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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 | #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;
int walk_count;
Solver(const TestCase& t) : tc(t), query_count(0), n(t.n), walk_count(0) { 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];
}
pair<long long, vector<int>> countLeq(long long mid, const vector<int>& jLo, const vector<int>& jHi) {
walk_count++;
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], hi = min(n, jHi[i]);
if (hi <= lo) { cutoff[i] = lo; cnt += lo; continue; }
if (j > hi) j = hi;
while (j > lo && do_query(i, j) > mid) j--;
if (j > lo) { cutoff[i] = j; cnt += j; }
else { cutoff[i] = lo; cnt += lo; }
}
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);
long long heap_k = min(k, NLL - k + 1);
if (heap_k + n <= 24000) {
if (k <= NLL - 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 = NLL - 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;
}
}
// Pure value binary search with bounded staircase walks
vector<int> jLo(n + 1, 0), jHi(n + 1, n);
long long cLo = 0, cHi = NLL;
long long loVal = do_query(1, 1) - 1;
long long hiVal = do_query(n, n);
// Get tighter initial upper bound
int rBound = max(1, min(n, (int)((k + n - 1) / n)));
long long initHi = do_query(rBound, n);
auto [ch, cutH] = countLeq(initHi, jLo, jHi);
if (ch >= k) {
jHi = cutH; cHi = ch; hiVal = initHi;
}
// Binary search on value
while (cHi - cLo > 0) {
long long budget = 49500 - query_count;
long long W = cHi - cLo;
long long needSmall = k - cLo;
long long needLarge = cHi - k + 1;
// Count non-empty segments
int nonempty = 0;
for (int i = 1; i <= n; i++) if (jHi[i] > jLo[i]) nonempty++;
// Can we enumerate?
if (min(needSmall + nonempty, min(needLarge + nonempty, W)) + 10 <= budget) {
if (W <= needSmall + nonempty && W <= needLarge + nonempty) {
// Enumerate all
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;
nth_element(cand.begin(), cand.begin() + (rank - 1), cand.end());
return cand[rank - 1];
} else 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 = jLo[i] + 1, R = jHi[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 <= jHi[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 = jLo[i] + 1, R = jHi[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 >= jLo[r] + 1) pq.emplace(do_query(r, c - 1), r, c - 1);
}
return result;
}
}
if (budget < 2 * n + 200) break; // can't afford more
if (loVal >= hiVal) break;
long long midVal = loVal + (hiVal - loVal) / 2;
if (midVal <= loVal) midVal = loVal + 1;
if (midVal >= hiVal) break;
auto [cnt, cut] = countLeq(midVal, jLo, jHi);
if (cnt >= k) {
jHi = cut; cHi = cnt; hiVal = midVal;
} else {
jLo = cut; cLo = cnt; loVal = midVal;
}
}
return hiVal;
}
};
int main() {
struct TestDef { string name; function<TestCase()> gen; };
vector<TestDef> tests;
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); }});
// Test type 3, 4, 5 from interactor
tests.push_back({"type4 n=2000 k=2000000", []{ return gen_matrix(2000, 2000000, [](int i, int j)->long long { return i + 2LL*j; }); }});
tests.push_back({"type5 n=2000 k=2000000", []{ return gen_matrix(2000, 2000000, [](int i, int j)->long long { return 2LL*i + j; }); }});
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 walks=%2d %s score=%.4f\n", t.name.c_str(), used, s.walk_count, correct ? "OK" : "WRONG", score);
}
}
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