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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 | #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 with L[i]/R[i] bounds, returns cle and p_le
pair<long long, vector<int>> walk_le(long long pivot, const vector<int>& active, const vector<int>& L, const vector<int>& R) {
int na = active.size();
vector<int> p_le(n + 1, 0);
int j = 0;
for (int idx = na - 1; idx >= 0; idx--) {
int i = active[idx];
j = max(j, L[i]);
while (j <= R[i] && do_query(i, j) <= pivot) j++;
p_le[i] = j - 1;
}
long long cle = 0;
for (int i : active) {
int rl = min(p_le[i], R[i]);
if (rl >= L[i]) cle += rl - L[i] + 1;
}
return {cle, p_le};
}
long long solve() {
long long k = tc.k;
long long N2 = (long long)n * n;
if (n == 1) return do_query(1, 1);
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;
vector<vector<bool>> vis(n + 1, vector<bool>(n + 1, false));
pq.emplace(do_query(1, 1), 1, 1); vis[1][1] = true;
long long result = -1;
for (long long i = 0; i < k; i++) {
auto [v, r, c] = pq.top(); pq.pop(); result = v;
if (r+1<=n && !vis[r+1][c]) { vis[r+1][c]=true; pq.emplace(do_query(r+1,c),r+1,c); }
if (c+1<=n && !vis[r][c+1]) { vis[r][c+1]=true; 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;
vector<vector<bool>> vis(n + 1, vector<bool>(n + 1, false));
pq.emplace(do_query(n,n),n,n); vis[n][n]=true;
long long result = -1;
for (long long i = 0; i < kk; i++) {
auto [v, r, c] = pq.top(); pq.pop(); result = v;
if (r-1>=1 && !vis[r-1][c]) { vis[r-1][c]=true; pq.emplace(do_query(r-1,c),r-1,c); }
if (c-1>=1 && !vis[r][c-1]) { vis[r][c-1]=true; pq.emplace(do_query(r,c-1),r,c-1); }
}
return result;
}
}
vector<int> L(n + 1, 1), R(n + 1, n);
long long k_rem = k;
// Keep track of value bounds for binary search refinement
long long val_lo = -1, val_hi = -1; // will be set after first walk
long long cnt_lo = 0, cnt_hi = -1;
for (int iter = 0; iter < 100; iter++) {
vector<int> active;
long long total_cand = 0;
for (int i = 1; i <= n; i++) {
if (L[i] <= R[i]) { active.push_back(i); total_cand += R[i] - L[i] + 1; }
}
int na = active.size();
if (total_cand == 0) break;
if (total_cand == 1) { for (int i : active) return do_query(i, L[i]); break; }
long long budget = 49500 - query_count;
if (k_rem + na <= budget) {
priority_queue<tuple<long long, int, int>, vector<tuple<long long, int, int>>, greater<>> pq;
for (int i : active) pq.emplace(do_query(i, L[i]), i, L[i]);
for (long long t = 1; t < k_rem; t++) {
auto [v, r, c] = pq.top(); pq.pop();
if (c + 1 <= R[r]) pq.emplace(do_query(r, c + 1), r, c + 1);
}
return get<0>(pq.top());
}
long long rev_k = total_cand - k_rem + 1;
if (rev_k + na <= budget) {
priority_queue<tuple<long long, int, int>> pq;
for (int i : active) pq.emplace(do_query(i, R[i]), i, R[i]);
for (long long t = 1; t < rev_k; t++) {
auto [v, r, c] = pq.top(); pq.pop();
if (c - 1 >= L[r]) pq.emplace(do_query(r, c - 1), r, c - 1);
}
return get<0>(pq.top());
}
// Pivot selection (original method)
double target_frac = (double)(k_rem - 0.5) / total_cand;
vector<long long> pvals;
int sample_n = max(1, min(na, (int)ceil(sqrt((double)na) * 4)));
int step = max(1, na / sample_n);
for (int idx = 0; idx < na; idx += step) {
int i = active[idx];
int width = R[i] - L[i] + 1;
int col = L[i] + (int)(target_frac * width);
col = max(L[i], min(R[i], col));
pvals.push_back(do_query(i, col));
}
sort(pvals.begin(), pvals.end());
long long pivot = pvals[pvals.size() / 2];
// Staircase walk
auto [cle, p_le] = walk_le(pivot, active, L, R);
// Track value bounds
if (cle >= k_rem) {
val_hi = pivot;
cnt_hi = cle;
} else {
val_lo = pivot;
cnt_lo = cle; // note: this is cle within current L/R bounds
}
// Apply the partition as usual
if (cle >= k_rem) {
for (int i : active) R[i] = min(R[i], p_le[i]);
} else {
k_rem -= cle;
for (int i : active) L[i] = max(L[i], p_le[i] + 1);
}
// After partition, check if we can do a VALUE-BASED binary search refinement
// If we have both val_lo and val_hi, and they're close enough, binary search between them
// Each binary search step is another staircase walk (O(n) queries)
// This is useful when the quickselect gets stuck with bad splits
if (val_lo >= 0 && val_hi >= 0 && val_lo < val_hi) {
// Re-check remaining candidates
long long new_total = 0;
for (int i = 1; i <= n; i++) {
if (L[i] <= R[i]) new_total += R[i] - L[i] + 1;
}
// If we haven't narrowed enough and budget allows, do one more walk with interpolated pivot
if (new_total > budget - 2000 && budget > 4 * n) {
long long mid_val = val_lo + (val_hi - val_lo) / 2;
if (mid_val > val_lo && mid_val < val_hi) {
vector<int> active2;
long long tc2 = 0;
for (int i = 1; i <= n; i++) {
if (L[i] <= R[i]) { active2.push_back(i); tc2 += R[i] - L[i] + 1; }
}
if (!active2.empty()) {
auto [cle2, p_le2] = walk_le(mid_val, active2, L, R);
if (cle2 >= k_rem) {
for (int i : active2) R[i] = min(R[i], p_le2[i]);
val_hi = mid_val;
} else {
k_rem -= cle2;
for (int i : active2) L[i] = max(L[i], p_le2[i] + 1);
val_lo = mid_val;
}
}
}
}
}
}
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({"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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