結果
問題 |
No.3000 Optimal Run Length Encoding
|
ユーザー |
👑 |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 1 |
other | AC * 142 |
ソースコード
#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) spacetemplate <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 bucketvector<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 bucketmemcpy(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 bucketmemcpy(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 bucketmemset(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 bucketmemcpy(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 bucketmemcpy(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): Lyndonpqs[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) timetemplate <class String>vector<int> lyndonPrefix(const String &as, const SuffixArray &sa) {const int n = as.size();// top: larger suffixint 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 astemplate <class String>vector<int> lyndonPrefixInverted(const String &as, const SuffixArray &sa) {assert(sa.rmq);const int n = as.size();// top: larger suffixint 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 callstemplate <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 sortconst 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) {// getfor (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 LOCALbreak;#endif}return 0;}