大意: 求重复$k$次的子串个数
枚举重复长度$i$, 把整个串分为$n/i$块, 如果每块可以$O(1)$计算, 那么最终复杂度就为$O(nlogn)$
有个结论是: 以$j$开头的子串重复次数最大为$1+\lfloor\frac{lcp(j,j+i)}{i}\rfloor$
先特判掉$k=1$的情况, 然后枚举每个块开头的位置, 计算出$lcp$的值$p$, 由于$k>1$, 合法位置的$lcp$值至少要跨越一个块, 可以得到
- 若$p\ge ki-1$, 那么这个块内所有点都合法
- 若$k(i-1)\le p< ki-1$, 那么这个块内只有前面一部分合法, 后面一部分一定不合法
- 若$p<k(i-1)$, 那么前面一部分一定不合法, 可能合法的点只有该块末尾与下一块的最长公共后缀的长度
#include <iostream> #include <sstream> #include <algorithm> #include <cstdio> #include <cmath> #include <set> #include <map> #include <queue> #include <string> #include <cstring> #include <bitset> #include <functional> #include <random> #define REP(i,a,n) for(int i=a;i<=n;++i) #define PER(i,a,n) for(int i=n;i>=a;--i) #define hr putchar(10) #define pb push_back #define lc (o<<1) #define rc (lc|1) #define mid ((l+r)>>1) #define ls lc,l,mid #define rs rc,mid+1,r #define x first #define y second #define io std::ios::sync_with_stdio(false) #define endl '\n' #define DB(a) ({REP(__i,1,n) cout<<a[__i]<<' ';hr;}) using namespace std; typedef long long ll; typedef pair<int,int> pii; const int P = 1e9+7, INF = 0x3f3f3f3f; ll gcd(ll a,ll b) {return b?gcd(b,a%b):a;} ll qpow(ll a,ll n) {ll r=1%P;for (a%=P;n;a=a*a%P,n>>=1)if(n&1)r=r*a%P;return r;} ll inv(ll x){return x<=1?1:inv(P%x)*(P-P/x)%P;} inline int rd() {int x=0;char p=getchar();while(p<'0'||p>'9')p=getchar();while(p>='0'&&p<='9')x=x*10+p-'0',p=getchar();return x;} //head const int N = 1e6+10; int c[N],rk[N],rk2[N],h[N],sa[N]; const int Max_N = N; namespace SA_IS { int *sa; template <typename _Char> void push_S(const _Char s[],const int x,int cur[]) { sa[--cur[static_cast<int>(s[x])]] = x; }; template <typename _Char> void push_L(const _Char s[],const int x,int cur[]) { sa[cur[static_cast<int>(s[x])]++] = x; }; template <typename _Char> void induced_sort(const int v[], const int n, const int m, const _Char s[], char type[], int cnt[], int n1) { std::fill(sa, sa + n, 0); int *cur = cnt + m; std::copy(cnt, cnt + m, cur); for (int i = n1 - 1; i >= 0; --i) push_S(s,v[i],cur); std::copy(cnt, cnt + m - 1, cur + 1); for (int i = 0; i < n; ++i) if (sa[i] > 0 && type[sa[i] - 1] == 0) push_L(s,sa[i] - 1,cur); std::copy(cnt, cnt + m, cur); for (int i = n - 1; i >= 0; --i) if (sa[i] > 0 && type[sa[i] - 1]) push_S(s,sa[i] - 1,cur); } template <typename _Char> bool lms_equal(const _Char s[],char type[],int x, int y) { if (s[x] == s[y]) while (s[++x] == s[++y] && type[x] == type[y]) if (type[x] == 2 || type[y] == 2) return true; return false; } char *tp; bool cmp(const int x) { return tp[x]!=2; } template <typename _Char> void sais_core(const int n, const int m, const _Char s[], char type[], int lms[], int cnt[]) { int n1 = 0, ch = -1; tp = type; type[n - 1] = 1; for (int i = n - 2; i >= 0; --i) type[i] = s[i] == s[i + 1] ? type[i + 1] : s[i] < s[i + 1]; std::fill(cnt, cnt + m, 0); for (int i = 0; i < n; ++i) ++cnt[static_cast<int>(s[i])]; std::partial_sum(cnt, cnt + m, cnt); for (int i = 1; i < n; ++i) if (type[i - 1] == 0 && type[i] == 1) type[i] = 2, lms[n1++] = i; induced_sort(lms,n,m,s,type,cnt,n1); int *s1 = std::remove_if(sa, sa + n, cmp); for (int i = 0; i < n1; ++i) s1[sa[i] >> 1] = ch += ch <= 0 || !lms_equal(s,type,sa[i], sa[i - 1]); for (int i = 0; i < n1; ++i) s1[i] = s1[lms[i] >> 1]; if (ch + 1 < n1) sais_core(n1, ch + 1, s1, type + n, lms + n1, cnt + m); else for (int i = 0; i < n1; ++i) sa[s1[i]] = i; for (int i = 0; i < n1; ++i) lms[n1 + i] = lms[sa[i]]; induced_sort(lms + n1,n,m,s,type,cnt,n1); } template <typename _Char> void main(const _Char s[], const int n, const int m) { static int _lms[Max_N], _cnt[Max_N << 1]; static char _type[Max_N << 1]; sais_core(n + 1, m, s, _type, _lms, _cnt); } } void calc(int *s,int *rk,int n) { REP(i,1,n) ++sa[i]; for(int i=1;i<=n;i++) rk[sa[i]]=i; for(int i=1,j,k=0;i<=n;i++) { if(k) k--; j=sa[rk[i]-1]; while (s[i+k]==s[j+k]) k++; h[rk[i]] = k; } } void build(int *a,int *rk,int n) { SA_IS::sa = sa; a[n+1] = 0; SA_IS::main(a+1,n,128); calc(a,rk,n); } int Log[N],f[20][N],g[20][N]; void init(int a[N],int f[20][N],int n) { Log[0] = -1; REP(i,1,n) f[0][i] = a[i], Log[i]=Log[i>>1]+1; REP(j,1,19) for (int i=0;i+(1<<j-1)-1<=n; ++i) { f[j][i] = min(f[j-1][i],f[j-1][i+(1<<j-1)]); } } int RMQ(int f[20][N], int l, int r) { int t = Log[r-l+1]; return min(f[t][l],f[t][r-(1<<t)+1]); } int n, k, a[N]; char s[N]; int lcp(int x, int y) { x = rk[x], y = rk[y]; if (x>y) swap(x,y); return RMQ(f,x+1,y); } int lcs(int x, int y) { x = rk2[n-x+1], y = rk2[n-y+1]; if (x>y) swap(x,y); return RMQ(g,x+1,y); } int main() { int t; scanf("%d", &t); while (t--) { scanf("%d%s", &k, s+1); n = strlen(s+1); if (k==1) { printf("%lld\n",(ll)n*(n+1)/2); continue; } REP(i,1,n) a[i]=s[i]-'a'+1; build(a,rk,n); init(h,f,n); reverse(a+1,a+1+n); build(a,rk2,n); init(h,g,n); ll ans = 0; REP(i,1,n) for (int j=1; j+i<=n; j+=i) { int p = lcp(j,j+i); if (p>=k*i) ans += i; else if (p>=k*i-i) ans += p-k*i+i+1; else { if (j+2*i-1>n) break; int s = lcs(j+i-1,j+2*i-1); if (!s) continue; s = min(s, i-1); int p2 = lcp(j+i-s,j+2*i-s); if (p2>=k*i-i) ans += min(p2-k*i+i+1,s); } } printf("%lld\n", ans); } }