题解：P2282 [HNOI2003] 历史年份
ZhongYuLin · · 题解
理论线性的做法
设：
其中字符串比较代价为
发现
这份代码是
#include<bits/stdc++.h>
using namespace std;
const int N=2e3+3;
namespace SA{
int sa[N],A[N],B[N],c[N],rk[N],hgt[N],f[22][N];
template<class T>
void SA(const T &s){
int n=s.size()-1,m=*max_element(s.begin(),s.end());
fill_n(c+1,m,0);
for(int i=1;i<=n;++i)++c[A[i]=s[i]];
for(int i=2;i<=m;++i)c[i]+=c[i-1];
for(int i=n;i;--i)sa[c[A[i]]--]=i;
for(int j=1;j<=n;j<<=1){
int cnt=0;
for(int i=n-j+1;i<=n;++i)B[++cnt]=i;
for(int i=1;i<=n;++i)if(sa[i]>j)B[++cnt]=sa[i]-j;
fill_n(c+1,m,0);
for(int i=1;i<=n;++i)++c[A[i]];
for(int i=2;i<=m;++i)c[i]+=c[i-1];
for(int i=n;i;--i)sa[c[A[B[i]]]--]=B[i];
copy(A+1,A+1+n,B+1);m=0;
for(int i=1;i<=n;++i)
A[sa[i]]=(m+=B[sa[i]]!=B[sa[i-1]]||B[sa[i]+j]!=B[sa[i-1]+j]);
if(n==m)break;
}
for(int i=1;i<=n;++i)rk[sa[i]]=i;
for(int i=1,k=0;i<=n;++i){
if(rk[i]==1)continue;
if(k)--k;
int j=sa[rk[i]-1];
while(i+k<=n&&j+k<=n&&s[i+k]==s[j+k])++k;
hgt[rk[i]]=k;
}
for(int i=1;i<=n;++i)f[0][i]=hgt[i];
for(int j=1;1<<j<=n;++j)
for(int i=1;i+(1<<j)-1<=n;++i)
f[j][i]=min(f[j-1][i],f[j-1][i+(1<<j-1)]);
}
int ask(int x,int y){
if(x==y)return x;
if((x=rk[x])>(y=rk[y]))swap(x,y);
int k=__lg(y-x);
return min(f[k][x+1],f[k][y-(1<<k)+1]);
}
}
int n;
string s;
int R[N],f[N],g[N],mx[N],L[N];
bool vis[N];
vector<int>tmp[N];
bool cmp(int x,int y,int u,int v){
x=R[x];u=R[u];
if(!u)return 0;
int l1=y-x+1,l2=v-u+1;
if(l1!=l2)return l1<l2;
int lcp=SA::ask(x,u);
if(lcp>=l1)return 0;
return s[x+lcp]<s[u+lcp];
}
void solve(){
n=s.size();
if(count(s.begin(),s.end(),'0')==n){
printf("%s\n",s.c_str());
return;
}
s="#"+s;SA::SA(s);R[n+1]=0;
for(int i=1;i<=n;++i){
L[i]=L[i-1];
if(s[i]!='0')L[i]=i;
}
for(int i=n;i;--i){
R[i]=R[i+1];
if(s[i]!='0')R[i]=i;
f[i]=1;g[i]=mx[i]=vis[i]=0;
tmp[i].clear();
}
for(int i=1,pre=0;i<=n;++i){
pre=max(pre,mx[i]);f[i]=pre+1;
int l=R[i+1],r=l+i-R[f[i]];
if(!l||r>n)continue;
if(cmp(f[i],i,l,r))
if(l==r)mx[i+1]=max(mx[i+1],i);
else mx[r]=max(mx[r],i);
else mx[r+1]=max(mx[r+1],i);
}
int now=f[n];
auto cg=[&](int i,int k){
g[i]=k;int l=max(1,min(i-(g[i]-min(R[i],g[i])),L[i-1]));
if(cmp(l,i-1,i,k-1))l=L[l-1];
if(l)tmp[l].push_back(i);
};
do cg(now--,n+1);while(now&&s[now]=='0');
for(int i=now,mx=f[n];i;--i){
for(auto x:tmp[i])vis[x]=1;
while(vis[mx])--mx;cg(i,mx);
}
for(int x=1;x<=n;x=g[x],printf("%c","\n,"[x<=n]))
for(int i=x;i<g[x];++i)
printf("%c",s[i]);
}
int main(){
int u,v,w,x,y,z;
ios::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
for(;cin>>s;)solve();
return 0;
}给出用各处板子拼出来的
#include<bits/stdc++.h>
using namespace std;
const int N=2e3+3;
namespace SA{
namespace atcoder {
namespace internal {
std::vector<int> sa_naive(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n);
std::iota(sa.begin(), sa.end(), 0);
std::sort(sa.begin(), sa.end(), [&](int l, int r) {
if (l == r) return false;
