結果

問題 No.3000 Optimal Run Length Encoding
ユーザー 👑 hos.lyric
提出日時 2024-12-25 01:15:50
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2,107 ms / 10,000 ms
コード長 15,647 bytes
コンパイル時間 3,263 ms
コンパイル使用メモリ 178,560 KB
実行使用メモリ 353,272 KB
最終ジャッジ日時 2024-12-25 19:52:06
合計ジャッジ時間 87,090 ms
ジャッジサーバーID
(参考情報)
judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 142
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ソースコード

diff #
プレゼンテーションモードにする

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i
    >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")
////////////////////////////////////////////////////////////////////////////////
// SA-IS
// String: string, vector<int>, vector<long long>
// if sigma <= n, O(n) time, O(n) space
// if sigma > n, O(n log n) time, O(n) space
template <class String> vector<int> suffixArrayRec(const String &as) {
const int n = as.size();
if (n == 0) return {};
const auto minmaxA = minmax_element(as.begin(), as.end());
const auto minA = *minmaxA.first, maxA = *minmaxA.second;
if (static_cast<unsigned long long>(maxA) - minA >=
static_cast<unsigned long long>(n)) {
vector<int> us(n);
for (int u = 0; u < n; ++u) us[u] = u;
std::sort(us.begin(), us.end(), [&](int u, int v) -> bool {
return (as[u] < as[v]);
});
int b = 0;
vector<int> bs(n, 0);
for (int i = 1; i < n; ++i) {
if (as[us[i - 1]] != as[us[i]]) ++b;
bs[us[i]] = b;
}
return suffixArrayRec(bs);
}
const int sigma = maxA - minA + 1;
vector<int> pt(sigma + 1, 0), poss(sigma);
for (int u = 0; u < n; ++u) ++pt[as[u] - minA + 1];
for (int a = 0; a < sigma; ++a) pt[a + 1] += pt[a];
// cmp[u] := (as[u, n) < as[u + 1, n))
vector<bool> cmp(n);
cmp[n - 1] = false;
for (int u = n - 1; --u >= 0; ) {
cmp[u] = (as[u] != as[u + 1]) ? (as[u] < as[u + 1]) : cmp[u + 1];
}
// ><, nn - id (0 <= id < n)
int nn = 0;
vector<int> ids(n, 0);
int last = n;
vector<int> nxt(n, 0);
// put ><, from the tail of each bucket
vector<int> us(n, 0);
memcpy(poss.data(), pt.data() + 1, sigma * sizeof(int));
for (int u = n - 1; --u >= 1; ) if (!cmp[u - 1] && cmp[u]) {
ids[u] = ++nn;
nxt[u] = last;
last = u;
us[--poss[as[u] - minA]] = u;
}
// follow > backwards, from the head of each bucket
memcpy(poss.data(), pt.data(), sigma * sizeof(int));
us[poss[as[n - 1] - minA]++] = n - 1;
for (int i = 0; i < n; ++i) {
const int u = us[i];
if (u && !cmp[u - 1]) us[poss[as[u - 1] - minA]++] = u - 1;
}
// follow < backwards, from the tail of each bucket
memcpy(poss.data(), pt.data() + 1, sigma * sizeof(int));
for (int i = n; --i >= 0; ) {
const int u = us[i];
if (u && cmp[u - 1]) us[--poss[as[u - 1] - minA]] = u - 1;
}
if (nn) {
int vsLen = 0;
vector<int> vs(nn);
for (const int u : us) if (ids[u]) vs[vsLen++] = u;
int b = 0;
vector<int> bs(nn, 0);
for (int j = 1; j < nn; ++j) {
// as[v1, w1] (< or =) as[v0, w0]
int v1 = vs[j - 1], v0 = vs[j];
const int w1 = nxt[v1], w0 = nxt[v0];
if (w1 - v1 != w0 - v0) {
++b;
} else {
for (; ; ++v1, ++v0) {
if (v1 == n) { ++b; break; }
if (as[v1] != as[v0]) { ++b; break; }
if (v1 == w1) break;
}
}
bs[nn - ids[vs[j]]] = b;
}
for (int u = 0; u < n; ++u) if (ids[u]) vs[nn - ids[u]] = u;
const auto sub = suffixArrayRec(bs);
// put ><, from the tail of each bucket
memset(us.data(), 0, n * sizeof(int));
memcpy(poss.data(), pt.data() + 1, sigma * sizeof(int));
for (int j = nn; --j >= 0; ) {
