結果
| 問題 | No.5023 Airlines Optimization |
| コンテスト | |
| ユーザー |
 ぴぃいいいい
|
| 提出日時 | 2026-03-01 01:16:21 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 15,237 bytes |
| 記録 | |
| コンパイル時間 | 5,227 ms |
| コンパイル使用メモリ | 367,416 KB |
| 実行使用メモリ | 11,344 KB |
| スコア | 30,070,799 |
| 最終ジャッジ日時 | 2026-03-01 01:20:09 |
| 合計ジャッジ時間 | 112,723 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 54 TLE * 46 |
ソースコード
// yukicoder No.5023 Airlines Optimization
// Greedy by plane: build k-th plane route by DP on time-expanded graph,
// where each flight-edge weight = (approx.) additional wins vs Square when ONLY that edge is added.
//
// Tuning parameters are at the top (ORIGIN_USE / START_USE / NEAR_CAND / POP_CAND).
// Compile: g++ -O2 -std=c++17 -pipe -static -s main.cpp -o main
#include <bits/stdc++.h>
using namespace std;
static constexpr int MAXN = 47;
static constexpr int SLOT_MIN = 5;
static constexpr int DAY_START_MIN = 6 * 60; // 06:00
static constexpr int DAY_END_MIN = 21 * 60; // 21:00
static constexpr int TS = (DAY_END_MIN - DAY_START_MIN) / SLOT_MIN + 1; // 181
static constexpr int V = MAXN * TS;
// ====== speed/quality knobs (heuristics) ======
// Use only top origins by population when computing edge weights (47 = exact over origins).
static constexpr int ORIGIN_USE = 30;
// DP start cities (planes can "start" at 06:00 and wait). Larger = more exploration.
static constexpr int START_USE = 12;
// Candidate destinations per city = NEAR_CAND nearest + POP_CAND most-populous (unique).
static constexpr int NEAR_CAND = 6;
static constexpr int POP_CAND = 6;
static constexpr int K_FIXED = 25;
static constexpr int M_FIXED = 400;
// Target arrival times: 11:00, 11:30, ..., 21:00 (21 values)
static constexpr int TGT = 21;
struct Edge {
uint8_t to;
uint8_t arr_t; // time index [0..180]
};
struct FlightOut {
int a, b; // 0-based cities
int dep_t; // time index
int arr_t; // time index
};
static inline int timeToIdx(int minute) {
return (minute - DAY_START_MIN) / SLOT_MIN;
}
static inline int idxToTime(int idx) {
return DAY_START_MIN + idx * SLOT_MIN;
}
static inline string fmtTimeIdx(int idx) {
int m = idxToTime(idx);
int hh = m / 60;
int mm = m % 60;
char buf[6];
snprintf(buf, sizeof(buf), "%02d:%02d", hh, mm);
return string(buf);
}
static inline int parseTimeStr(const string& s) {
int hh = (s[0]-'0')*10 + (s[1]-'0');
int mm = (s[3]-'0')*10 + (s[4]-'0');
return hh*60 + mm;
}
// weights sum table by chunks for fast sum of w[d] over 47-bit mask
struct MaskWeighter {
vector<uint64_t> t0, t1, t2; // 16,16,15 bits
uint32_t w[MAXN]{};
void build(const uint32_t* ww) {
for (int i=0;i<MAXN;i++) w[i]=ww[i];
t0.assign(1u<<16, 0);
t1.assign(1u<<16, 0);
t2.assign(1u<<15, 0);
// chunk0: bits 0..15
for (uint32_t m=1; m<(1u<<16); m++) {
uint32_t b = __builtin_ctz(m);
uint32_t pm = m & (m-1);
t0[m] = t0[pm] + w[b];
}
// chunk1: bits 16..31
for (uint32_t m=1; m<(1u<<16); m++) {
uint32_t b = __builtin_ctz(m);
uint32_t pm = m & (m-1);
t1[m] = t1[pm] + w[16 + b];
}
// chunk2: bits 32..46 (15 bits)
for (uint32_t m=1; m<(1u<<15); m++) {
uint32_t b = __builtin_ctz(m);
uint32_t pm = m & (m-1);
t2[m] = t2[pm] + w[32 + b];
}
}
inline uint64_t sumW(uint64_t mask) const {
uint32_t a = (uint32_t)(mask & 0xFFFFull);
uint32_t b = (uint32_t)((mask >> 16) & 0xFFFFull);
uint32_t c = (uint32_t)((mask >> 32) & 0x7FFFull); // 15 bits
return t0[a] + t1[b] + t2[c];
}
};
// ===== global-ish buffers (fixed sizes) =====
static uint32_t popW[MAXN];
