简略题意:求两个串长度不小于k的公共子串的个数。
我喜欢这题!
首先按height分组,随后对于每个A后缀,看之前出现的B后缀与其的LCP,若其长度为x,则对答案的贡献为想一想,为什么, 因此维护一个单调栈,以及栈内元素贡献总和。显然从栈底到栈顶元素逐渐增大。对A统计完答案之后再对B统计一次即可。
#include <iostream>
#include <cstring>
#include <map>
#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
typedef long long LL;
const LL N = 220000;
LL n, k;
char str[N], str2[N];
LL f = 0;
namespace SA {
LL sa[N], rank[N], height[N], s[N<<1], t[N<<1], p[N], cnt[N], cur[N];
LL MIN[N][30];
#define pushS(x) sa[cur[s[x]]--] = x
#define pushL(x) sa[cur[s[x]]++] = x
#define inducedSort(v) fill_n(sa, n, -1); fill_n(cnt, m, 0); \
for (LL i = 0; i < n; i++) cnt[s[i]]++; \
for (LL i = 1; i < m; i++) cnt[i] += cnt[i-1]; \
for (LL i = 0; i < m; i++) cur[i] = cnt[i]-1; \
for (LL i = n1-1; ~i; i--) pushS(v[i]); \
for (LL i = 1; i < m; i++) cur[i] = cnt[i-1]; \
for (LL i = 0; i < n; i++) if (sa[i] > 0 && t[sa[i]-1]) pushL(sa[i]-1); \
for (LL i = 0; i < m; i++) cur[i] = cnt[i]-1; \
for (LL i = n-1; ~i; i--) if (sa[i] > 0 && !t[sa[i]-1]) pushS(sa[i]-1)
void sais(LL n, LL m, LL *s, LL *t, LL *p) {
LL n1 = t[n-1] = 0, ch = rank[0] = -1, *s1 = s+n;
for (LL i = n-2; ~i; i--) t[i] = s[i] == s[i+1] ? t[i+1] : s[i] > s[i+1];
for (LL i = 1; i < n; i++) rank[i] = t[i-1] && !t[i] ? (p[n1] = i, n1++) : -1;
inducedSort(p);
for (LL i = 0, x, y; i < n; i++) if (~(x = rank[sa[i]])) {
if (ch < 1 || p[x+1] - p[x] != p[y+1] - p[y]) ch++;
else for (LL j = p[x], k = p[y]; j <= p[x+1]; j++, k++)
if ((s[j]<<1|t[j]) != (s[k]<<1|t[k])) {ch++; break;}
s1[y = x] = ch;
}
if (ch+1 < n1) sais(n1, ch+1, s1, t+n, p+n1);
else for (LL i = 0; i < n1; i++) sa[s1[i]] = i;
for (LL i = 0; i < n1; i++) s1[i] = p[sa[i]];
inducedSort(s1);
}
template<typename T>
LL mapCharToLL(LL n, const T *str) {
LL m = *max_element(str, str+n);
fill_n(rank, m+1, 0);
for (LL i = 0; i < n; i++) rank[str[i]] = 1;
for (LL i = 0; i < m; i++) rank[i+1] += rank[i];
for (LL i = 0; i < n; i++) s[i] = rank[str[i]] - 1;
return rank[m];
}
template<typename T>
void suffixArray(LL n, const T *str) {
LL m = mapCharToLL(++n, str);
sais(n, m, s, t, p);
for (LL i = 0; i < n; i++) rank[sa[i]] = i;
for (LL i = 0, h = height[0] = 0; i < n-1; i++) {
LL j = sa[rank[i]-1];
while (i+h < n && j+h < n && s[i+h] == s[j+h]) h++;
if (height[rank[i]] = h) h--;
}
}
void RMQ_init(){
for(LL i=0; i<n; i++) MIN[i][0] = height[i+1];
for(LL j=1; (1<<j)<=n; j++){
for(LL i=0; i+(1<<j)<=n; i++){
MIN[i][j] = min(MIN[i][j-1], MIN[i+(1<<(j-1))][j-1]);
}
}
}
LL RMQ(LL L, LL R){
LL k = 0;
while((1<<(k+1)) <= R-L+1) k++;
return min(MIN[L][k], MIN[R-(1<<k)+1][k]);
}
LL LCP(LL i, LL j){
if(rank[i] > rank[j]) swap(i, j);
return RMQ(rank[i], rank[j]-1);
}
void init(char *str){
suffixArray(n, str);
}
LL stk[N], count[N], top;
void solve(LL k, LL pos) {
top = 0;
LL ans = 0, sum = 0;
for(LL i = 2; i <= n; i++) {
if(height[i] < k) {
top = 0;
sum = 0;
continue;
}
LL cnt = 0;
while(top && stk[top] > height[i]) {
sum -= (stk[top] - k + 1) * count[top];
cnt += count[top];
top--;
}
if(sa[i-1] < pos) {
stk[++top] = height[i];
count[top] = cnt + 1;
sum += (stk[top] - k + 1)*count[top];
} else if(cnt)
stk[++top] = height[i], count[top] = cnt, sum += (stk[top] - k + 1)*count[top];
if(sa[i] > pos)
ans += sum;
}
top = sum = 0;
for(LL i = 2; i <= n; i++) {
if(height[i] < k) {
top = 0;
sum = 0;
continue;
}
LL cnt = 0;
while(top && stk[top] > height[i]) {
sum -= (stk[top] - k + 1) * count[top];
cnt += count[top];
top--;
}
if(sa[i-1] > pos) {
stk[++top] = height[i];
count[top] = cnt + 1;
sum += (stk[top] - k + 1)*count[top];
} else if(cnt)
stk[++top] = height[i], count[top] = cnt, sum += (stk[top] - k + 1)*count[top];
if(sa[i] < pos)
ans += sum;
}
cout<<ans<<endl;
}
};
int main() {
while(~scanf("%lld", &k) && k) {
scanf("%s", str);
scanf("%s", str2);
LL x = strlen(str);
str[x] = '@'; str[x+1] = 0;
strcat(str, str2);
n = strlen(str);
SA::init(str);
SA::solve(k, x);
};
return 0;
}