File size: 5,560 Bytes
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 | #include <bits/stdc++.h>
using namespace std;
int n;
long long k;
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);
}
void solve() {
long long total = (long long)n * n;
if (n == 1) { done(do_query(1, 1)); return; }
// 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
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: sample sqrt(na) rows, query at target fraction
vector<long long> pvals;
double target_frac = (double)(k_rem - 0.5) / total_cand;
int sample_n = max(1, min(na, (int)ceil(sqrt((double)na) * 2)));
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 - 1));
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 walks
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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