static int N, R;
static int durSlot[MAXN][MAXN]; // travel duration in slots (multiple of 5 min)
static double distMat[MAXN][MAXN];
static bool validPair[MAXN][MAXN]; // dist >= 0.25R
// outEdges per schedule (Square and current Circle)
static vector<Edge> outSq[V];
static vector<Edge> outCi[V];
// earliestDest[dest][city][time] = min arrival time index at dest starting from (city,time), INF if unreachable
static uint16_t earliestSq[MAXN][MAXN][TS];
static uint16_t earliestCi[MAXN][MAXN][TS];
static constexpr uint16_t INF16 = 65535;
// latestStart[origin][dest][deadline] = latest start time index to reach dest by deadline, -1 if impossible
static int16_t latestSq[MAXN][MAXN][TS];
static int16_t latestCi[MAXN][MAXN][TS];
// for targets: s_sq[origin][dest][tgtIdx], s_ci similarly (time indices, -1 if unreachable)
static int16_t s_sq[MAXN][MAXN][TGT];
static int16_t s_ci[MAXN][MAXN][TGT];
// reachMask[vertex][tgt] = destinations reachable by target arrival time from vertex (city,time) on current circle schedule
static uint64_t reachMask[V][TGT];
// oldWin[origin][dest][tgt] = (circle already wins) on current schedule (before adding k-th plane)
static bool oldWin[MAXN][MAXN][TGT];
// flipMask[originUsedIndex][tgt][startTime] = destinations that would flip (not already win, and startTime > s_sq)
// (47-bit mask over destinations)
static uint64_t flipMask[ORIGIN_USE][TGT][TS];
// target arrival indices
static int tgtIdx[TGT];
// helpers
static MaskWeighter weighter;
// ===== Build earliest and latest arrays for a schedule =====
static void buildEarliestAndLatest(const vector<Edge> outEdges[V],
uint16_t earliest[MAXN][MAXN][TS],
int16_t latest[MAXN][MAXN][TS]) {
// earliest
for (int d=0; d<N; d++) {
for (int c=0; c<N; c++) {
for (int t=0; t<TS; t++) earliest[d][c][t] = INF16;
}
for (int t=TS-1; t>=0; t--) {
for (int c=0; c<N; c++) {
uint16_t best = INF16;
if (c == d) best = (uint16_t)t;
if (t+1 < TS) best = min(best, earliest[d][c][t+1]); // wait
const auto& outs = outEdges[c*TS + t];
for (const auto& e: outs) {
best = min(best, earliest[d][e.to][e.arr_t]);
}
earliest[d][c][t] = best;
}
}
}
// latestStart from earliest
static int16_t bucket[TS];
for (int o=0; o<N; o++) {
for (int d=0; d<N; d++) {
for (int i=0;i<TS;i++) bucket[i] = -1;
for (int s=0; s<TS; s++) {
uint16_t arr = earliest[d][o][s];
if (arr != INF16) {
bucket[arr] = max(bucket[arr], (int16_t)s);
}
}
int16_t best = -1;
for (int dead=0; dead<TS; dead++) {
best = max(best, bucket[dead]);
latest[o][d][dead] = best;
}
}
}
}
static void buildTargetsFromLatest(const int16_t latest[MAXN][MAXN][TS],
int16_t out[MAXN][MAXN][TGT]) {
for (int o=0; o<N; o++) {
for (int d=0; d<N; d++) {
for (int ti=0; ti<TGT; ti++) {
out[o][d][ti] = latest[o][d][tgtIdx[ti]];
}
}
}
}
// reachMask for current circle schedule, using earliestCi
static void buildReachMaskFromEarliest(const uint16_t earliest[MAXN][MAXN][TS]) {
for (int vtx=0; vtx<N*TS; vtx++) {
int c = vtx / TS;
int t = vtx % TS;
for (int ti=0; ti<TGT; ti++) {
uint64_t m = 0;
int deadline = tgtIdx[ti];
for (int d=0; d<N; d++) {
uint16_t arr = earliest[d][c][t];
if (arr != INF16 && (int)arr <= deadline) {
m |= (1ull << d);
}
}
reachMask[vtx][ti] = m;
}
}
}
static void buildOldWin() {
for (int o=0;o<N;o++){
for (int d=0;d<N;d++){
for (int ti=0;ti<TGT;ti++){
if (!validPair[o][d]) { oldWin[o][d][ti]=false; continue; }
int16_t sq = s_sq[o][d][ti];
int16_t ci = s_ci[o][d][ti];
oldWin[o][d][ti] = (ci > sq);
}
}