while (l < n && r < n) {
if (s[l] != s[r]) return s[l] < s[r];
l++;
r++;
}
return l == n;
});
return sa;
}
std::vector<int> sa_doubling(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n), rnk = s, tmp(n);
std::iota(sa.begin(), sa.end(), 0);
for (int k = 1; k < n; k *= 2) {
auto cmp = [&](int x, int y) {
if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
int rx = x + k < n ? rnk[x + k] : -1;
int ry = y + k < n ? rnk[y + k] : -1;
return rx < ry;
};
std::sort(sa.begin(), sa.end(), cmp);
tmp[sa[0]] = 0;
for (int i = 1; i < n; i++) {
tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
}
std::swap(tmp, rnk);
}
return sa;
}
// SA-IS, linear-time suffix array construction
// Reference:
// G. Nong, S. Zhang, and W. H. Chan,
// Two Efficient Algorithms for Linear Time Suffix Array Construction
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
int n = int(s.size());
if (n == 0) return {};
if (n == 1) return {0};
if (n == 2) {
if (s[0] < s[1]) {
return {0, 1};
} else {
return {1, 0};
}
}
if (n < THRESHOLD_NAIVE) {
return sa_naive(s);
}
if (n < THRESHOLD_DOUBLING) {
return sa_doubling(s);
}
std::vector<int> sa(n);
std::vector<bool> ls(n);
for (int i = n - 2; i >= 0; i--) {
ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
}
std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
for (int i = 0; i < n; i++) {
if (!ls[i]) {
sum_s[s[i]]++;
} else {
sum_l[s[i] + 1]++;
}
}
for (int i = 0; i <= upper; i++) {
sum_s[i] += sum_l[i];
if (i < upper) sum_l[i + 1] += sum_s[i];
}
auto induce = [&](const std::vector<int>& lms) {
std::fill(sa.begin(), sa.end(), -1);
std::vector<int> buf(upper + 1);
std::copy(sum_s.begin(), sum_s.end(), buf.begin());
for (auto d : lms) {
if (d == n) continue;
sa[buf[s[d]]++] = d;
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
sa[buf[s[n - 1]]++] = n - 1;
for (int i = 0; i < n; i++) {
int v = sa[i];
if (v >= 1 && !ls[v - 1]) {
sa[buf[s[v - 1]]++] = v - 1;
}
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
for (int i = n - 1; i >= 0; i--) {
int v = sa[i];
if (v >= 1 && ls[v - 1]) {
sa[--buf[s[v - 1] + 1]] = v - 1;
}
}
};
std::vector<int> lms_map(n + 1, -1);
int m = 0;
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms_map[i] = m++;
}
}
std::vector<int> lms;
lms.reserve(m);
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms.push_back(i);
}
}
induce(lms);
if (m) {
std::vector<int> sorted_lms;
sorted_lms.reserve(m);
for (int v : sa) {
if (lms_map[v] != -1) sorted_lms.push_back(v);
}
std::vector<int> rec_s(m);
int rec_upper = 0;
rec_s[lms_map[sorted_lms[0]]] = 0;
for (int i = 1; i < m; i++) {
int l = sorted_lms[i - 1], r = sorted_lms[i];
int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
bool same = true;
if (end_l - l != end_r - r) {
same = false;
} else {
while (l < end_l) {
if (s[l] != s[r]) {
break;
}
l++;
r++;
}
