题解 | #Honeycomb#

思路：随便选两条轴作为x、y轴，把蜂巢映射到二维平面后找规律即可。

找到规律后可直接二分到某个区间然后分类讨论确定坐标求解即可。

#include <bits/stdc++.h>
using namespace std;
#define _for(i, a, b) for(int i = a; i <= b; i ++) 
#define _rep(i, a, b) for(int i = a; i >= b; i --) 
inline void read(int &x) { scanf("%d", &x); }
inline void read(int &x, int &y) { scanf("%d%d", &x, &y); }
inline void read(int &x, int &y, int &z) { scanf("%d%d%d", &x, &y, &z); }
#define lbt(x) ((x) & -(x)) 
#define ll long long 
#define _mp(x, y) make_pair((int)x, (int)y) 
typedef pair<int, int> pii;
const string SX = "   XXX   ", SY = "   YYY   ", FG = "\n     -----------------  \n";
const double eps = 1e-8, pi = acos(-1);

ll a[100009], tot;

void init() {
	a[0] = 1;  ll sum = 5;
	for(ll i = 1; ;) {
		i += sum;  sum += 6;
		if(i > 1.5e9) break;
		a[++ tot] = i;
	}
}
pii fu(int x) {
	if(x == 1) return _mp(0, 0);
	else if(x == 2) return _mp(0, -1);
	else if(x == 3) return _mp(-1, 0);
	else if(x == 4) return _mp(-1, 1);
	else if(x == 5) return _mp(0, 1);
	int l = 0, r = tot;
	while(l < r) {
		int mid = l + r + 1 >> 1;
		if(a[mid] <= x) l = mid;
		else r = mid - 1;
	}
	pii ans;
	int y = x - a[l];
	if(y <= l + 1) {
		ans = {l, -y};
	} else {
		l ++;
		y -= l;
		if(y < l) {
			ans = {l - 1 - y, -l};
		} else {
			y -= l - 1;
			if(y <= l) {
				ans = {0 - y, -l + y};
			} else {
				y -= l;
				if(y <= l) ans = {-l, y};
				else {
					y -= l;
					if(y <= l) ans = {-l + y , l};
					else {
						y -= l;
						ans = {y, l - y};
					}
				}
			}
		}
	}
	return ans;
}
int main() {
	init();
	int ttx;  cin >> ttx;
	while(ttx --) {
		int x, y;  read(x, y);
		pii a = fu(x), b = fu(y);
		int ans = 0;
		if(x == y) ans = 1;
		else if(a.first == b.first || a.second == b.second) ans = abs(a.first - b.first + a.second - b.second) + 1;
		else {
			if((a.first < b.first) ^ (a.second < b.second)) {
				x = abs(a.first - b.first);  y = abs(a.second - b.second);
				ans = max(x, y) + 1;
			} else ans = abs(a.first - b.first) + abs(a.second - b.second) + 1;
		}
		printf("%d\n", ans);
	}
	return 0;
}