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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 | #include <bits/stdc++.h>
using namespace std;
struct TestCase {
int n; long long k;
vector<vector<long long>> A; 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_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_additive(int n, long long k) { return gen_matrix(n, k, [](int i, int j) -> long long { return i + j; }); }
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));
for (int i = 1; i <= n; i++) for (int j = 1; j <= n; j++) tc.A[i][j] = (long long)i * 1000000 + (long long)j * 1000 + (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;
}
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];
}
// Staircase walk counting elements <= mid, respecting jLo/jHi bounds
// jLo[i] = number of elements in row i KNOWN to be <= some lower bound (0-based count from left)
// jHi[i] = number of elements in row i KNOWN to be <= some upper bound
// Walk from top, j starts at jHi[1], goes down
pair<long long, vector<int>> countLeq(long long mid, const vector<int>& jLo, const vector<int>& jHi) {
vector<int> cutoff(n + 1, 0);
long long cnt = 0;
int j = min(n, jHi[1]);
for (int i = 1; i <= n; i++) {
int lo = jLo[i];
int hi = min(n, jHi[i]);
if (hi <= lo) {
cutoff[i] = lo;
cnt += lo;
continue;
}
if (j > hi) j = hi;
while (j > lo) {
long long v = do_query(i, j);
if (v <= mid) {
cutoff[i] = j;
cnt += j;
goto next;
}
j--;
}
cutoff[i] = lo;
cnt += lo;
next:;
}
return {cnt, cutoff};
}
long long solve() {
long long k = tc.k;
long long NLL = (long long)n * n;
if (n == 1) return do_query(1, 1);
if (k == 1) return do_query(1, 1);
if (k == NLL) return do_query(n, n);
// Phase 1: Sample random values
int countsBudget = min(30, max(1, 45000 / max(1, 2 * n)));
int reserved = 100;
long long left = 50000 - (long long)countsBudget * 2 * n - reserved;
if (left < 0) left = 0;
int E = (int)min(5000LL, max(400LL, left / 3));
long long SBudget = left - E;
if (SBudget < 0) SBudget = 0;
long long Ssize = min(SBudget, min(6000LL, (long long)n * n));
if (Ssize < 0) Ssize = 0;
vector<long long> sampleVals;
{
mt19937_64 rng(1469598103934665603ULL ^ (uint64_t)n * 1181783497276652981ULL ^ ((uint64_t)k << 1));
set<long long> seen;
// Grid sampling
int g = (int)floor(sqrt((double)Ssize));
if (g > 0) {
for (int ri = 1; ri <= g && (long long)sampleVals.size() < Ssize; ri++) {
int r = max(1, min(n, (int)((ri * (long long)n) / (g + 1))));
for (int ci = 1; ci <= g && (long long)sampleVals.size() < Ssize; ci++) {
int c = max(1, min(n, (int)((ci * (long long)n) / (g + 1))));
long long key = (long long)r * 10000 + c;
if (seen.insert(key).second)
sampleVals.push_back(do_query(r, c));
}
}
}
// Random fill
while ((long long)sampleVals.size() < Ssize) {
int r = 1 + rng() % n;
int c = 1 + rng() % n;
long long key = (long long)r * 10000 + c;
if (seen.insert(key).second)
sampleVals.push_back(do_query(r, c));
}
sort(sampleVals.begin(), sampleVals.end());
sampleVals.erase(unique(sampleVals.begin(), sampleVals.end()), sampleVals.end());
}
// Phase 2: Binary search over sample values
vector<int> jLo(n + 1, 0), jHi(n + 1, n);
long long cLo = 0, cHi = NLL;
int li = -1, hiIndex = (int)sampleVals.size();
int usedCounts = 0;
while (usedCounts < countsBudget && hiIndex - li > 1 && cHi - cLo > E) {
int midIndex = li + (hiIndex - li) / 2;
long long pivot = sampleVals[midIndex];
auto [cnt, cutoff] = countLeq(pivot, jLo, jHi);
usedCounts++;
if (cnt >= k) {
hiIndex = midIndex;
jHi = cutoff;
cHi = cnt;
} else {
li = midIndex;
jLo = cutoff;
cLo = cnt;
}
}
// Phase 3: Numeric binary search if still too wide
long long loVal = (li >= 0 ? sampleVals[li] : (sampleVals.empty() ? do_query(1,1) : sampleVals.front()));
long long hiVal = (hiIndex < (int)sampleVals.size() ? sampleVals[hiIndex] : (sampleVals.empty() ? do_query(n,n) : sampleVals.back()));
while (usedCounts < countsBudget && cHi - cLo > E) {
if (loVal >= hiVal) break;
long long mid = loVal + (hiVal - loVal) / 2;
if (mid == loVal) mid++;
if (mid >= hiVal) break;
auto [cnt, cutoff] = countLeq(mid, jLo, jHi);
usedCounts++;
if (cnt >= k) {
jHi = cutoff;
cHi = cnt;
hiVal = mid;
} else {
jLo = cutoff;
cLo = cnt;
loVal = mid;
}
}
// Phase 4: Enumerate remaining candidates
long long W = cHi - cLo;
vector<long long> cand;
cand.reserve((size_t)W);
for (int i = 1; i <= n; i++) {
for (int j = jLo[i] + 1; j <= jHi[i]; j++) {
cand.push_back(do_query(i, j));
}
}
long long rank = k - cLo;
if (rank <= 0 || cand.empty()) return loVal;
if (rank > (long long)cand.size()) return hiVal;
nth_element(cand.begin(), cand.begin() + (rank - 1), cand.end());
return cand[rank - 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({"mult 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({"mult 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({"mult 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({"mult n=2000 k=100000", []{ return gen_multiplicative(2000, 100000); }});
tests.push_back({"mult 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);
int used = s.query_count;
double score = !correct ? 0.0 : (used <= tc.n ? 1.0 : (used >= 50000 ? 0.0 : (50000.0 - used) / (50000.0 - tc.n)));
printf("%-45s q=%6d %s score=%.4f\n", t.name.c_str(), used, correct ? "OK" : "WRONG", score);
}
}
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