Initial commit

2022/republic/d0/problem06/maxim_solution.cpp

@@ -0,0 +1,53 @@
+#include <bits/stdc++.h>
+using namespace std;
+ 
+typedef long long ll;
+#define f first
+#define s second
+#define pb push_back
+#define mp make_pair
+#define pi pair<ll, ll>
+#define sz(x) (int)((x).size())
+#define all(a) (a).begin(), (a).end()
+
+const ll mod = 1e9+7;
+ll n, k, m, mi, ma;
+
+void solve(){
+	cin >> n;
+	
+	map<ll, ll> q;
+	vector<pi> ans;
+	for(int i = 1; i*i < n; i++) q[i*i] = i;
+	for(int i = 1; i*i < n - i*i; i++){
+		if(q[n - i*i] == 0) continue;
+		ll j = q[n - i*i];
+		ll b = j*j - i*i;
+		ll a = 2*i*j;
+		if(a > b) swap(a, b);
+		if(a < 0) continue;
+		if(__gcd(a, b) != 1 || __gcd(b, n) != 1) continue;
+		ans.pb({a, b});
+	}
+	sort(all(ans));
+	for(int i = 0; i<ans.size(); i++) cout << ans[i].f << " " << ans[i].s << " " << n << "\n";
+	if(ans.size() == 0){
+		cout << "NOPE\n";
+		return;
+	}
+	
+}
+
+int main(){
+	ios::sync_with_stdio(0);
+	cin.tie(0);
+
+	//init();
+	
+	int t=1;
+//	cin >> t;
+	while(t--) solve();
+	
+	return 0;
+}
+

2022/republic/d0/problem06/problem06.cpp

@@ -0,0 +1,72 @@
+#include <iostream>
+#include <cmath>
+#include <map>
+#include <algorithm>
+#include <set>
+#include <utility>
+using namespace std;
+
+bool areCoprimes(int a, int b, int c) {
+	return __gcd(a, b) == 1 && __gcd(a, c) == 1 && __gcd(b, c) == 1;
+}
+
+
+
+int main() {
+	int64_t c;
+	cin >> c;
+
+	map<int64_t, int64_t> roots;
+
+	int64_t i = 1;
+	while (true) {
+		int64_t tmp = pow(i, 2);
+		if (tmp > c) {
+			break;
+		}
+
+		roots[tmp] = i;
+		i++;
+	}
+
+	int64_t rightLimit = i - 1;
+	set<pair<int64_t, int64_t>> results;
+
+	for (int64_t x = 1; x <= rightLimit; x++) {
+		int64_t xSqr = pow(x, 2);
+
+		int64_t y = roots[c - xSqr];
+		if (y == 0) {
+			continue;
+		}
+
+		// x^4 + 2*x^2*y^2 + y^4 = r^2
+		// x^4 - 2*x^2*y^2 + y^4 + 4*x^2*y^2 = r^2
+		// (x^2-y^2)^2 + (2*x*y)^2 = r^2
+		// a = x^2-y^2  b = 2*x*y
+		int64_t a = pow(y, 2) - pow(x, 2);
+		int64_t b = 2 * x * y;
+
+		if (a > b) {
+			swap(a, b);
+		}
+
+		if (a < 0) {
+			continue;
+		}
+
+		if (areCoprimes(a, b, c)) {
+			results.insert(make_pair(a, b));
+		}
+	}
+
+	if (results.size() == 0) {
+		cout << "NOPE" << endl;
+	} else {
+		for (auto it = results.begin(); it != results.end(); it++) {
+			cout << (it -> first) << " " << (it -> second) << " " << c << endl;
+		}
+	}
+
+	return 0;
+}

2022/republic/d0/problem06/try1.cpp

@@ -0,0 +1,88 @@
+#include <iostream>
+#include <cmath>
+#include <set>
+#include <algorithm>
+using namespace std;
+
+set<int> findFactors(int N) {
+	set<int> factors;
+
+	int stop = sqrt(N);
+	for (int i = 2; i <= stop; i++) {
+		if (N % i == 0) {
+			factors.insert(i);
+			factors.insert(N / i);
+		}
+	}
+
+	return factors;
+}
+
+
+
+bool areCoprimes(set<int> cFactors, int a, int b) {
+	auto setEnd = cFactors.end();
+
+	int stop = sqrt(a);
+	int i = 2;
+
+	for (i; i <= stop; i++) {
+		if (a % i == 0) {
+			int f1 = i;
+			int f2 = a / i;
+
+			if (b % f1 == 0 || b % f2 == 0 || cFactors.find(f1) != setEnd || cFactors.find(f2) != setEnd) {
+				return false;
+			}
+		} else if (b % i == 0) {
+			int f1 = i;
+			int f2 = b / i;
+
+			if (cFactors.find(f1) != setEnd || cFactors.find(f2) != setEnd) {
+				return false;
+			}
+		}
+	}
+
+	stop = sqrt(b);
+	for (i; i <= stop; i++) {
+		if (b % i == 0) {
+			int f1 = i;
+			int f2 = b / i;
+
+			if (cFactors.find(f1) != setEnd || cFactors.find(f2) != setEnd) {
+				return false;
+			}
+		}
+	}
+
+	return true;
+}
+
+
+
+int main() {
+	int c;
+	cin >> c;
+
+	set<int> cFactors = findFactors(c);
+
+
+	uint64_t cSqr = pow(c, 2);
+	bool found = false;
+	for (int a = 1; a <= c; a++) {
+		uint64_t aSqr = pow(a, 2);
+		for (int b = a; b <= c; b++) {
+			if (aSqr + pow(b, 2) == cSqr && areCoprimes(cFactors, a, b)) {
+				cout << a << " " << b << " " << c << endl;
+				found = true;
+			}
+		}
+	}
+
+	if (!found) {
+		cout << "NOPE" << endl;
+	}
+
+	return 0;
+}

2022/republic/d0/problem06/try2.cpp

@@ -0,0 +1,33 @@
+#include <iostream>
+#include <cmath>
+#include <algorithm>
+using namespace std;
+
+bool areCoprimes(int a, int b, int c) {
+	return __gcd(a, b) == 1 && __gcd(a, c) == 1 && __gcd(b, c) == 1;
+}
+
+
+
+int main() {
+	int c;
+	cin >> c;
+
+	uint64_t cSqr = pow(c, 2);
+	bool found = false;
+	for (int a = 1; a <= c; a++) {
+		uint64_t aSqr = pow(a, 2);
+		for (int b = a; b <= c; b++) {
+			if (aSqr + pow(b, 2) == cSqr && areCoprimes(a, b, c)) {
+				cout << a << " " << b << " " << c << endl;
+				found = true;
+			}
+		}
+	}
+
+	if (!found) {
+		cout << "NOPE" << endl;
+	}
+
+	return 0;
+}