--wss[wv[i]]] = a[i];
}
void dc3(int *r,int *sa,int n,int m)
{ int i, j, *rn = r + n; int *san = sa + n, ta = 0, tb = (n+1)/3, tbc = 0, p; r[n] = r[n+1] = 0; for(i = 0;i < n;i++)if(i %3 != 0)wa[tbc++] = i; sort(r + 2, wa, wb, tbc, m); sort(r + 1, wb, wa, tbc, m); sort(r, wa, wb, tbc, m); for(p = 1, rn[F(wb[0])] = 0, i = 1;i < tbc;i++) rn[F(wb[i])] = c0(r, wb[i-1], wb[i]) ? p - 1 : p++; if(p < tbc)dc3(rn,san,tbc,p); else for(i = 0;i < tbc;i++)san[rn[i]] = i; for(i = 0;i < tbc;i++) if(san[i] < tb)wb[ta++] = san[i] * 3; if(n % 3 == 1)wb[ta++] = n - 1; sort(r, wb, wa, ta, m); for(i = 0;i < tbc;i++)wv[wb[i] = G(san[i])] = i; for(i = 0, j = 0, p = 0;i < ta && j < tbc;p++) sa[p] = c12(wb[j] % 3, r, wa[i], wb[j]) ? wa[i++] : wb[j++]; for(;i < ta;p++)sa[p] = wa[i++]; for(;j < tbc;p++)sa[p] = wb[j++];
}
//str和sa也要三倍
void da(int str[],int sa[],int rank[],int height[],int n,int m)
{ for(int i = n;i < n*3;i++) str[i] = 0; dc3(str, sa, n+1, m); int i,j,k = 0; for(i = 0;i <= n;i++)rank[sa[i]] = i; for(i = 0;i < n; i++) { if(k) k--; j = sa[rank[i]-1]; while(str[i+k] == str[j+k]) k++; height[rank[i]] = k; }
}
int sa[size],rrank[size],height[size]; int n,k; int str[size],len;
int zone[size];
char s[size];int vis[200];
queue<int> que;
bool isok(int ll){memset(vis,0,sizeof(vis));while (!que.empty()) que.pop();que.push(zone[sa[1]]);vis[zone[sa[1]]] = 1;//# for (int i=1;i<=n;i++){//# cout << height[i] << (i==n?'\n':' ');//# }//# cout << endl;for (int i=2;i<=len;i++){//# cout << "height " << i << " " << height[i] << endl;if (height[i]>=ll){if (vis[zone[sa[i]]]==0){que.push(zone[sa[i]]);vis[zone[sa[i]]] = 1;}}else {//# cout << "que.size = " << que.size() << endl; if (que.size()>n/2) return true;while (!que.empty()){vis[que.front()] = 0;que.pop();}que.push(zone[sa[i]]);vis[zone[sa[i]]] = 1;}}if (que.size()>n/2)return true;return false;
}void Debug(int n){for (int i=1;i<=n;i++){cout << "*" << i << "*\t" << height[i] << "\t" << zone[sa[i]] << '\t';PrintArray(str+sa[i],str+n,'\t');}
}int main()
{ int i,j; int ncase = 0;while (~scanf("%d",&n)){ if (!n) break;if (ncase++) cout << endl;len = 0;for (i=0;i<n;i++){scanf("%s",s); for (j=0;s[j];j++){str[len] = s[j] + 200;zone[len] = i;len++;}if (i==n-1){str[len] = 0;}else {zone[len] = i;str[len++] = 1+i;}}//# void da(char str[],int sa[],int rrank[],int height[],int n,int m){ da(str,sa,rrank,height,len,500);int l = 0,r = len+1;while (l < r-1){int mid = l+r>>1;if (isok(mid)){l = mid;}else {r = mid;}}//# cout << "l = " << l << endl;//# Debug(len);if (l==0){cout << "?" << endl;}else {memset(vis,0,sizeof(vis));while (!que.empty()) que.pop();que.push(zone[sa[1]]);vis[zone[sa[1]]] = 1;for (i=1;i<=len;i++){if (height[i]>=l){if (vis[zone[sa[i]]]==0){que.push(zone[sa[i]]);vis[zone[sa[i]]] = 1;}}else {if (que.size()>n/2){for (j=sa[i-1];j<sa[i-1]+l;j++){cout << char(str[j]-200);}cout << endl;}while (!que.empty()){vis[que.front()] = 0; que.pop();}que.push(zone[sa[i]]);vis[zone[sa[i]]] = 1;}}if (que.size()>n/2){for (j=sa[i-1];j<sa[i-1]+l;j++){cout << char(str[j]-200);}cout << endl;}}}return 0;
