POJ 3415 (后缀自动机)

POJ 3415 Common Substrings

Problem : 给两个串S、T (len <= 10^5), 询问两个串有多少个长度大于等于k的子串(位置不同也算)。

Solution :最开始的想法是将S串和T串先后插入后缀自动机，统计出每个节点对应串的出现次数，不过这种做法被卡空间了。

第二种想法是只将S串插入后缀自动机，建立后缀树，统计出每个节点对应串的出现次数，在统计出每个节点的所有父亲节点的出现次数之和。之后将T串在后缀自动机上进行匹配，假设当前T串在p节点匹配成功，且匹配成功长度为len，那么对答案的贡献就是p节点所有长度超过k的父亲节点，再加上当前节点中长度超过k但不超过

tmp的串。

#include <iostream>
#include <string>

using namespace std;

const int N = 200008;

struct edge
{
	int v, nt;
};

struct Suffix_Automanon
{
	int nt[N][60], a[N], fail[N];
	int tot, last, root;
	int lt[N], sum;
	int p, q, np, nq;
	int cnt[N];
	long long f[N];
	edge eg[N];

	int newnode(int len)
	{
		for (int i = 0; i < 60; ++i) nt[tot][i] = -1;
		fail[tot] = -1; cnt[tot] = f[tot] = lt[tot] = 0; a[tot] = len;
		return tot++;
	}
	void clear()
	{
		tot = sum = 0;
		last = root = newnode(0);
	}
	void add(int u, int v)
	{
		eg[++sum] = (edge){v, lt[u]}; lt[u] = sum;
	}
	void insert(int ch)
	{
		p = last; np = last = newnode(a[p] + 1); cnt[np] = 1;
		for (; ~p && nt[p][ch] == -1; p = fail[p]) nt[p][ch] = np;
		if (p == -1) fail[np] = root;
		else
		{
			q = nt[p][ch];
			if (a[p] + 1 == a[q]) fail[np] = q;
			else
			{
				nq = newnode(a[p] + 1);
				for (int i = 0; i < 60; ++i) nt[nq][i] = nt[q][i];
				fail[nq] = fail[q]; fail[q] = fail[np] = nq;
				for (; ~p && nt[p][ch] == q; p = fail[p]) nt[p][ch] = nq;
			}
		}
	}
	void dfs(int u)
	{
		for (int i = lt[u]; i; i = eg[i].nt)
		{
			dfs(eg[i].v);
			cnt[u] += cnt[eg[i].v];
		}
	}
	void dfs(int u, int k)
	{
		for (int i = lt[u]; i; i = eg[i].nt)
		{
			if (u != root && k <= a[u])
			{
				f[eg[i].v] += f[u] + (a[u] - max(k, a[fail[u]] + 1) + 1) * cnt[u];
			}
			dfs(eg[i].v, k);
		}
	}
	void build(int k)
	{
		for (int i = 1; i < tot; ++i) add(fail[i], i);
		dfs(root);
		dfs(root, k);
	}
	void solve(const string &s, int k)
	{
		int p = root, tmp = 0;
		long long ans = 0;
		for (int i = 0, len = s.length(); i < len; ++i)
		{
			int ch = s[i] - 'A';
			if (~nt[p][ch]) p = nt[p][ch], tmp++;
			else
			{
				for (; ~p && nt[p][ch] == -1; p = fail[p]);
				if (p == -1) p = root, tmp = 0;
				else
				{
					tmp = a[p] + 1;
					p = nt[p][ch];
				}
			}
			if (p != root)
			{
				ans += f[p];
				if (tmp >= k && k <= a[p]) ans += (min(a[p], tmp) - max(k, a[fail[p]] + 1) + 1) * cnt[p];
			}
		}
		cout << ans << endl;
	}

}sam;

int main()
{
	int n; string s, t;
	while (cin >> n >> s >> t)
	{
		sam.clear();
		for (int i = 0, len = s.length(); i < len; ++i)
			sam.insert(s[i] - 'A');
		sam.build(n);
		sam.solve(t, n);
	}
}