const int u = vs[sub[j]];
us[--poss[as[u] - minA]] = u;
}
// follow > backwards, from the head of each bucket
memcpy(poss.data(), pt.data(), sigma * sizeof(int));
us[poss[as[n - 1] - minA]++] = n - 1;
for (int i = 0; i < n; ++i) {
const int u = us[i];
if (u && !cmp[u - 1]) us[poss[as[u - 1] - minA]++] = u - 1;
}
// follow < backwards, from the tail of each bucket
memcpy(poss.data(), pt.data() + 1, sigma * sizeof(int));
for (int i = n; --i >= 0; ) {
const int u = us[i];
if (u && cmp[u - 1]) us[--poss[as[u - 1] - minA]] = u - 1;
}
}
return us;
}
// us[i]: i-th suffix
// su[u]: index of as[u, n)
// hs[i]: longest common prefix of as[us[i - 1], n) and as[us[i], n)
struct SuffixArray {
int n;
bool rmq;
vector<int> us, su, hs;
SuffixArray() : n(0), rmq(false) {}
SuffixArray(const string &as, bool rmq_) : rmq(rmq_) { build(as); }
SuffixArray(const vector<int> &as, bool rmq_) : rmq(rmq_) { build(as); }
SuffixArray(const vector<long long> &as, bool rmq_) : rmq(rmq_) { build(as); }
template <class String> void build(const String &as) {
n = as.size();
us = suffixArrayRec(as);
su.resize(n + 1);
for (int i = 0; i < n; ++i) su[us[i]] = i;
su[n] = -1;
hs.assign(n, 0);
for (int h = 0, u = 0; u < n; ++u) if (su[u]) {
for (int v = us[su[u] - 1]; v + h < n && as[v + h] == as[u + h]; ++h) {}
hs[su[u]] = h;
if (h) --h;
}
if (rmq) {
const int logN = n ? (31 - __builtin_clz(n)) : 0;
hs.resize((logN + 1) * n - (1 << logN) + 1);
for (int e = 0; e < logN; ++e) {
int *hes = hs.data() + e * n;
for (int i = 0; i <= n - (1 << (e + 1)); ++i) {
hes[n + i] = min(hes[i], hes[i + (1 << e)]);
}
}
}
}
// Returns longest common prefix of as[u, n) and as[v, n).
// 0 <= u, v <= n
// Assumes rmq.
inline int lcp(int u, int v) const {
if (u == v) return n - u;
int i = su[u], j = su[v];
if (i > j) swap(i, j);
const int e = 31 - __builtin_clz(j - i);
return min(hs[e * n + i + 1], hs[e * n + j + 1 - (1 << e)]);
}
};
////////////////////////////////////////////////////////////////////////////////
// https://codeforces.com/blog/entry/106725
// Lyndon
// * smaller than non-trivial suffix
// * smaller than other cyclic shift
// Lyndon factorization (Lyndon factors in non-incr. order):
// * longest Lyndon prefix greedily
// * min suffix greedily (removing min suffix does not change the suffix order)
// pqs[v] = (p, q): Lyndon factorization of as[0, v) ends with a[v - p, v)^q
// String: string, vector<int>, vector<long long>
// O(n) time
//
// min_u as[u, v) bs:
// for (int u = v; ; ) {
// // candidate u
// if (v == 0) break;
// const int p = pqs[u].first, q = pqs[u].second;
// const int uu = u - q * p;
// if (!(p >= v - u && sa.lcp(uu, u) >= v - u)) break;
// // (v - u) is at least doubled
// u = uu;
// }
// }
template <class String>
vector<pair<int, int>> lyndonSuffix(const String &as) {
const int n = as.size();
vector<pair<int, int>> pqs(n + 1);
pqs[0] = make_pair(0, 0);
for (int u = 0; u < n; ) {
for (int p = 1, q = 1, r = 0, v = u + 1; ; ++v) {
// as[u, v) = as[u, u + p)^q as[u, u + r)
// as[u, u + p): Lyndon
pqs[v] = (r != 0) ? pqs[u + r] : make_pair(p, q);
if (v == n || as[v - p] > as[v]) {
u = v - r;
break;
} else if (as[v - p] < as[v]) {
p = v + 1 - u; q = 1; r = 0;
} else {
if (++r == p) { ++q; r = 0; }
}
}
}
return pqs;
}
// as[u, vs[u]): longest Lyndon prefix of as[u, n)
