#include <bits/stdc++.h>

using namespace std;
/*
aabaaab
答案：
[0,1,0,1,2,2,3]
*/

//朴素版本求字符串的前缀函数
vector<int> prefix_function1(string s) {
    int n = (int)s.length();
    vector<int> pi(n);
    for (int i = 1; i < n; i++)
        for (int j = i; j >= 0; j--)
            if (s.substr(0, j) == s.substr(i - j + 1, j)) {
                pi[i] = j;
                break;
            }
    return pi;
}
// 第一轮优化后的版本
vector<int> prefix_function2(string s) {
    int n = (int)s.length();
    vector<int> pi(n);
    for (int i = 1; i < n; i++)
        for (int j = pi[i - 1] + 1; j >= 0; j--) // improved: j=i => j=pi[i-1]+1
            if (s.substr(0, j) == s.substr(i - j + 1, j)) {
                pi[i] = j;
                break;
            }
    return pi;
}
// 第二轮优化后的版本
vector<int> prefix_function3(string s) {
    int n = (int)s.length();
    vector<int> pi(n);
    for (int i = 1; i < n; i++) {
        int j = pi[i - 1];
        while (j > 0 && s[i] != s[j]) j = pi[j - 1];
        if (s[i] == s[j]) j++;
        pi[i] = j;
    }
    return pi;
}
int main() {
    string s = "aabaaab";
    vector<int> res = prefix_function1(s);
    for (int i = 0; i < (int)res.size(); i++)
        cout << res[i] << " ";
    puts("");

    res = prefix_function2(s);
    for (int i = 0; i < (int)res.size(); i++)
        cout << res[i] << " ";
    puts("");

    res = prefix_function3(s);
    for (int i = 0; i < (int)res.size(); i++)
        cout << res[i] << " ";
    puts("");

    return 0;
}