题解：P13867 [SWERC 2020] Unique Activities

sccc_ · 2025-10-15 21:33:16 · 题解

Sol

因为长度为 len 的子串满足，\ge len 的也满足，发现重复子串的长度具有单调性，考虑二分答案。

在 \operatorname{check} 函数中，对长度为 len 的子串的哈希值进行统计，再检查是否有唯一的，若有，记录起始下标 st = i。

Code

#include <bits/stdc++.h>
#define ull unsigned long long

using namespace std;

const int N = 3e5 + 10, P = 13331;

string s;
int n, st;
ull hs[N], pw[N];
map<ull, int> mp;

ull get_hs(int l, int r) {
    return hs[r] - hs[l - 1] * pw[r - l + 1];
}

bool check(int mid) {
    if (mid == 0 || mid > n)
        return 0;
    mp.clear();
    for (int i = 1; i + mid - 1 <= n; i++) {
        int j = i + mid - 1;
        mp[get_hs(i, j)]++;
    }
    for (int i = 1; i + mid - 1 <= n; i++) {
        int j = i + mid - 1;
        if (mp[get_hs(i, j)] == 1) {
            st = i;
            return 1;
        }
    }
    return 0;
}

signed main() {
    cin >> s;
    n = s.size();
    s = ' ' + s;
    pw[0] = 1;
    for (int i = 1; i <= n; i++) {
        pw[i] = pw[i - 1] * P;
        hs[i] = hs[i - 1] * P + s[i];
    }
    int l = 0, r = n + 1;
    while (l + 1 < r) {
        int mid = l + r >> 1;
        if (check(mid))
            r = mid;
        else
            l = mid;
    }
    cout << s.substr(st, r);
    return 0;
}