Hash(LCP) || 后缀数组 LA 4513 Stammering Aliens

题目传送门

题意：训练指南P225

分析：二分寻找长度，用hash值来比较长度为L的字串是否相等。

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

typedef unsigned long long ull;
const int N = 4e4 + 5;
const int x = 123;
ull H[N], _hash[N], xp[N];
int rk[N];
char str[N];
int m;

void get_hash(char *s, int len)  {
    H[len] = 0;
    for (int i=len-1; i>=0; --i) {
        H[i] = H[i+1] * x + (s[i] - 'a');
    }
    xp[0] = 1;
    for (int i=1; i<len; ++i) {
        xp[i] = xp[i-1] * x;
    }
}

bool cmp(const int &a, const int &b) {
    return (_hash[a] < _hash[b] || (_hash[a] == _hash[b] && a < b));
}

int check(int L, int len)    {
    int cnt = 0, pos = -1, c = 0;
    for (int i=0; i<len-L+1; ++i)   {
        rk[i] = i;
        _hash[i] = H[i] - H[i+L] * xp[L];
    }
    sort (rk, rk+len-L+1, cmp);
    for (int i=0; i<len-L+1; ++i)   {
        if (i == 0 || _hash[rk[i]] != _hash[rk[i-1]])   c = 0;
        if (++c >= m)   pos = max (pos, rk[i]);
    }
    return pos;
}

int main(void)  {
    while (scanf ("%d", &m) == 1)   {
        if (!m) break;
        scanf ("%s", &str);
        int len = strlen (str);
        get_hash (str, len);
        if (check (1, len) == -1) puts ("none");
        else    {
            int l = 1, r = len + 1;
            while (r - l > 1)   {
                int mid = l + r >> 1;
                if (check (mid, len) >= 0)    l = mid;
                else    r = mid;
            }
            printf ("%d %d\n", l, check (l, len));
        }
    }

    return 0;
}

后缀数组也可以求解，具体就是二分答案，height数组分组判断是否满足存在题意的解，并使最优。（m=1时特判处理）

#include <bits/stdc++.h>

const int N = 4e4 + 5;
int sa[N], rank[N], height[N];
int ws[N], wa[N], wb[N];
char s[N];

bool cmp(int *r, int a, int b, int l) {
    return (r[a] == r[b] && r[a+l] == r[b+l]);
}
void DA(char *r, int n, int m = 128) {
    int i, j, p, *x = wa, *y = wb;
    for (i=0; i<m; ++i) ws[i] = 0;
    for (i=0; i<n; ++i) ws[x[i]=r[i]]++;
    for (i=1; i<m; ++i) ws[i] += ws[i-1];
    for (i=n-1; i>=0; --i) sa[--ws[x[i]]] = i;
    for (j=1, p=1; p<n; j<<=1, m=p) {
        for (p=0, i=n-j; i<n; ++i) y[p++] = i;
        for (i=0; i<n; ++i) if (sa[i] >= j) y[p++] = sa[i] - j;
        for (i=0; i<m; ++i) ws[i] = 0;
        for (i=0; i<n; ++i) ws[x[y[i]]]++;
        for (i=1; i<m; ++i) ws[i] += ws[i-1];
        for (i=n-1; i>=0; --i) sa[--ws[x[y[i]]]] = y[i];
        std::swap (x, y);
        for (p=1, x[sa[0]]=0, i=1; i<n; ++i) {
            x[sa[i]] = cmp (y, sa[i-1], sa[i], j) ? p - 1 : p++;
        }
    }
}
void calc_height(char *r, int *sa, int n) {
    int i, j, k = 0;
    for (i=1; i<=n; ++i) rank[sa[i]] = i;
    for (i=0; i<n; ++i) {
        if (k) k--;
        j = sa[rank[i]-1];
        while (r[i+k] == r[j+k]) k++;
        height[rank[i]] = k;
    }
}

int m;
int check(int len, int n) {
    int p = -1;
    int cnt = 0, ret = -1;
    for (int i=1; i<=n; ++i) {
        if (height[i] >= len) {
            if (p == -1) {
                p = std::max (sa[i-1], sa[i]);
            } else {
                p = std::max (p, std::max (sa[i-1], sa[i]));
            }
            cnt++;
            if (cnt + 1 >= m) {
                ret = std::max (ret, p);
            }
        } else {
            p = -1;
            cnt = 0;
        }
    }
    return ret;
}

int main() {
    while (scanf ("%d", &m) == 1) {
        if (!m) break;
        scanf ("%s", s);
        int n = strlen (s);

        if (m == 1) {
            printf ("%d %d\n", n, 0);
            continue;
        }

        DA (s, n + 1);
        calc_height (s, sa, n);

        int best = 0, pos = -1;
        int left = 0, right = n;
        while (left <= right) {
            int mid = left + right >> 1;
            int res = check (mid, n);
            if (res != -1) {
                if (best < mid) {
                    best = mid;
                    pos = res;
                } else if (mid > 0 && best == mid && pos < res) {
                    pos = res;
                }
                left = mid + 1;
            } else {
                right = mid - 1;
            }
        }
        if (pos == -1) {
            puts ("none");
        } else {
            printf ("%d %d\n", best, pos);
        }
    }

    return 0;
}