洛谷P5108 仰望半月的夜空(后缀数组)

题意

题目链接

sol

warning：下面这个做法只有95分，本地拍了1w+组都没找到错误我表示十分无能为力

我们考虑每个串的排名去更新答案，显然排名为\(1\)的后缀的前缀一定是当前长度的字典序最小的答案，但不一定是左端点最小的答案，因此还需要用一个数据结构去维护一下所有可行的左端点。然后枚举所有后缀更新答案就行了。

#include<bits/stdc++.h> 
using namespace std;
const int maxn = 2e6 + 10, ss = 6e5 + 10, inf = 1e9 + 10;
template <typename a, typename b> inline bool chmin(a &a, b b){if(a > b) {a = b; return 1;} return 0;}
template <typename a, typename b> inline bool chmax(a &a, b b){if(a < b) {a = b; return 1;} return 0;}
inline int read() {
    char c = getchar(); int x = 0, f = 1;
    while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
int charset, n, m, ans[ss];
int s[ss]; char stmp[ss];
int rak[ss], tp[ss], tax[maxn * 10], sa[ss], height[ss];
void sort() {
    for(int i = 0; i <= m; i++) tax[i] = 0;
    for(int i = 1; i <= n; i++) tax[rak[i]]++;
    for(int i = 1; i <= m; i++) tax[i] += tax[i - 1];
    //for(int i = n; i >= 1; i--) sa[i] = tp[tax[rak[i]]--];
    for(int i = n; i >= 1; i--) sa[tax[rak[tp[i]]]--] = tp[i];
}
void suffixarrarybuild() {
    m = charset;
    for(int i = 1; i <= n; i++) rak[i] = s[i], tp[i] = i;
    sort();
    for(int w = 1, p; w < n; w <<= 1, m = p) {
        p = 0;
        for(int i = n - w + 1; i <= n; i++) tp[++p] = i;
        for(int i = 1; i <= n; i++) if(sa[i] > w) tp[++p] = sa[i] - w;
        sort(); swap(rak, tp);
        rak[sa[1]] = p = 1; 
        for(int i = 2; i <= n; i++) 
            rak[sa[i]] = (tp[sa[i]] == tp[sa[i - 1]] && tp[sa[i] + w] == tp[sa[i - 1] + w] ? p : ++p);
    }
    for(int i = 1, k = 0; i <= n; i++) {
    
        int j = sa[rak[i] - 1];
        if(k) k--;
        while(j && s[i + k] == s[j + k]) k++;//mmp一开始没写j.. 
            height[rak[i]] = k;//tag
    }
}
#define ls k << 1
#define rs k << 1 | 1
int mn[maxn];
void update(int k) {
    mn[k] = min(mn[ls], mn[rs]);
}
void build(int k, int l, int r) {
    if(l == r) {mn[k] = sa[l]; return ;}
    int mid = l + r >> 1;
    build(ls, l, mid); build(rs, mid + 1, r);
    update(k);
}
int intquery(int k, int l, int r, int ql, int qr) {
    if(ql <= l && r <= qr) return mn[k];
    int mid = l + r >> 1;
    if(ql > mid) return intquery(rs, mid + 1, r, ql, qr);
    else if(qr <= mid) return intquery(ls, l, mid, ql, qr);
    else return min(intquery(ls, l, mid, ql, qr), intquery(rs, mid + 1, r, ql, qr));
}
int f[maxn][20];
int find(int pos, int cur) {//从pos开始的height，第一个 < cur的位置 
    if(height[pos] < cur) return pos - 1;
    for(int i = 19; i >= 1; i--) {
        while(f[pos][i] >= cur && f[pos][i] <= inf && pos + (1 << i) - 1 <= n) 
            pos = pos + (1 << i) - 1;
    }
    return pos;
}

void solve() {
    build(1, 1, n);
    memset(f, 0x3f, sizeof(f));
    for(int i = 1; i <= n; i++) f[i][0] = height[i];
    for(int j = 1; j <= 19; j++) 
        for(int i = 1; i + (1 << j) - 1<= n; i++) 
            chmin(f[i][j], min(f[i][j - 1], f[i + (1 << j - 1)][j - 1]));
    
    
    int cur = 1;//马上要找的答案 
    for(int rk = 1; rk <= n; rk++) {
        if((n - sa[rk] + 1) < cur) continue;
        int pos = sa[rk];
        for(int i = pos + cur - 1; i <= n; i++) {
            int j = find(rk + 1, cur);
            ans[cur++] = intquery(1, 1, n, rk, j);
        }
    }
}
signed main() {
    charset = read(); n = read();
    if(charset == 26) {
        scanf("%s", stmp + 1);
        for(int i = 1; i <= n; i++) s[i] = stmp[i] - 'a';
    }
    else for(int i = 1; i <= n; i++) s[i] = read();
    suffixarrarybuild();
    solve();
    for(int i = 1; i <= n; i++) cout << ans[i] << ' ';
    return 0;
}