}第二种思路
/***************************************************************** > File Name: Cpp_Acm.cpp > Author: Uncle_Sugar > Mail: uncle_sugar@qq.com > Created Time: 2016年08月01日 星期一 18时50分27秒 *****************************************************************/
# include <cstdio>
# include <cstring>
# include <cctype>
# include <cmath>
# include <cstdlib>
# include <climits>
# include <iostream>
# include <iomanip>
# include <set>
# include <map>
# include <vector>
# include <stack>
# include <queue>
# include <algorithm>
using namespace std; # define rep(i,a,b) for (i=a;i<=b;i++)
# define rrep(i,a,b) for (i=b;i>=a;i--) template<class T>void PrintArray(T* first,T* last,char delim=' '){ for (;first!=last;first++) cout << *first << (first+1==last?'\n':delim);
} const int debug = 1;
const int size = 1000 + 300000 ;
const int INF = INT_MAX>>1;
typedef long long ll; const int MAXN = 500000 + 1000;
#define F(x) ((x)/3+((x)%3==1?0:tb))
#define G(x) ((x)<tb?(x)*3+1:((x)-tb)*3+2)
int wa[MAXN*3],wb[MAXN*3],wv[MAXN*3],wss[MAXN*3];
int c0(int *r,int a,int b)
{ return r[a] == r[b] && r[a+1] == r[b+1] && r[a+2] == r[b+2];
}
int c12(int k,int *r,int a,int b)
{ if(k == 2) return r[a] < r[b] || ( r[a] == r[b] && c12(1,r,a+1,b+1) ); else return r[a] < r[b] || ( r[a] == r[b] && wv[a+1] < wv[b+1] );
}
void sort(int *r,int *a,int *b,int n,int m)
{ int i; for(i = 0;i < n;i++)wv[i] = r[a[i]]; for(i = 0;i < m;i++)wss[i] = 0; for(i = 0;i < n;i++)wss[wv[i]]++; for(i = 1;i < m;i++)wss[i] += wss[i-1]; for(i = n-1;i >= 0;i--) b[--wss[wv[i]]] = a[i];
}
void dc3(int *r,int *sa,int n,int m)
{ int i, j, *rn = r + n; int *san = sa + n, ta = 0, tb = (n+1)/3, tbc = 0, p; r[n] = r[n+1] = 0; for(i = 0;i < n;i++)if(i %3 != 0)wa[tbc++] = i; sort(r + 2, wa, wb, tbc, m); sort(r + 1, wb, wa, tbc, m); sort(r, wa, wb, tbc, m); for(p = 1, rn[F(wb[0])] = 0, i = 1;i < tbc;i++) rn[F(wb[i])] = c0(r, wb[i-1], wb[i]) ? p - 1 : p++; if(p < tbc)dc3(rn,san,tbc,p); else for(i = 0;i < tbc;i++)san[rn[i]] = i; for(i = 0;i < tbc;i++) if(san[i] < tb)wb[ta++] = san[i] * 3; if(n % 3 == 1)wb[ta++] = n - 1; sort(r, wb, wa, ta, m); for(i = 0;i < tbc;i++)wv[wb[i] = G(san[i])] = i; for(i = 0, j = 0, p = 0;i < ta && j < tbc;p++) sa[p] = c12(wb[j] % 3, r, wa[i], wb[j]) ? wa[i++] : wb[j++]; for(;i < ta;p++)sa[p] = wa[i++]; for(;j < tbc;p++)sa[p] = wb[j++];