// String: string, vector<int>, vector<long long>
// O(n) time
template <class String>
vector<int> lyndonPrefix(const String &as, const SuffixArray &sa) {
const int n = as.size();
// top: larger suffix
int stackLen = 0;
vector<int> stack(n + 1);
vector<int> vs(n);
for (int u = 0; u <= n; ++u) {
for (; stackLen > 0 && sa.su[stack[stackLen - 1]] > sa.su[u]; --stackLen) {
vs[stack[stackLen - 1]] = u;
}
stack[stackLen++] = u;
}
return vs;
}
template <class String>
vector<int> lyndonPrefix(const String &as) {
return lyndonPrefix(as, SuffixArray(as, /*rmq=*/false));
}
// lyndonPrefix for invert(as), using suffix array of as
template <class String>
vector<int> lyndonPrefixInverted(const String &as, const SuffixArray &sa) {
assert(sa.rmq);
const int n = as.size();
// top: larger suffix
int stackLen = 0;
vector<int> stack(n + 1);
vector<int> vs(n);
for (int u = 0; u <= n; ++u) {
for (; stackLen > 0; --stackLen) {
const int uu = stack[stackLen - 1];
const int l = sa.lcp(uu, u);
if (u + l < n && as[uu + l] > as[u + l]) break;
vs[uu] = u;
}
stack[stackLen++] = u;
}
return vs;
}
// (p, [u, v)): run <=>
// * p: min period of as[u, v)
// * v - u >= 2 p
// * [u, v): maximal
// \sum 1 <= n
// \sum (v - u) / p <= 3 n
// \sum (v - u - 2 p + 1) \in O(n log n) (TODO: proof)
// Returns runs (p, [u, v)) in lex. order.
// String: string, vector<int>, vector<long long>
// O(n log n) time, (<= 6 n + 2) SuffixArray::lcp calls
template <class String>
vector<pair<int, pair<int, int>>> repetitions(const String &as, const SuffixArray &sa) {
assert(sa.rmq);
const int n = as.size();
if (n == 0) return {};
String asRev = as;
std::reverse(asRev.begin(), asRev.end());
const SuffixArray saRev(asRev, /*rmq=*/true);
const vector<int> vs = lyndonPrefix(as, sa);
const vector<int> vsInverted = lyndonPrefixInverted(as, sa);
vector<pair<int, pair<int, int>>> runs;
for (int u = 0; u < n; ++u) {
// from longest lyndon prefix of as[u, n) or invert(as)[u, n)
{
const int v = vs[u];
const int p = v - u, uu = u - saRev.lcp(n - u, n - v), vv = v + sa.lcp(u, v);
if (vv - uu >= 2 * p) runs.emplace_back(p, make_pair(uu, vv));
}
if (vs[u] != vsInverted[u]) {
const int v = vsInverted[u];
const int p = v - u, uu = u - saRev.lcp(n - u, n - v), vv = v + sa.lcp(u, v);
if (vv - uu >= 2 * p) runs.emplace_back(p, make_pair(uu, vv));
}
}
// radix sort
const int runsLen = runs.size();
auto runsWork = runs;
vector<int> pt(n + 1, 0);
for (int i = 0; i < runsLen; ++i) ++pt[runs[i].second.first];
for (int u = 0; u < n - 1; ++u) pt[u + 1] += pt[u];
for (int i = runsLen; --i >= 0; ) runsWork[--pt[runs[i].second.first]] = runs[i];
memset(pt.data() + 1, 0, n * sizeof(int));
for (int i = 0; i < runsLen; ++i) ++pt[runsWork[i].first];
for (int p = 1; p < n; ++p) pt[p + 1] += pt[p];
for (int i = runsLen; --i >= 0; ) runs[--pt[runsWork[i].first]] = runsWork[i];
runs.erase(std::unique(runs.begin(), runs.end()), runs.end());
return runs;
}
template <class String>
vector<pair<int, pair<int, int>>> repetitions(const String &as) {
return repetitions(as, SuffixArray(as, /*rmq=*/true));
}
////////////////////////////////////////////////////////////////////////////////
constexpr int INF = 1001001001;
constexpr int TEN[7] = {
1,
10,
100,
1000,
10000,
100000,
1000000,
};
int N;
char S[500'010];
int main() {
