POI2005SZA-Template

字符串 #kmp #POI #Year2005

考虑字符串做 \(kmp\)

考虑第 \(i\) 位的答案，假设 \(p=nxt_i\)，考虑 \(res_p\) 在什么情况下是合法的

当最后一个 \(res_x=res_p\) 的 \(x\) 满足 \(x\geq i-res_p\) 时，那么 \(res_i=res_p\)

同时用一个 \(la_i\) 维护答案为 \(i\) 的最后的位置，直接转移即可

// Author: xiaruize
#ifndef ONLINE_JUDGE
bool start_of_memory_use;
#endif
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
clock_t start_clock = clock();
#endif
#define int long long
#define ull unsigned long long
#define ALL(a) (a).begin(), (a).end()
#define pb push_back
#define mk make_pair
#define pii pair<int, int>
#define pis pair<int, string>
#define sec second
#define fir first
#define sz(a) int((a).size())
#define Yes cout << "Yes" << endl
#define YES cout << "YES" << endl
#define No cout << "No" << endl
#define NO cout << "NO" << endl
#define mms(arr, n) memset(arr, n, sizeof(arr))
#define rep(i, a, n) for (int i = (a); i <= (n); ++i)
#define per(i, n, a) for (int i = (n); i >= (a); --i)
int max(int a, int b)
{
	if (a > b)
		return a;
	return b;
}
int min(int a, int b)
{
	if (a < b)
		return a;
	return b;
}
const int INF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1000000007;
const int N = 5e5 + 10;

char s[N];
int res[N], la[N];
int p[N];
int n;

void solve()
{
	cin >> (s + 1);
	n = strlen(s + 1);
	for (int i = 2, j = 0; i <= n; i++)
	{
		while (j && s[j + 1] != s[i])
			j = p[j];
		if (s[j + 1] == s[i])
			j++;
		p[i] = j;
	}
	rep(i, 1, n)
	{
		res[i] = i;
		if (la[res[p[i]]] >= i - res[p[i]])
			res[i] = res[p[i]];
		la[res[i]] = i;
	}
	cout << res[n] << endl;
}

#ifndef ONLINE_JUDGE
bool end_of_memory_use;
#endif

signed main()
{
	// freopen(".in","r",stdin);
	// freopen(".out","w",stdout);
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int testcase = 1;
	// cin >> testcase;
	while (testcase--)
		solve();
#ifndef ONLINE_JUDGE
	cerr << "Memory use:" << (&end_of_memory_use - &start_of_memory_use) / 1024.0 / 1024.0 << "MiB" << endl;
	cerr << "Time use:" << (double)clock() / CLOCKS_PER_SEC * 1000.0 << "ms" << endl;
#endif
	return 0;
}