File size: 6,155 Bytes
14c9c2b | 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 | #include <bits/stdc++.h>
using namespace std;
int n;
long long k;
// Flat memo array: memo[r*2001+c], -1 means not queried
vector<long long> memo;
int query_count = 0;
long long do_query(int r, int c) {
int key = r * 2001 + c;
if (memo[key] != -1) return memo[key];
cout << "QUERY " << r << " " << c << "\n";
cout.flush();
long long v;
cin >> v;
memo[key] = v;
query_count++;
return v;
}
void done(long long ans) {
cout << "DONE " << ans << "\n";
cout.flush();
exit(0);
}
// Staircase count: count elements <= val in full matrix
// Returns count and fills boundary array
// boundary[i] = number of elements in row i that are <= val
// Uses at most O(n) NEW queries (staircase property), but with memoization could be 0
long long staircase_le(long long val, vector<int>& boundary) {
boundary.resize(n + 1);
long long count = 0;
int j = n;
for (int i = 1; i <= n; i++) {
while (j >= 1 && do_query(i, j) > val) j--;
boundary[i] = j;
count += j;
}
return count;
}
void solve() {
long long total = (long long)n * n;
// Heap for extreme k
long long heap_k = min(k, total - k + 1);
if (heap_k + n <= 24000) {
if (k <= total - 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); }
}
done(result);
} else {
long long kk = total - 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); }
}
done(result);
}
}
// Quickselect approach: walk only active rows, use weighted pivot
vector<int> L(n + 1, 1), R(n + 1, n);
long long k_rem = k;
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) done(do_query(i, L[i]));
break;
}
// Heap fallback
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);
}
done(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);
}
done(get<0>(pq.top()));
}
// Pick pivot from quantiles of active rows
// Query at k_rem/total_cand fraction within each row's range
// This targets the expected rank better than midpoints
vector<long long> pvals;
double target_frac = (double)(k_rem - 0.5) / total_cand;
for (int i : active) {
int width = R[i] - L[i] + 1;
int col = L[i] + (int)(target_frac * (width - 1));
col = max(L[i], min(R[i], col));
pvals.push_back(do_query(i, col));
}
sort(pvals.begin(), pvals.end());
// Take median of these values
long long pivot = pvals[na / 2];
// Staircase for <= over active rows only
vector<int> p_le(n + 1, 0), p_lt(n + 1, 0);
{
int j = n;
for (int i : active) {
j = min(j, R[i]);
while (j >= L[i] && do_query(i, j) > pivot) j--;
p_le[i] = j;
}
}
{
int j = n;
for (int i : active) {
j = min(j, R[i]);
while (j >= L[i] && do_query(i, j) >= pivot) j--;
p_lt[i] = j;
}
}
long long cle = 0, clt = 0;
for (int i : active) {
int rl = min(p_le[i], R[i]);
if (rl >= L[i]) cle += rl - L[i] + 1;
int rt = min(p_lt[i], R[i]);
if (rt >= L[i]) clt += rt - L[i] + 1;
}
if (k_rem <= clt) {
for (int i : active) R[i] = min(R[i], p_lt[i]);
} else if (k_rem <= cle) {
done(pivot);
} else {
k_rem -= cle;
for (int i : active) L[i] = max(L[i], p_le[i] + 1);
}
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> k;
memo.assign(2002 * 2002, -1);
solve();
return 0;
}
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