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1fd0050 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 | #include <bits/stdc++.h>
using namespace std;
// ---- Matrix generation ----
struct TestCase {
int n;
long long k;
vector<vector<long long>> A; // 1-indexed
long long answer;
};
mt19937_64 rng_gen(42);
TestCase gen_matrix(int n, long long k, function<long long(int,int)> valfn) {
TestCase tc;
tc.n = n; tc.k = k;
tc.A.assign(n+1, vector<long long>(n+1, 0));
vector<long long> all;
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) {
tc.A[i][j] = valfn(i, j);
all.push_back(tc.A[i][j]);
}
sort(all.begin(), all.end());
tc.answer = all[k-1];
return tc;
}
TestCase gen_additive(int n, long long k) {
return gen_matrix(n, k, [](int i, int j) -> long long { return i + j; });
}
TestCase gen_multiplicative(int n, long long k) {
return gen_matrix(n, k, [](int i, int j) -> long long { return (long long)i * j; });
}
TestCase gen_shifted(int n, long long k) {
return gen_matrix(n, k, [n](int i, int j) -> long long { return (long long)(i + n) * (j + n); });
}
TestCase gen_random_sorted(int n, long long k) {
TestCase tc;
tc.n = n; tc.k = k;
tc.A.assign(n+1, vector<long long>(n+1, 0));
long long C = 1000000, D = 1000;
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++)
tc.A[i][j] = (long long)i * C + (long long)j * D + (rng_gen() % 500);
for (int i = 1; i <= n; i++)
for (int j = 2; j <= n; j++)
tc.A[i][j] = max(tc.A[i][j], tc.A[i][j-1]);
for (int j = 1; j <= n; j++)
for (int i = 2; i <= n; i++)
tc.A[i][j] = max(tc.A[i][j], tc.A[i-1][j]);
vector<long long> all;
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++)
all.push_back(tc.A[i][j]);
sort(all.begin(), all.end());
tc.answer = all[k-1];
return tc;
}
// ---- Solver (new value-based approach) ----
struct Solver {
const TestCase& tc;
int query_count;
vector<long long> memo;
int n;
Solver(const TestCase& t) : tc(t), query_count(0), n(t.n) {
memo.assign(2002 * 2002, -1);
}
long long do_query(int r, int c) {
int key = r * 2001 + c;
if (memo[key] != -1) return memo[key];
query_count++;
memo[key] = tc.A[r][c];
return memo[key];
}
long long count_leq(long long x, vector<int>& pos) {
pos.assign(n + 1, 0);
long long cnt = 0;
int j = n;
for (int i = 1; i <= n; i++) {
while (j >= 1 && do_query(i, j) > x) j--;
pos[i] = j;
cnt += j;
if (j == 0) {
for (int ii = i + 1; ii <= n; ii++) pos[ii] = 0;
break;
}
}
return cnt;
}
long long count_lt(long long x, vector<int>& pos) {
pos.assign(n + 1, 0);
long long cnt = 0;
int j = n;
for (int i = 1; i <= n; i++) {
while (j >= 1 && do_query(i, j) >= x) j--;
pos[i] = j;
cnt += j;
if (j == 0) {
for (int ii = i + 1; ii <= n; ii++) pos[ii] = 0;
break;
}
}
return cnt;
}
long long solve() {
long long k = tc.k;
long long N2 = (long long)n * n;
if (n == 1) return do_query(1, 1);
if (k == 1) return do_query(1, 1);
if (k == N2) return do_query(n, n);
// Heap for extreme k
long long heap_k = min(k, N2 - k + 1);
if (heap_k + n <= 24000) {
if (k <= N2 - k + 1) {
priority_queue<tuple<long long, int, int>, vector<tuple<long long, int, int>>, greater<>> pq;
for (int i = 1; i <= n; i++)
pq.emplace(do_query(i, 1), i, 1);
long long result = -1;
for (long long t = 0; t < k; t++) {
auto [v, r, c] = pq.top(); pq.pop();
result = v;
if (c + 1 <= n) pq.emplace(do_query(r, c + 1), r, c + 1);
}
return result;
} else {
long long kk = N2 - k + 1;
priority_queue<tuple<long long, int, int>> pq;
for (int i = 1; i <= n; i++)
pq.emplace(do_query(i, n), i, n);
long long result = -1;
for (long long t = 0; t < kk; t++) {
auto [v, r, c] = pq.top(); pq.pop();
result = v;
if (c - 1 >= 1) pq.emplace(do_query(r, c - 1), r, c - 1);
}
return result;
}
}
// Value-based narrowing
mt19937_64 rng(12345);
vector<int> posHigh(n + 1, n), posLow(n + 1, 0);
long long cntHigh = N2, cntLow = 0;
long long highTh, lowTh;
int rBound = (int)min((long long)n, (k + n - 1) / n);
highTh = do_query(rBound, n);
cntHigh = count_leq(highTh, posHigh);
if (cntHigh < k) {
highTh = do_query(n, n);
cntHigh = count_leq(highTh, posHigh);
}
lowTh = do_query(1, 1) - 1;
const int SAMPLES = 15;
for (int iter = 0; iter < 200; iter++) {
if (cntHigh < k) {
highTh = do_query(n, n);
cntHigh = count_leq(highTh, posHigh);
if (cntHigh < k) break;
}
long long candTotal = cntHigh - cntLow;
if (candTotal <= 0) return highTh; // shouldn't happen with correct answer
