File size: 3,862 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 | #include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <tuple>
using namespace std;
// Function to perform a query
long long query(int r, int c) {
cout << "QUERY " << r << " " << c << endl;
long long v;
cin >> v;
return v;
}
// Function to submit the final answer
void done(long long ans) {
cout << "DONE " << ans << endl;
}
long long n;
long long k;
// Heap-based solution for small k
void solve_heap_rev() {
priority_queue<tuple<long long, int, int>, vector<tuple<long long, int, int>>, greater<tuple<long long, int, int>>> pq;
for (int i = 1; i <= n; ++i) {
pq.emplace(query(i, 1), i, 1);
}
for (int i = 0; i < k - 1; ++i) {
auto [val, r, c] = pq.top();
pq.pop();
if (c < n) {
pq.emplace(query(r, c + 1), r, c + 1);
}
}
done(get<0>(pq.top()));
}
// Heap-based solution for large k
void solve_heap() {
priority_queue<tuple<long long, int, int>> pq;
for (int i = 1; i <= n; ++i) {
pq.emplace(query(i, n), i, n);
}
long long k_rev = n * n - k + 1;
for (int i = 0; i < k_rev - 1; ++i) {
auto [val, r, c] = pq.top();
pq.pop();
if (c > 1) {
pq.emplace(query(r, c - 1), r, c - 1);
}
}
done(get<0>(pq.top()));
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin >> n >> k;
// Use heap method if k is small enough
if (n + k - 1 <= 50000) {
solve_heap_rev();
return 0;
}
// Use heap method if k is large enough (k-th smallest is (n*n-k+1)-th largest)
if (n + (n * n - k + 1) - 1 <= 50000) {
solve_heap();
return 0;
}
// General case: divide and conquer
vector<int> L(n + 1, 1), R(n + 1, n);
long long k_rem = k;
while (true) {
vector<pair<long long, int>> pivots;
vector<int> active_rows;
for (int i = 1; i <= n; ++i) {
if (L[i] <= R[i]) {
active_rows.push_back(i);
}
}
if (active_rows.empty()) {
break;
}
for (int r : active_rows) {
int mid_col = L[r] + (R[r] - L[r]) / 2;
pivots.push_back({query(r, mid_col), r});
}
sort(pivots.begin(), pivots.end());
long long pivot_val = pivots[pivots.size() / 2].first;
vector<int> pos_le(n + 1);
vector<int> pos_lt(n + 1);
int j = n;
for (int i = 1; i <= n; ++i) {
if (L[i] > R[i]) {
pos_le[i] = L[i] - 1;
continue;
}
if (j > R[i]) j = R[i];
while (j >= L[i] && query(i, j) > pivot_val) {
j--;
}
pos_le[i] = j;
}
j = n;
for (int i = 1; i <= n; ++i) {
if (L[i] > R[i]) {
pos_lt[i] = L[i] - 1;
continue;
}
if (j > R[i]) j = R[i];
while (j >= L[i] && query(i, j) >= pivot_val) {
j--;
}
pos_lt[i] = j;
}
long long count_le = 0;
long long count_lt = 0;
for (int i = 1; i <= n; ++i) {
if (pos_le[i] >= L[i]) {
count_le += pos_le[i] - L[i] + 1;
}
if (pos_lt[i] >= L[i]) {
count_lt += pos_lt[i] - L[i] + 1;
}
}
if (k_rem <= count_lt) {
for (int i = 1; i <= n; ++i) {
R[i] = pos_lt[i];
}
} else if (k_rem > count_le) {
k_rem -= count_le;
for (int i = 1; i <= n; ++i) {
L[i] = pos_le[i] + 1;
}
} else {
done(pivot_val);
return 0;
}
}
return 0;
} |