39 lines
1 KiB
C++
39 lines
1 KiB
C++
#include <bits/stdc++.h>
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using namespace std;
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int main() {
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if (fopen("in", "r")) freopen("in", "r", stdin), freopen("out", "w", stdout);
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int T;
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cin >> T;
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for (int t = 0; t < T; ++t) {
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cout << "Case #" << t + 1 << ":\n";
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int N;
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cin >> N;
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if (N <= 30) {
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// if N <= 30 then just use naïve method
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for (int i = 0; i < N; ++i) cout << i + 1 << " " << 1 << '\n';
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}
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else {
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// first we try to make N - 30
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int sum = 0, side = 0, goal = N - 30;
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for (int i = 0; i < 30; ++i) {
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cout << i + 1 << " " << (side ? i + 1 : 1) << '\n';
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// each row sums to 2 ^ i
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// check if goal has a 2 ^ i in its binary representation
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if (goal & (1 << i)) {
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// walk across the row
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for (int j = 1; j <= i; ++j) cout << i + 1 << " " << (side ? i - j + 1 : j + 1) << '\n';
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side = !side; // toggle the side
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sum += (1 << i);
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}
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else ++sum;
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}
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// we've undershot so we still need to walk down until our sum is N
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for (int i = 30; sum < N; ++i, ++sum) cout << i + 1 << ' ' << (side ? i + 1 : 1) << '\n';
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}
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}
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} |