if (l == n || s[l] != s[r]) same = false;
}
if (!same) rec_upper++;
rec_s[lms_map[sorted_lms[i]]] = rec_upper;
}
auto rec_sa =
sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);
for (int i = 0; i < m; i++) {
sorted_lms[i] = lms[rec_sa[i]];
}
induce(sorted_lms);
}
return sa;
}
} // namespace internal
std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
assert(0 <= upper);
for (int d : s) {
assert(0 <= d && d <= upper);
}
auto sa = internal::sa_is(s, upper);
return sa;
}
template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
int n = int(s.size());
std::vector<int> idx(n);
iota(idx.begin(), idx.end(), 0);
sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
std::vector<int> s2(n);
int now = 0;
for (int i = 0; i < n; i++) {
if (i && s[idx[i - 1]] != s[idx[i]]) now++;
s2[idx[i]] = now;
}
return internal::sa_is(s2, now);
}
std::vector<int> suffix_array(const std::string& s) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return internal::sa_is(s2, 255);
}
// Reference:
// T. Kasai, G. Lee, H. Arimura, S. Arikawa, and K. Park,
// Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its
// Applications
template <class T>
std::vector<int> lcp_array(const std::vector<T>& s,
const std::vector<int>& sa) {
int n = int(s.size());
assert(n >= 1);
std::vector<int> rnk(n);
for (int i = 0; i < n; i++) {
rnk[sa[i]] = i;
}
std::vector<int> lcp(n - 1);
int h = 0;
for (int i = 0; i < n; i++) {
if (h > 0) h--;
if (rnk[i] == 0) continue;
int j = sa[rnk[i] - 1];
for (; j + h < n && i + h < n; h++) {
if (s[j + h] != s[i + h]) break;
}
lcp[rnk[i] - 1] = h;
}
return lcp;
}
std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return lcp_array(s2, sa);
}
// Reference:
// D. Gusfield,
// Algorithms on Strings, Trees, and Sequences: Computer Science and
// Computational Biology
template <class T> std::vector<int> z_algorithm(const std::vector<T>& s) {
int n = int(s.size());
if (n == 0) return {};
std::vector<int> z(n);
z[0] = 0;
for (int i = 1, j = 0; i < n; i++) {
int& k = z[i];
k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);
while (i + k < n && s[k] == s[i + k]) k++;
if (j + z[j] < i + z[i]) j = i;
}
z[0] = n;
return z;
}
std::vector<int> z_algorithm(const std::string& s) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return z_algorithm(s2);
}
}
const int MAXN=2e6+3;
const int MAXM=22;
struct RMQ {
int N, A[MAXN];
int blockSize;
int S[MAXN][MAXM], Pow[MAXM], Log[MAXN];
int Belong[MAXN], Pos[MAXN];
int Pre[MAXN], Sub[MAXN];
int F[MAXN];
void buildST() {
int cur = 0, id = 1;
Pos[0] = -1;
for (int i = 1; i <= N; ++i) {
S[id][0] = max(S[id][0], A[i]);
Belong[i] = id;
if (Belong[i - 1] != Belong[i])
Pos[i] = 0;
else
Pos[i] = Pos[i - 1] + 1;
if (++cur == blockSize) {
cur = 0;
++id;
}
}
if (N % blockSize == 0) --id;
Pow[0] = 1;
for (int i = 1; i < MAXM; ++i) Pow[i] = Pow[i - 1] * 2;