}
//str和sa也要三倍
void da(int str[],int sa[],int rank[],int height[],int n,int m)
{ for(int i = n;i < n*3;i++) str[i] = 0; dc3(str, sa, n+1, m); int i,j,k = 0; for(i = 0;i <= n;i++)rank[sa[i]] = i; for(i = 0;i < n; i++) { if(k) k--; j = sa[rank[i]-1]; while(str[i+k] == str[j+k]) k++; height[rank[i]] = k; }
}
int sa[size],rrank[size],height[size]; int n,k; int str[size],len;
int zone[size];
char s[size]; int vis[200];
set<int> st;void Debug(int n){ for (int i=1;i<=n;i++){ cout << "*" << i << "*\t" << height[i] << "\t" << zone[sa[i]] << '\t'; PrintArray(str+sa[i],str+n,'\t'); }
} struct Comper{ int operator () (const int x,const int y){ if (height[x]==height[y])return x<y?y:x;return height[x] < height[y]?x:y; }
}comp;
/* * 这种情况下会返回最小值的下标 */ const int MAXRMQSIZE = 110000; struct RMQ{ int dp[MAXRMQSIZE][25]; int mm[MAXRMQSIZE]; //初始化RMQ, b数组下标从1开始,从0开始简单修改 RMQ(){} void initRMQ(int n){ mm[0] = -1; for(int i = 1; i <= n;i++){ mm[i] = ((i&(i-1)) == 0)?mm[i-1]+1:mm[i-1]; dp[i][0] = i; } for(int j = 1; j <= mm[n];j++) for(int i = 1;i + (1<<j) -1 <= n;i++) dp[i][j] = comp(dp[i][j-1],dp[i+(1<<(j-1))][j-1]); } //查询最大值 int rmq(int x,int y){ if (x > y)swap(x,y);int k = mm[y-x+1]; return comp(dp[x][k],dp[y-(1<<k)+1][k]); }
};
RMQ rmqq;int ans = 0;
vector<int> anspos;
int main()
{ int i,j; int ncase = 0; while (~scanf("%d",&n)){ if (!n) break; if (ncase++) cout << endl; len = 0; for (i=0;i<n;i++){ scanf("%s",s); for (j=0;s[j];j++){ str[len] = s[j] + 200; zone[len] = i; len++; } if (i==n-1){ str[len] = 0; } else { zone[len] = i; str[len++] = 1+i; } } //# void da(char str[],int sa[],int rrank[],int height[],int n,int m){ da(str,sa,rrank,height,len,500); //# Debug(len); int left,right;st.clear();anspos.clear();memset(vis,0,sizeof(vis));rmqq.initRMQ(len);ans = 0;for (left=right=1;left<=len;left++){while (st.size() <= n/2 && right<=len){if (vis[zone[sa[right]]]++==0){st.insert(zone[sa[right]]); }right++;}if (st.size() <= n/2) break;//# cout << "left " << left << " right " << right ;int k = rmqq.rmq(left+1,right-1);//# cout << "left + 1 " << left+1 << " right-1 " << right-1 << " " << height[k]<< endl;if (height[k] > ans){ans = height[k];anspos.clear();anspos.push_back(k);}else if (height[k] == ans){if (anspos.empty()||height[rmqq.rmq(anspos.back(),k)] < ans)anspos.push_back(k);}if (--vis[zone[sa[left]]]==0){st.erase(zone[sa[left]]);}}if (ans==0){putchar('?');putchar('\n');}else{for (i=0;i<anspos.size();i++){int loc = sa[anspos[i]];for (j=loc;j<loc+ans;j++){putchar(char(str[j] - 200));}putchar('\n');}}}return 0;
}
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