四平方和(第七届蓝桥杯省赛C++A/B组,第七届蓝桥杯省赛JAVAB/C组)

二分+哈希：
代码：

#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
const int N = 5e6 + 10;
int h[N];
int n, m = 0;
struct node
{
	int sum, c, d;
	bool operator < (const node &a) const{
		if (sum == a.sum)
		{
			if (c == a.c)
				return d < a.d;
			return c < a.c;
		}
		return sum < a.sum;
	}
}q[N];

int main ()
{
	ios::sync_with_stdio (false);
	cin.tie (0); cout.tie(0);
	cin >> n;
	for (int i = 0; i * i <= n; i ++)
		for (int j = i; j * j + i * i <= n; j ++)
			q[m ++] = {i * i + j * j, i, j};
	
	sort (q, q + m);

	for (int i = 0; i * i <= n; i ++)
		for (int j = i; j * j + i * i <= n; j ++)
		{
			int t = n - i * i - j * j;
			int l = 0, r = m - 1;
			while (l < r)
			{
				int mid = (l + r) >> 1;
				if (t <= q[mid].sum) r = mid;
				else l = mid + 1;
			}
			if (q[l].sum == t)
			{
				cout << i << " " << j << " " << q[l].c << " " << q[l].d;
				return 0;
			}
		}
}