for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
scanf("%s", S);
N = strlen(S);
const auto runs = repetitions(string(S));
// cerr<<"runs = "<<runs<<endl;
const int len = runs.size();
vector<vector<int>> headss[6];
vector<vector<vector<pair<int, int>>>> quess[6];
for (int e = 0; e < 6; ++e) {
headss[e].assign(len, {});
quess[e].assign(len, {});
}
for (int i = 0; i < len; ++i) {
const int p = runs[i].first;
const int u = runs[i].second.first;
const int v = runs[i].second.second;
const int lim = (v - u) / p;
const int sz = min(v - u - 2*p + 1, p);
for (int e = 0, ten = 1; ten <= lim; ++e, ten *= 10) {
headss[e][i].assign(sz, 0);
quess[e][i].assign(sz, {});
}
}
vector<vector<int>> addssL(N + 1), remssL(N + 1);
vector<vector<int>> addssR(N + 1), remssR(N + 1);
for (int i = 0; i < len; ++i) {
const int p = runs[i].first;
const int u = runs[i].second.first;
const int v = runs[i].second.second;
addssL[u].push_back(i);
remssL[v - 2*p].push_back(i);
addssR[u + 2*p].push_back(i);
remssR[v].push_back(i);
}
pair<int, int> norun(INF, -1);
vector<int> dp(N + 1, INF);
vector<pair<int, int>> prv(N + 1, make_pair(-1, -1));
set<int> onL, onR;
dp[0] = 0;
for (int x = 0; x <= N; ++x) {
if (x) {
// get
for (const int i : addssR[x]) onR.insert(i);
for (const int i : onR) {
const int p = runs[i].first;
const int u = runs[i].second.first;
const int v = runs[i].second.second;
const int lim = (v - u) / p;
const int r = (x - u) % p;
for (int e = 0, ten = 1; ten <= lim; ++e, ten *= 10) {
int &head = headss[e][i][r];
auto &que = quess[e][i][r];
for (; head < (int)que.size() && que[head].second + (TEN[e + 1] - 1) * p < x; ++head) {}
if (head < (int)que.size()) {
// cerr<<COLOR("94")<<"get "<<x<<" "<<i<<" "<<que[head]<<COLOR()<<endl;
if (chmin(dp[x], que[head].first)) {
prv[x] = make_pair(i, que[head].second);
}
}
}
}
for (const int i : remssR[x]) {
onR.erase(i);
const int p = runs[i].first;
const int u = runs[i].second.first;
const int v = runs[i].second.second;
const int lim = (v - u) / p;
for (int e = 0, ten = 1; ten <= lim; ++e, ten *= 10) {
quess[e][i].clear();
quess[e][i].shrink_to_fit();
}
}
if (chmin(dp[x], norun.first + x)) {
prv[x] = make_pair(-1, norun.second);
}
}
// push
{
for (const int i : addssL[x]) onL.insert(i);
for (const int i : onL) {
const int p = runs[i].first;
const int u = runs[i].second.first;
const int v = runs[i].second.second;
const int lim = (v - u) / p;
const int r = (x - u) % p;
for (int e = 0, ten = 1; ten <= lim; ++e, ten *= 10) {
auto &head = headss[e][i][r];
auto &que = quess[e][i][r];
const pair<int, int> val(dp[x] + p + (e + 1), x);
for (; head < (int)que.size() && que.back() >= val; que.pop_back()) {}
// cerr<<COLOR("91")<<"push "<<x<<" "<<i<<" "<<val<<COLOR()<<endl;
que.push_back(val);
}
}
for (const int i : remssL[x]) onL.erase(i);
chmin(norun, make_pair(dp[x] - x + 1, x));
}
}
// cerr<<"dp = "<<dp<<endl;
// cerr<<"prv = "<<prv<<endl;
vector<string> ops;
for (int x = N; x > 0; ) {
const int i = prv[x].first;
const int y = prv[x].second;
const int p = (~i) ? runs[i].first : (x - y);
ops.push_back(string(S + y, S + (y + p)) + to_string((x - y) / p));
x = y;
}
reverse(ops.begin(), ops.end());
string ans;
for (const auto &op : ops) ans += op;
puts(ans.c_str());
}
#ifndef LOCAL
break;
#endif
}
return 0;
}
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