}
}
// originsUsed: indices of origins (0-based), size O (<=ORIGIN_USE)
static void buildFlipMaskForOrigins(const vector<int>& originsUsed) {
for (int oi=0; oi<(int)originsUsed.size(); oi++) {
int o = originsUsed[oi];
for (int ti=0; ti<TGT; ti++) {
uint64_t addAt[TS];
for (int s=0;s<TS;s++) addAt[s]=0;
for (int d=0; d<N; d++) {
if (!validPair[o][d]) continue;
if (oldWin[o][d][ti]) continue;
int16_t sq = s_sq[o][d][ti];
int thr = (sq < 0 ? 0 : (int)sq + 1); // need start > sq
if (thr <= TS-1) addAt[thr] |= (1ull << d);
}
uint64_t cur=0;
for (int s=0; s<TS; s++) {
cur |= addAt[s];
flipMask[oi][ti][s] = cur;
}
}
}
}
// ===== Edge weight computation =====
static inline uint64_t edgeGain(int fromCity, int depT, int toCity, int arrT,
const vector<int>& originsUsed) {
int vtx = toCity*TS + arrT;
uint64_t gain = 0;
// loop originsUsed
for (int oi=0; oi<(int)originsUsed.size(); oi++) {
int o = originsUsed[oi];
int16_t sIdx = latestCi[o][fromCity][depT]; // latest departure to reach fromCity by depT
if (sIdx < 0) continue;
uint64_t wo = popW[o];
// loop target times
for (int ti=0; ti<TGT; ti++) {
uint64_t m = flipMask[oi][ti][sIdx] & reachMask[vtx][ti];
if (!m) continue;
uint64_t sumDestW = weighter.sumW(m);
gain += wo * sumDestW;
}
}
return gain;
}
// ===== Solve one plane by DP on time-expanded graph =====
static vector<FlightOut> solveOnePlaneDP(const vector<vector<int>>& candDest,
const vector<int>& startCities,
const vector<int>& originsUsed) {
static __int128 dp[V];
static int prevv[V];
const __int128 NEG = -((__int128)1<<120);
for (int i=0;i<V;i++){ dp[i]=NEG; prevv[i]=-1; }
// start vertices at 06:00 (t=0) in selected cities
for (int c: startCities) {
dp[c*TS + 0] = 0;
}
__int128 bestVal = 0;
int bestVtx = startCities.empty() ? 0 : startCities[0]*TS;
// process in topological order by time
for (int t=0;t<TS;t++){
for (int c=0;c<N;c++){
int u = c*TS + t;
__int128 cur = dp[u];
if (cur==NEG) continue;
if (cur > bestVal) { bestVal=cur; bestVtx=u; }
// wait
if (t+1 < TS) {
int v = u+1;
if (cur > dp[v]) { dp[v]=cur; prevv[v]=u; }
}
// flights (candidate destinations only)
for (int j: candDest[c]) {
int dt = durSlot[c][j];
int at = t + dt;
if (at >= TS) continue;
int v = j*TS + at;
uint64_t g = edgeGain(c, t, j, at, originsUsed);
__int128 nv = cur + (__int128)g;
if (nv > dp[v]) {
dp[v]=nv;
prevv[v]=u;
}
}
}
}
// take global best end
for (int u=0;u<V;u++){
if (dp[u] > bestVal) { bestVal=dp[u]; bestVtx=u; }
}
// reconstruct path
vector<FlightOut> revFlights;
int cur = bestVtx;
while (cur!=-1) {
int p = prevv[cur];
if (p==-1) break;
int pc = p/TS, pt = p%TS;
int cc = cur/TS, ct = cur%TS;
if (pc != cc) {
// flight
revFlights.push_back(FlightOut{pc, cc, pt, ct});
}
cur = p;
}
reverse(revFlights.begin(), revFlights.end());
return revFlights;
}
// ===== score evaluation (debug) =====
static long long evalScoreEstimate() {
// compute current circle latest + s_ci already built outside if called appropriately
__int128 vci=0, vsq=0;
for (int o=0;o<N;o++){
for (int d=0;d<N;d++){
if (!validPair[o][d]) continue;
__int128 ww = (__int128)popW[o] * (__int128)popW[d];
for (int ti=0;ti<TGT;ti++){
int16_t sq = s_sq[o][d][ti];
int16_t ci = s_ci[o][d][ti];
if (ci > sq) vci += ww;
else vsq += ww;
}
}
}
if (vci+vsq==0) return 0;
long double S = (long double)vci / (long double)(vci+vsq);
long long score = (long long)floor(1e6L * S + 1e-12L);
return score;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> N >> R;
