Luogu P1117 [NOI2016]优秀的拆分

题目链接 \(Click\) \(Here\)

这题质量不错，就是暴力分有点足\(hhhhhhhh\)，整整有\(95\)分。

（搞得我写完暴力都不想写正解直接理解思路之后就直接水过去了\(QwQ\)）

（啊好啦好啦水过去是我的锅啦，我自己出来挨打还不行嘛\(QAQ\)）

其实就是把\(AABB\)换成求\(AA\)然后组合在一块，最后的部分需要推一个奇妙的性质，这里我也不好叙述，详情请见这个大佬的博客。至于求\(AA\)的方法可以考虑使用后缀数组+\(RMQ\)实现\(O(1)\)匹配。

（别跟我提哈希听着就来气\(TwT\)，为什么还可以用\(Hash\)水啊喂！）

\(95pts:\)

#include <bits/stdc++.h>
using namespace std;

const int N = 4010;

char s[N];
int n, m, T;
int sa[N], tp[N], rk[N], _rk[N], bin[N], height[N];

void get_height () {
	int k = 0;
	for (int i = 1; i <= n; ++i) {
		if (k != 0) --k;
		int j = sa[rk[i] - 1];
		while (s[i + k - 1] == s[j + k - 1]) ++k;
		height[rk[i]] = k;
	}
}

void base_sort () {
	for (int i = 1; i <= m; ++i) bin[i] = 0;
	for (int i = 1; i <= n; ++i) bin[rk[tp[i]]]++;
	for (int i = 1; i <= m; ++i) bin[i] += bin[i - 1];
	for (int i = n; i >= 1; --i) sa[bin[rk[tp[i]]]--] = tp[i];
}

void suffix_sort () {
	m = 255;
	for (int i = 1; i <= n; ++i) {
		tp[i] = i, rk[i] = s[i - 1];
	}
	base_sort ();
	for (int w = 1; w <= n; w <<= 1) {
		int cnt = 0;
		for (int i = n - w + 1; i <= n; ++i) {
			tp[++cnt] = i;
		}
		for (int i = 1; i <= n; ++i) {
			if (sa[i] > w) {
				tp[++cnt] = sa[i] - w;
			}
		}
		base_sort ();
		memcpy (_rk, rk, sizeof (rk));
		rk[sa[1]] = cnt = 1;
		for (int i = 2; i <= n; ++i) {
			rk[sa[i]] = (_rk[sa[i]] == _rk[sa[i - 1]]) && (_rk[sa[i] + w] == _rk[sa[i - 1] + w]) ? cnt : ++cnt;
		}
		if (cnt == n) break;
		m = cnt;
	}
}

int a[N], b[N], st[N][25];

void get_STlist () {
	memset (st, 0, sizeof (st));
	for (int i = 1; i <= n; ++i) {
		st[i][0] = height[i];
	}
	int mx = log2 (n);
	for (int i = 1; i <= mx; ++i) {
		for (int j = 1; j + (1 << i) - 1 <= n; ++j) {
			st[j][i] = min (st[j][i - 1], st[j + (1 << (i - 1))][i - 1]);
		}
	}
}

int lcp (int x, int y) {
	if (x > y) swap (x, y); ++x;
	if (x > y) return 0;
	int mx = log2 (y - x + 1);
	return min (st[x][mx], st[y - (1 << mx) + 1][mx]);
}

void Initialize () {
	memset (a, 0, sizeof (a));
	memset (b, 0, sizeof (b));
	memset (s, 0, sizeof (s));
	memset (sa, 0, sizeof (sa));
	memset (tp, 0, sizeof (tp));
	memset (rk, 0, sizeof (rk));
	memset (height, 0, sizeof (height));	
	scanf ("%s", s);
	n = strlen (s);
}

int main () {
	cin >> T;
	while (T--) {
		Initialize ();
		suffix_sort ();
		get_height ();
		get_STlist ();
		for (int i = 0; i < n; ++i) { //枚举每一个后缀
			for (int l = 1; i + l * 2 - 1 < n; ++l) {
				// printf ("lcp (rk[%d] = %d, rk[%d] = %d) = %d\n", i, rk[i], i + l, rk[i + l], lcp (rk[i], rk[i + l]))
				if (lcp (rk[i + 1], rk[i + l + 1]) >= l) {
					a[i + l * 2 - 1]++, b[i]++;
				}
			}
		}
		long long ans = 0;
		for (int i = 0; i < n; ++i) {
			ans += a[i] * b[i + 1];
		}
		cout << ans << endl;
	}
}

