HDU4436 str2int 子串之和

vjudge传送


这题还真挺难,没想出来。


首先我们要做的是,为了判断所有的重复串,要把这些串放在一个SAM里,但要用特殊字符分隔开来(这里用数字10,以缩小字符集大小)。
接下来我想的是在后缀链接树上dfs,但复杂度是(O(sum len[i])(i in 叶子节点)),这个复杂度上限是(O(n^2))的。


题解的做法是在转移边上拓扑排序(转移边构成了一个DAG)。
(sum[u])表示到节点(u)上的数字和,(num[u])表示到(u)的路径条数,于是对于一条转移边((uoverset{i}{ ightarrow} v))
(num[v] += num[u]),
(sum[v] += sum[u]*10+i*num[u]).
刚开始我没想明白为什么要维护(num[u]),后来手动模拟后才知道,(num[u])表示的是到(u)的路径条数,对应的就是以(u)结尾不同数字个数,所以当这些数字后面都加了一个数码(i)后,对于(v)的影响就是加上了(i*num[u]).
时间复杂度(O(2nK)(K)为字符集大小())

#include<cstdio>
#include<iostream>
#include<cmath>
#include<algorithm>
#include<cstring>
#include<cstdlib>
#include<cctype>
#include<vector>
#include<queue>
#include<assert.h>
#include<ctime>
using namespace std;
#define enter puts("") 
#define space putchar(' ')
#define Mem(a, x) memset(a, x, sizeof(a))
#define In inline
#define forE(i, x, y) for(int i = head[x], y; ~i && (y = e[i].to); i = e[i].nxt)
typedef long long ll;
typedef double db;
const int INF = 0x3f3f3f3f;
const db eps = 1e-8;
const int maxn = 1e5 + 5;
const int mod = 2012;
const int maxs = 12;
In ll read()
{
	ll ans = 0;
	char ch = getchar(), las = ' ';
	while(!isdigit(ch)) las = ch, ch = getchar();
	while(isdigit(ch)) ans = (ans << 1) + (ans << 3) + ch - '0', ch = getchar();
	if(las == '-') ans = -ans;
	return ans;
}
In void write(ll x)
{
	if(x < 0) x = -x, putchar('-');
	if(x >= 10) write(x / 10);
	putchar(x % 10 + '0');
}

int n, len, p[maxn];
char s2[maxn], s[maxn];
struct Sam
{
	int tra[maxn << 1][maxs], link[maxn << 1], len[maxn << 1], cnt, las;
	In void init() 
	{
		link[cnt = las = 0] = -1;
		Mem(tra[0], 0), Mem(buc, 0);
		Mem(sum, 0), Mem(num, 0);
	}
	In void insert(int c, int id)
	{
		int now = ++cnt, p = las; Mem(tra[now], 0);
		len[now] = len[las] + 1;
		while(~p && !tra[p][c]) tra[p][c] = now, p = link[p];
		if(p == -1) link[now] = 0;
		else
		{
			int q = tra[p][c];
			if(len[q] == len[p] + 1) link[now] = q;
			else
			{
				int clo = ++cnt; 
				len[clo] = len[p] + 1;
				memcpy(tra[clo], tra[q], sizeof(tra[q]));
				link[clo] = link[q]; link[q] = link[now] = clo;
				while(~p && tra[p][c] == q) tra[p][c] = clo, p = link[p];
			}

		}
		las = now;		
	}
	int buc[maxn << 1], pos[maxn << 1], sum[maxn << 1], num[maxn << 1];
	In int solve()
	{
		for(int i = 1; i <= cnt; ++i) buc[len[i]]++;
		for(int i = 1; i <= cnt; ++i) buc[i] += buc[i - 1];
		for(int i = 0; i <= cnt; ++i) pos[buc[len[i]]--] = i;
		num[0] = 1;
		for(int i = 0; i <= cnt; ++i)
		{
			int now = pos[i];
			for(int j = 0; j < 10; ++j)
			{
				if((!now && !j) || !tra[now][j]) continue;
				int v = tra[now][j];
				int tp = (sum[now] * 10 + j * num[now]) % mod;
				sum[v] = (sum[v] + tp) % mod;
				num[v] = (num[v] + num[now]) % mod;			
			}
		}
		int ans = 0;
		for(int i = 1; i <= cnt; ++i) ans = (ans + sum[i]) % mod;
		return ans;
	}
}S;

int main()
{
	while(scanf("%d", &n) != EOF)
	{
		len = 0, S.init();
		for(int i = 1; i <= n; ++i)
		{
			scanf("%s", s2);
			int l = strlen(s2); S.insert(10, len);
			for(int j = 0; j < l; ++j) S.insert(s2[j] - '0', len);
		}
		write(S.solve()), enter;
	}
	return 0;
}
原文地址:https://www.cnblogs.com/mrclr/p/14556995.html