vector<int> xs(N), ys(N);
for (int i=0;i<N;i++){
cin >> xs[i] >> ys[i] >> popW[i];
}
// target indices
for (int i=0;i<TGT;i++){
int minute = 11*60 + 30*i;
tgtIdx[i] = timeToIdx(minute);
}
// distances + validPair + durations
double thr = 0.25 * (double)R;
for (int i=0;i<N;i++){
for (int j=0;j<N;j++){
double dx = (double)xs[i]-xs[j];
double dy = (double)ys[i]-ys[j];
double d = sqrt(dx*dx + dy*dy);
distMat[i][j]=d;
validPair[i][j] = (d >= thr);
if (i==j) durSlot[i][j]=0;
else {
double raw = 60.0 * d / 800.0 + 40.0;
int q = (int)ceil(raw / 5.0 - 1e-12);
int durMin = q * 5;
durSlot[i][j] = durMin / 5;
}
}
}
// build weight sum tables
weighter.build(popW);
int M;
cin >> M;
for (int i=0;i<V;i++) outSq[i].clear();
for (int k=0;k<M;k++){
int a,b;
string ss, tt;
cin >> a >> ss >> b >> tt;
--a; --b;
int s = timeToIdx(parseTimeStr(ss));
int t = timeToIdx(parseTimeStr(tt));
outSq[a*TS + s].push_back(Edge{(uint8_t)b,(uint8_t)t});
}
int K;
cin >> K; // should be 25
(void)K;
// current circle schedule initially empty
for (int i=0;i<V;i++) outCi[i].clear();
// Precompute Square: earliestSq, latestSq, s_sq
buildEarliestAndLatest(outSq, earliestSq, latestSq);
buildTargetsFromLatest(latestSq, s_sq);
// candidate destinations per city
vector<int> popOrder(N);
iota(popOrder.begin(), popOrder.end(), 0);
sort(popOrder.begin(), popOrder.end(), [&](int a,int b){ return popW[a]>popW[b]; });
vector<vector<int>> candDest(N);
for (int i=0;i<N;i++){
vector<pair<double,int>> near;
near.reserve(N-1);
for (int j=0;j<N;j++){
if (i==j) continue;
near.push_back({distMat[i][j], j});
}
sort(near.begin(), near.end());
vector<int> cand;
cand.reserve(NEAR_CAND + POP_CAND + 4);
// nearest
for (int k=0;k<(int)near.size() && (int)cand.size()<NEAR_CAND;k++){
cand.push_back(near[k].second);
}
// populous
for (int k=0;k<N && (int)cand.size()<NEAR_CAND+POP_CAND;k++){
int j = popOrder[k];
if (j==i) continue;
cand.push_back(j);
}
sort(cand.begin(), cand.end());
cand.erase(unique(cand.begin(), cand.end()), cand.end());
candDest[i]=cand;
}
// start cities
vector<int> startCities;
for (int i=0;i<min(START_USE, N); i++) startCities.push_back(popOrder[i]);
// origins used for edge weights
vector<int> originsUsed;
for (int i=0;i<min(ORIGIN_USE, N); i++) originsUsed.push_back(popOrder[i]);
vector<vector<FlightOut>> routes(K_FIXED);
for (int plane=0; plane<K_FIXED; plane++) {
// compute current circle earliest/latest + reach masks + s_ci
buildEarliestAndLatest(outCi, earliestCi, latestCi);
buildTargetsFromLatest(latestCi, s_ci);
buildReachMaskFromEarliest(earliestCi);
// old win status and flip masks
buildOldWin();
buildFlipMaskForOrigins(originsUsed);
// solve plane by DP
auto fl = solveOnePlaneDP(candDest, startCities, originsUsed);
routes[plane] = fl;
// add flights to circle schedule
for (auto &f: fl) {
int u = f.a*TS + f.dep_t;
outCi[u].push_back(Edge{(uint8_t)f.b, (uint8_t)f.arr_t});
}
// debug
cerr << "[plane " << (plane+1) << "] flights=" << fl.size() << "\n";
}
// final debug score estimate (exact scoring compare vs square on targets + validPair)
{
buildEarliestAndLatest(outCi, earliestCi, latestCi);
buildTargetsFromLatest(latestCi, s_ci);
long long est = evalScoreEstimate();
cerr << "[final estimated score] " << est << "\n";
}
// output routes
for (int p=0;p<K_FIXED;p++){
cout << routes[p].size() << "\n";
for (auto &f: routes[p]) {
cout << (f.a+1) << " " << fmtTimeIdx(f.dep_t) << " " << (f.b+1) << " " << fmtTimeIdx(f.arr_t) << "\n";
}
}
return 0;
}