Added math algorithms

Author: fredbr

graph/lca_binary_lifting.cpp

@@ -34,8 +34,7 @@ int lca(int x, int y)
 		if (dep[y]-(1<<i) >= dep[x])
 			y = anc[y][i];
 
-	if (x == y) return x;
-
+	if (x == y) return x
 	for (int i = maxlog-1; i >= 0; i--)
 		if (anc[x][i] != anc[y][i] and
 			anc[x][i] != 0 and anc[y][i] != 0)

math/gcdext.cpp

@@ -0,0 +1,33 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+typedef long long ll;
+
+tuple<ll, ll, ll> gcdext(ll a, ll b)
+{
+	if (a == 0)
+		return {1, 0, a};
+	int x, y, g;
+	tie(x, y, g) = gcdext(b, a%b);
+	return {y, x-(a/b)*y, g};
+}
+
+ostream& operator<<(ostream& out, const tuple<ll,ll,ll>& x)
+{
+	out << "(";
+	out << get<0>(x) << ", ";
+	out << get<1>(x) << ", ";
+	out << get<2>(x) << ")";
+	return out;
+}
+
+int main()
+{	
+	ll x, y;
+	cin >> x >> y;
+
+	auto ans = gcdext(x, y);
+
+	cout << ans << "\n";
+}

math/phi.cpp

@@ -0,0 +1,39 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+const int maxn = 1010101;
+int s[maxn];
+
+void sieve_phi()
+{
+	for (int i = 1; i < maxn; i++)
+		s[i] = i;
+
+	for (int i = 2; i < maxn; i++)
+		if (s[i] == i)
+			for (int j = i; j < maxn; j += i)
+				s[j] -= s[j]/i;
+}
+
+int phi(int x)
+{
+	int ans = x, k = x;
+	for (int i = 2; i*i <= x and k > 1; i++) {
+		if (k%i ==0) {	
+			ans -= ans/i;
+			while (k%i == 0)
+				k /= i;
+		}
+	}
+
+	if (k != 1)
+		ans -= ans/k;
+
+	return ans;
+}
+
+int main()
+{	
+	sieve_phi();
+}

math/sieve.cpp

@@ -0,0 +1,26 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+const int maxn = 10101010;
+
+char s[maxn];
+// bitset<maxn> s;
+vector<int> primes;
+
+
+void init()
+{
+	for (int i = 2; i*i < maxn; i++)
+		if (!s[i]) 
+			for (int j = i*i; j < maxn; j++)
+				s[j] = 1;
+
+	for (int i = 2; i < maxn; i++)
+		if (!s[i]) primes.push_back(i);
+}
+
+int main()
+{
+	init();
+}