【BZOJ2119】股市的预测（SA）

Description

click me

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Solution

将题目给出的数组差分一下，题目转化成：
有多少个串满足：
1. 形式为$ABA$
2. $B$的长度为$m$

跟优秀的拆分类似，我们考虑枚举$A$的长度$len$并设立关键点。
对于关键点$i$，我们令$j=i+m+len$，求前缀$i,j$的最长公共后缀$l$、后缀$i,j$的最长公共前缀$r$，从而得到经过这两个关键点且相同的最长的串，那么方案数等于$\sum l+r-len$。

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Code

/************************************************
 * Au: Hany01
 * Date: May 30th, 2018
 * Prob: [BZOJ2119] 股市的预测
 * Email: [email protected]
************************************************/

#include<bits/stdc++.h>

using namespace std;

typedef long long LL;
typedef pair<int, int> PII;
#define File(a) freopen(a".in", "r", stdin), freopen(a".out", "w", stdout)
#define rep(i, j) for (register int i = 0, i##_end_ = (j); i < i##_end_; ++ i)
#define For(i, j, k) for (register int i = (j), i##_end_ = (k); i <= i##_end_; ++ i)
#define Fordown(i, j, k) for (register int i = (j), i##_end_ = (k); i >= i##_end_; -- i)
#define Set(a, b) memset(a, b, sizeof(a))
#define Cpy(a, b) memcpy(a, b, sizeof(a))
#define x first
#define y second
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define ALL(a) (a).begin(), (a).end()
#define SZ(a) ((int)(a).size())
#define INF (0x3f3f3f3f)
#define INF1 (2139062143)
#define Mod (1000000007)
#define debug(...) fprintf(stderr, __VA_ARGS__)
#define y1 wozenmezhemecaia

template <typename T> inline bool chkmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
template <typename T> inline bool chkmin(T &a, T b) { return b < a ? a = b, 1 : 0; }

inline int read()
{
    register int _, __; register char c_;
    for (_ = 0, __ = 1, c_ = getchar(); c_ < '0' || c_ > '9'; c_ = getchar()) if (c_ == '-') __ = -1;
    for ( ; c_ >= '0' && c_ <= '9'; c_ = getchar()) _ = (_ << 1) + (_ << 3) + (c_ ^ 48);
    return _ * __;
}

const int maxn = 50005;

int n, m, s[maxn], Log[maxn], Ans, ls[maxn], cnt, c[maxn], mm;

struct SA_ST
{
    int rk[maxn << 1], sa[maxn << 1], tp[maxn << 1], height[maxn << 1], mn[maxn][17];

    inline void RadixSort()
    {
        For(i, 1, mm) c[i] = 0;
        For(i, 1, n) ++ c[rk[i]];
        For(i, 1, mm) c[i] += c[i - 1];
        Fordown(i, n, 1) sa[c[rk[tp[i]]] --] = tp[i];
    }

    inline void build(int *s)
    {
        For(i, 1, n) rk[i] = s[i], tp[i] = i;
        mm = n, RadixSort();
        for (register int k = 1, p; k <= n; k <<= 1) {
            p = 0;
            For(i, n - k + 1, n) tp[++ p] = i;
            For(i, 1, n) if (sa[i] > k) tp[++ p] = sa[i] - k;
            RadixSort(), swap(rk, tp), rk[sa[1]] = 1, mm = 1;
            For(i, 2, n) rk[sa[i]] = tp[sa[i - 1]] == tp[sa[i]] && tp[sa[i] + k] == tp[sa[i - 1] + k] ? mm : ++ mm;
            if (mm == n) break;
        }

        for (int i = 1, j, k = 0; i <= n; height[rk[i ++]] = k)
            for (k = k ? k - 1 : 0, j = sa[rk[i] - 1]; s[i + k] == s[j + k]; ++ k) ;
    }

    inline void Reverse() {
        reverse(rk + 1, rk + 1 + n);
        For(i, 1, n) sa[i] = n - i + 1;
    }

    inline void initST() {
        For(i, 1, n) mn[i][0] = height[i];
        For(j, 1, Log[n]) For(i, 1, n - (1 << j) + 1) mn[i][j] = min(mn[i][j - 1], mn[i + (1 << (j - 1))][j - 1]);
    }

    inline int queryST(int x, int y) {
        x = rk[x], y = rk[y];
        if (x > y) swap(x, y);
        ++ x;
        int t = Log[y - x + 1];
        return min(mn[x][t], mn[y - (1 << t) + 1][t]);
    }

}sa1, sa2;

int main()
{
#ifdef hany01
    File("bzoj2119");
#endif

    n = read(), m = read();
    For(i, 1, n) s[i] = read();
    -- n;
    For(i, 1, n) s[i] = ls[i] = s[i + 1] - s[i];
    s[n + 1] = 0;
    sort(ls + 1, ls + 1 + n), cnt = unique(ls + 1, ls + 1 + n) - ls - 1;
    For(i, 1, n) s[i] = lower_bound(ls + 1, ls + 1 + n, s[i]) - ls;

    sa1.build(s);
    reverse(s + 1, s + 1 + n), sa2.build(s), sa2.Reverse();
    For(i, 2, n) Log[i] = Log[i >> 1] + 1;
    sa1.initST(), sa2.initST();

    For(len, 1, (n - m) >> 1)
        for (int i = 1, j; (j = i + len + m) <= n; i += len) {
            int el = min(sa2.queryST(i, j), len), er = min(sa1.queryST(i, j), len);
            if (el + er >= len) Ans += el + er - len;
        }
    printf("%d\n", Ans);

    return 0;
}
//一寸相思千万绪。人间没个安排处。
//    -- 李冠《蝶恋花·春暮》