long long needSmall = k - cntLow;
long long needLarge = cntHigh - k + 1;
vector<long long> pref(n + 1, 0);
int nonempty = 0;
for (int i = 1; i <= n; i++) {
int len = posHigh[i] - posLow[i];
if (len > 0) nonempty++;
pref[i] = pref[i - 1] + max(0, len);
}
candTotal = pref[n];
if (candTotal <= 0) return highTh;
long long budget = 49500 - query_count;
long long enumCost = min(needSmall, needLarge) + nonempty + 10;
if (enumCost <= budget) {
if (needSmall <= needLarge) {
priority_queue<tuple<long long, int, int>, vector<tuple<long long, int, int>>, greater<>> pq;
for (int i = 1; i <= n; i++) {
int L = posLow[i] + 1, R = posHigh[i];
if (L >= 1 && L <= n && L <= R) pq.emplace(do_query(i, L), i, L);
}
long long result = 0;
for (long long t = 0; t < needSmall; t++) {
auto [v, r, c] = pq.top(); pq.pop();
result = v;
if (c + 1 <= posHigh[r]) pq.emplace(do_query(r, c + 1), r, c + 1);
}
return result;
} else {
priority_queue<tuple<long long, int, int>> pq;
for (int i = 1; i <= n; i++) {
int L = posLow[i] + 1, R = posHigh[i];
if (R >= 1 && R <= n && L <= R) pq.emplace(do_query(i, R), i, R);
}
long long result = 0;
for (long long t = 0; t < needLarge; t++) {
auto [v, r, c] = pq.top(); pq.pop();
result = v;
if (c - 1 >= posLow[r] + 1) pq.emplace(do_query(r, c - 1), r, c - 1);
}
return result;
}
}
if (budget < 2 * n + SAMPLES + 200) {
return highTh; // last resort
}
// Sample pivots
vector<long long> samp;
samp.reserve(SAMPLES);
for (int s = 0; s < SAMPLES; s++) {
long long pick = 1 + rng() % candTotal;
int row = (int)(lower_bound(pref.begin() + 1, pref.end(), pick) - pref.begin());
if (row < 1 || row > n) continue;
int len = posHigh[row] - posLow[row];
if (len <= 0) continue;
int col = posLow[row] + 1 + rng() % len;
col = max(1, min(n, col));
samp.push_back(do_query(row, col));
}
if (samp.empty()) return highTh;
sort(samp.begin(), samp.end());
double q = (double)needSmall / (double)candTotal;
int idx = (int)(q * (double)(samp.size() - 1));
idx = max(0, min((int)samp.size() - 1, idx));
long long pivot = samp[idx];
vector<int> posPivot;
long long cntPivot = count_leq(pivot, posPivot);
if (cntPivot >= k) {
if (pivot == highTh && cntPivot == cntHigh) {
vector<int> posLess;
long long cntLess = count_lt(pivot, posLess);
if (cntLess < k) return pivot;
highTh = pivot - 1;
posHigh = posLess;
cntHigh = cntLess;
} else {
highTh = pivot;
posHigh = posPivot;
cntHigh = cntPivot;
}
} else {
lowTh = pivot;
posLow = posPivot;
cntLow = cntPivot;
}
}
return -1;
}
};
int main() {
struct TestDef {
string name;
function<TestCase()> gen;
};
vector<TestDef> tests;
tests.push_back({"additive n=100 k=5000", []{ return gen_additive(100, 5000); }});
tests.push_back({"multiplicative n=100 k=5000", []{ return gen_multiplicative(100, 5000); }});
tests.push_back({"additive n=500 k=125000", []{ return gen_additive(500, 125000); }});
tests.push_back({"multiplicative n=500 k=125000", []{ return gen_multiplicative(500, 125000); }});
tests.push_back({"random n=500 k=125000", []{ return gen_random_sorted(500, 125000); }});
tests.push_back({"additive n=2000 k=2000000", []{ return gen_additive(2000, 2000000); }});
tests.push_back({"multiplicative n=2000 k=2000000", []{ return gen_multiplicative(2000, 2000000); }});
tests.push_back({"shifted n=2000 k=2000000", []{ return gen_shifted(2000, 2000000); }});
tests.push_back({"random n=2000 k=2000000", []{ return gen_random_sorted(2000, 2000000); }});
tests.push_back({"multiplicative n=2000 k=1", []{ return gen_multiplicative(2000, 1); }});
tests.push_back({"multiplicative n=2000 k=4000000", []{ return gen_multiplicative(2000, 4000000); }});
tests.push_back({"multiplicative n=2000 k=100000", []{ return gen_multiplicative(2000, 100000); }});
tests.push_back({"multiplicative n=2000 k=3900000", []{ return gen_multiplicative(2000, 3900000); }});
for (auto& t : tests) {
auto tc = t.gen();
Solver s(tc);
long long result = s.solve();
bool correct = (result == tc.answer);
double score;
int n = tc.n;
int used = s.query_count;
if (!correct) score = 0.0;
else if (used <= n) score = 1.0;
else if (used >= 50000) score = 0.0;
else score = (50000.0 - used) / (50000.0 - n);
printf("%-45s n=%4d k=%8lld queries=%6d correct=%s score=%.4f\n",
t.name.c_str(), tc.n, tc.k, used, correct ? "YES" : "NO", score);
}
return 0;
}
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