Count all possible triangles with distinct lengths <= n

triangle.cpp

#include <iostream>
#include <cstdio>
using namespace std;

int sumsquare(int n) {
	return n * (n + 1) / 2 * (2 * n + 1) / 3;
}

int range(int n) {
	return n * (n + 1) / 2;
}

int main() {
	int n; 
	while (cin >> n) {
		int n2 = n / 2, n1 = n - n2 - 1;
		int c = 0;
		for (int i = 1; i <= n; ++i) {
			for (int j = i + 1; j <= n; ++j) {
				for (int k = j + 1; k <= n; ++k) {
					if (i + j > k)
						c++;
				}
			}
		}
		cout << c << endl;
		c = 0;
		for (int i = 1; i <= n / 2; ++i) {
			// c += max(0, (i - 1) * (n - 2 * i - 1));
			int occ = min(i, n - i);
			c += max(0, n - 2*i) * (i - 1);
			c += occ * occ - occ * (occ + 1) / 2;
		}
		// cout << '\t' << c << endl;
		for (int i = n / 2 + 1; i <= n; ++i) {
			// c += max(0, (i - 1) * (n - 2 * i - 1));
			int occ = min(i, n - i);
			c += max(0, n - 2*i) * (i - 1);
			c += occ * occ - occ * (occ + 1) / 2;
		}
		cout << c << endl;
		c = 0;
		for (int i = 1; i <= n / 2; ++i) {
			// c += (n - 2 * i) * (i - 1) + i * i - i * (i + 1) / 2;
			// c += n * i - 2 * i * i + 2 * i - n + i * i - i * (i + 1) / 2;
			c += (n + 2) * i - n - i * i - i * (i + 1) / 2;
		}
		// cout << '\t' << c << endl;
		for (int i = n / 2 + 1; i <= n; ++i)
			c += (n - i) * (n - i) - (n - i) * (n - i + 1) / 2;
		cout << c << endl;
		c = 0;
		c += (n + 2) * range(n2) - n*n2 - sumsquare(n2) - (sumsquare(n2) + range(n2)) / 2;
		// cout << '\t' << c << endl;
		for (int i = n / 2 + 1; i <= n; ++i)
			c += (n - i) * (n - i) - (n - i) * (n - i + 1) / 2;
		cout << c << endl;
		c = 0;
		c += (n + 2) * range(n2) - n*n2 - sumsquare(n2) - (sumsquare(n2) + range(n2)) / 2;
		c += sumsquare(n1) - (sumsquare(n1) + range(n1)) / 2;
		cout << c << endl;
		c = 0;
		if (n & 1) {
			int r = range(n / 2);
			int s = sumsquare(n / 2);
			c += (n + 2) * r - n * n1 - s - (s + r) / 2 + s - (s + r) / 2;
		} else {
			// n1 == n2 - 1
			int r = range(n / 2);
			int s = sumsquare(n / 2);
			c += (n + 2) * r - n * n2 - s - (s + r)/2;
			c += s - n2 * n2 - (s - n2 * n2 + r - n2)/2;
			// c += (n + 2) * range(n2) - n*n2 - sumsquare(n2) - (sumsquare(n2) + range(n2)) / 2;
			// c += sumsquare(n1) - (sumsquare(n1) + range(n1)) / 2;
		}
		cout << c << endl;
		/// FINAL FORMULA
		int r = range(n / 2);
		int s = sumsquare(n / 2);
		c = (n + 1) * r - n / 2 * n - s;
		if (n % 2 == 0) c -= range(n/2 - 1);
		cout << c << endl;
	}
}