for (int i = 2; i <= id; ++i) Log[i] = Log[i / 2] + 1;
for (int i = 1; i <= Log[id]; ++i) {
for (int j = 1; j + Pow[i] - 1 <= id; ++j) {
S[j][i] = std::max(S[j][i - 1], S[j + Pow[i - 1]][i - 1]);
}
}
}
void buildSubPre() {
Sub[N+1]=0;
for (int i = 1; i <= N; ++i) {
if (Belong[i] != Belong[i - 1])
Pre[i] = A[i];
else
Pre[i] = std::max(Pre[i - 1], A[i]);
}
for (int i = N; i >= 1; --i) {
if (Belong[i] != Belong[i + 1])
Sub[i] = A[i];
else
Sub[i] = std::max(Sub[i + 1], A[i]);
}
}
void buildBlock() {
static int S[MAXN], top;
top=0;
for (int i = 1; i <= N; ++i) {
if (Belong[i] != Belong[i - 1])
top = 0;
else
F[i] = F[i - 1];
while (top > 0 && A[S[top]] <= A[i]) F[i] &= ~(1 << Pos[S[top--]]);
S[++top] = i;
F[i] |= (1 << Pos[i]);
}
}
void init() {
for(int i=1;i<=N;++i)S[i][0]=0;
blockSize = log2(N) * 1.5;
buildST();
buildSubPre();
buildBlock();
}
int queryMax(int l, int r) {
int bl = Belong[l], br = Belong[r];
if (bl != br) {
int ans1 = 0;
if (br - bl > 1) {
int p = Log[br - bl - 1];
ans1 = std::max(S[bl + 1][p], S[br - Pow[p]][p]);
}
int ans2 = std::max(Sub[l], Pre[r]);
return std::max(ans1, ans2);
} else {
return A[l + __builtin_ctz(F[r] >> Pos[l])];
}
}
} R;
int rk[N];
const int INF=0x3f3f3f3f;
void SA(const string &s){
auto sa=atcoder::suffix_array(s);
auto hgt=atcoder::lcp_array(s,sa);
int n=s.size();R.N=n+1;
for(int i=1;i<=n;++i)rk[sa[i-1]+1]=i;
for(int i=2;i<=n;++i)R.A[i]=INF-hgt[i-2];
R.A[1]=0;R.A[n+1]=0;R.init();
}
int ask(int x,int y){
if(x==y)return x;
if((x=rk[x])>(y=rk[y]))swap(x,y);
return INF-R.queryMax(x+1,y);
}
}int n;
string s;
int R[N],f[N],g[N],mx[N],L[N];
bool vis[N];
vector<int>tmp[N];
bool cmp(int x,int y,int u,int v){
x=R[x];u=R[u];
if(!u)return 0;
int l1=y-x+1,l2=v-u+1;
if(l1!=l2)return l1<l2;
int lcp=SA::ask(x,u);
if(lcp>=l1)return 0;
return s[x+lcp]<s[u+lcp];
}
void solve(){
n=s.size();
if(count(s.begin(),s.end(),'0')==n){
printf("%s\n",s.c_str());
return;
}
SA::SA(s);s="#"+s;R[n+1]=0;
for(int i=1;i<=n;++i){
L[i]=L[i-1];
if(s[i]!='0')L[i]=i;
}
for(int i=n;i;--i){
R[i]=R[i+1];
if(s[i]!='0')R[i]=i;
f[i]=1;g[i]=mx[i]=vis[i]=0;
tmp[i].clear();
}
for(int i=1,pre=0;i<=n;++i){
pre=max(pre,mx[i]);f[i]=pre+1;
int l=R[i+1],r=l+i-R[f[i]];
if(!l||r>n)continue;
if(cmp(f[i],i,l,r))
if(l==r)mx[i+1]=max(mx[i+1],i);
else mx[r]=max(mx[r],i);
else mx[r+1]=max(mx[r+1],i);
}
int now=f[n];
auto cg=[&](int i,int k){
g[i]=k;int l=max(1,min(i-(g[i]-min(R[i],g[i])),L[i-1]));
if(cmp(l,i-1,i,k-1))l=L[l-1];
if(l)tmp[l].push_back(i);
};
do cg(now--,n+1);while(now&&s[now]=='0');
for(int i=now,mx=f[n];i;--i){
for(auto x:tmp[i])vis[x]=1;
while(vis[mx])--mx;cg(i,mx);
}
for(int x=1;x<=n;x=g[x],printf("%c","\n,"[x<=n]))
for(int i=x;i<g[x];++i)
printf("%c",s[i]);
}
int main(){
int u,v,w,x,y,z;
ios::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
for(;cin>>s;)solve();
return 0;
}