UVa 11488 - Hyper Prefix Sets （Trie）

UVA - 11488

Hyper Prefix Sets

Time Limit: 2000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

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Description

H	Hyper Prefix Sets

Prefix goodness of a set string is length of longest common prefix*number of strings in the set. For example the prefix goodness of the set {000,001,0011} is 6.You are given a set of binary strings. Find the maximum prefix goodness among all possible subsets of these binary strings.

Input

First line of the input contains T(≤20) the number of test cases. Each of the test cases start with n(≤50000) the number of strings. Each of the next n lines contains a string containing only 0 and 1. Maximum length of each of these string is 200.

Output

For each test case output the maximum prefix goodness among all possible subsets of n binary strings.

Sample Input                             Output for Sample Input

4 4 0000 0001 10101 010 2 01010010101010101010 11010010101010101010 3 010101010101000010001010 010101010101000010001000 010101010101000010001010 5 01010101010100001010010010100101 01010101010100001010011010101010 00001010101010110101 0001010101011010101 00010101010101001

6 20 66 44

Problem Setter : Abdullah Al Mahmud

Special Thanks : ManzururRahman Khan

Source

Root :: AOAPC I: Beginning Algorithm Contests -- Training Guide (Rujia Liu) :: Chapter 3. Data Structures :: String Algorithms :: Exercises: Beginner

Root :: Prominent Problemsetters ::  Abdullah-al-Mahmud (Satej)

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题意：

给定一个字符串集合S，定义P(S)为所有字符串的公共前缀长度与S中字符串个数的乘积。

给定n个01字符串，从中选择一个集合S，是的P(S)最大。

Trie简单维护一下每个节点下有多少字符串就行了，然后插入的时候更新下答案即可

#include <cstdio>
#include <iostream>
#include <vector>
#include <algorithm>
#include <cstring>
#include <string>
#include <map>
#include <cmath>
#include <queue>
#include <set>

using namespace std;

//#define WIN
#ifdef WIN
typedef __int64 LL;
#define iform "%I64d"
#define oform "%I64d\n"
#define oform1 "%I64d"
#else
typedef long long LL;
#define iform "%lld"
#define oform "%lld\n"
#define oform1 "%lld"
#endif

#define S64I(a) scanf(iform, &(a))
#define P64I(a) printf(oform, (a))
#define P64I1(a) printf(oform1, (a))
#define REP(i, n) for(int (i)=0; (i)<n; (i)++)
#define REP1(i, n) for(int (i)=1; (i)<=(n); (i)++)
#define FOR(i, s, t) for(int (i)=(s); (i)<=(t); (i)++)

const int INF = 0x3f3f3f3f;
const double eps = 1e-9;
const double PI = (4.0*atan(1.0));

const int maxn = 50000 + 20;
const int maxnode = maxn * 200 + 20;
int ch[maxnode][2];
int val[maxnode];
int sz;

void init() {
    sz = 1;
    memset(ch[0], 0, sizeof(ch[0]));
}

int insert(char * s) {
    int ret = 0;
    int u = 0, n = strlen(s);
    for(int i=0; i<n; i++) {
        val[u]++;
        ret = max(ret, i*val[u]);
        int c = s[i] - '0';
        if(!ch[u][c]) {
            memset(ch[sz], 0, sizeof(ch[sz]));
            val[sz] = 0;
            ch[u][c] = sz++;
        }
        u = ch[u][c];
    }
    val[u]++;
    ret = max(ret, val[u] * n);
    return ret;
}

char str[maxn];

int main() {
    int T;

    scanf("%d", &T);
    while(T--) {
        int n;
        int ans = 0;
        scanf("%d", &n);
        init();
        for(int i=0; i<n; i++) {
            scanf("%s", str);
            int ret = insert(str);
            ans = max(ans, ret);
        }
        printf("%d\n", ans);
    }

    return 0;
}