\(100pts\)

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define LL long long
#define Set(a, v) memset(a, v, sizeof(a))
#define For(i, a, b) for(int i = (a); i <= (int)(b); i++)
#define Forr(i, a, b) for(int i = (a); i >= (int)(b); i--)
#define LOG (15+5)
#define MAXN (30000+5)
int n, c[MAXN], c1[MAXN], c2[MAXN], Log[MAXN];
struct SuffixArray{
    char s[MAXN];
    int sa[MAXN], h[MAXN][LOG], rank[MAXN];
    void init(){
        Set(c1, 0); Set(c2, 0);
    }
    void buildsa(int m='z'){
        int *x = c1, *y = c2;
        For(i, 1, m) c[i] = 0;
        For(i, 1, n) c[x[i]=s[i]]++; 
        For(i, 1, m) c[i] += c[i-1];
        Forr(i, n, 1) sa[c[x[i]]--] = i;
        int p;
        for(int k = 1; k <= n; k <<= 1){
            p = 0;
            For(i, n-k+1, n) y[++p] = i;
            For(i, 1, n) if(sa[i] > k) y[++p] = sa[i]-k;    
            For(i, 1, m) c[i] = 0;
            For(i, 1, n) c[x[y[i]]]++;
            For(i, 1, m) c[i] += c[i-1];
            Forr(i, n, 1) sa[c[x[y[i]]]--] = y[i];
            swap(x, y);
            p = x[sa[1]] = 1;
            For(i, 2, n) x[sa[i]] = (y[sa[i]]==y[sa[i-1]] && y[sa[i]+k]==y[sa[i-1]+k])? p: ++p;
            if(p >= n) break;
            m = p;
        }
    }
    void getheight(){
        For(i, 1, n) rank[sa[i]] = i;
        int k = 0, j;
        For(i, 1, n){
            if(k) k--;
            j = sa[rank[i]+1];
            if(rank[i] == n) continue;
            while(s[i+k] == s[j+k]) k++;
            h[rank[i]][0] = k;
        }
        For(j, 1, 15) For(i, 1, n){
            if(i+(1<<(j-1)) > n) break;
            h[i][j] = min(h[i][j-1], h[i+(1<<(j-1))][j-1]);
        }
    }
    int LCP(int x, int y){
        x = rank[x]; y = rank[y];
        if(x > y) swap(x, y);
        int k = Log[y-x];    
        return min(h[x][k], h[y-(1<<k)][k]);
    }
}A, B;
int st[MAXN], en[MAXN];
int main(){
    For(i, 2, MAXN-1) Log[i] = Log[i>>1]+1;
    int T;
    scanf("%d", &T);
    while(T--){
        A.init(); B.init();
        Set(st, 0); Set(en, 0);
        scanf("%s", A.s+1);
        n = strlen(A.s+1);
        For(i, 1, n) B.s[i] = A.s[n-i+1];
        A.buildsa(); A.getheight();
        B.buildsa(); B.getheight();
        int j, x, y, t;
        For(L, 1, n/2){
            for(int i=L, j=i+L; j <= n; i+=L,j+=L){
                x = min(A.LCP(i,j), L), y = min(B.LCP(n-(i-1)+1, n-(j-1)+1), L-1);
                t = x+y-L+1;
                if(x+y >= L){
                    st[i-y]++; st[i-y+t]--;
                    en[j+x-t]++; en[j+x]--;
                }
            }
        }
        For(i, 1, n) st[i]+=st[i-1], en[i]+=en[i-1];
        LL ans = 0;
        For(i, 1, n) ans += 1LL*en[i]*st[i+1];
        printf("%lld\n", ans);
    }
    return 0;
}