[coj 1353 Guessing the Number]kmp，字符串最小表示法

题意：给一个字符串，求它的最小子串，使得原串是通过它重复得到的字符串的一个子串。

思路：先求最小长度，最小循环长度可以利用kmp的next数组快速得到，求出长度后然后利用字符串最小表示法求循环节的最小表示即可。

#pragma comment(linker, "/STACK:10240000")
#include <map>
#include <set>
#include <cmath>
#include <ctime>
#include <deque>
#include <queue>
#include <stack>
#include <vector>
#include <cstdio>
#include <string>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

#define X                   first
#define Y                   second
#define pb                  push_back
#define mp                  make_pair
#define all(a)              (a).begin(), (a).end()
#define fillchar(a, x)      memset(a, x, sizeof(a))
#define fillarray(a, b)     memcpy(a, b, sizeof(a))

typedef long long ll;
typedef pair<int, int> pii;
typedef unsigned long long ull;

#ifndef ONLINE_JUDGE
namespace Debug {
void RI(vector<int>&a,int n){a.resize(n);for(int i=;i<n;i++)scanf("%d",&a[i]);}
void RI(){}void RI(int&X){scanf("%d",&X);}template<typename...R>
void RI(int&f,R&...r){RI(f);RI(r...);}void RI(int*p,int*q){int d=p<q?:-;
while(p!=q){scanf("%d",p);p+=d;}}void print(){cout<<endl;}template<typename T>
void print(const T t){cout<<t<<endl;}template<typename F,typename...R>
void print(const F f,const R...r){cout<<f<<", ";print(r...);}template<typename T>
void print(T*p, T*q){int d=p<q?:-;while(p!=q){cout<<*p<<", ";p+=d;}cout<<endl;}
}
#endif // ONLINE_JUDGE

template<typename T>bool umax(T&a, const T&b){return b<=a?false:(a=b,true);}
template<typename T>bool umin(T&a, const T&b){return b>=a?false:(a=b,true);}

const double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
const double EPS = 1e-8;

/* -------------------------------------------------------------------------------- */

const int maxn = 2e5 + ;

struct KMP {
    int next[maxn];
    void GetNext(char s[]) {
        fillchar(next, );
        next[] = next[] = ;
        for(int i = ; s[i]; i++) {
            int j = next[i];
            while(j && s[i] != s[j]) j = next[j];
            next[i + ] = s[j] == s[i]? j +  : ;
        }
    }
};
KMP kmp;

char s[maxn];

void work(char s[], int n) {
    int i = , j = ; /** 用i存最小表示的最小可能位置， 同时令j>i，因为0~i-1都不是最小表示*/
    while (i < n && j < n) {
        while (s[i] == '0') i ++;
        umax(j, i + );
        while (s[j] == '0') j ++;
        //Debug::print(i, j, n);
        if (j >= n) break;
        int k = ;
        while (s[i + k] == s[j + k] && k <= n) k ++;
        if (s[i + k] > s[j + k]) if (s[j + k] != '0') i += k + ; else i += k;
        else if (s[i + k] != '0') j += k + ; else j += k;
        //Debug::print(i, j, n);
    }
    int x = i < n? i : j; /** 最后一次可能跳跃导致i大于等于n，那么此时的j一定是最小表示 */
    for (int i = x; i < x + n; i ++) {
        putchar(s[i]);
    }
    putchar('\n');
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("in.txt", "r", stdin);
//    //freopen("out.txt", "w", stdout);
#endif // ONLINE_JUDGE
    int T;
    cin >> T;
    while (T --) {
        scanf("%s", s);
        int n = strlen(s);
        bool ok = false;
        for (int i = ; s[i]; i ++) {
            if (s[i] != '0') {
                ok = true;
                break;
            }
        }
        if (!ok) {
            s[n ++] = '1';
            s[n] = ;
        }
        kmp.GetNext(s);
        int len = n - kmp.next[n];
        for (int i = len; i <  * len; i ++) s[i] = s[i - len];
        s[ * len] = ;
        work(s, len);
    }
    return ;
}