From 5ab8a5088b729a9953b8dff1b2a985dc8fb2098b Mon Sep 17 00:00:00 2001
From: mzuenni <michi.zuendorf@gmail.com>
Date: Mon, 27 Jun 2022 17:19:28 +0200
Subject: updated tcr

---
 math/piLegendre.cpp | 23 +++++++++++++++++++++++
 1 file changed, 23 insertions(+)
 create mode 100644 math/piLegendre.cpp

(limited to 'math/piLegendre.cpp')

diff --git a/math/piLegendre.cpp b/math/piLegendre.cpp
new file mode 100644
index 0000000..f45ee85
--- /dev/null
+++ b/math/piLegendre.cpp
@@ -0,0 +1,23 @@
+constexpr ll cache = 500; // requires O(cache^3)
+vector<vector<ll>> memo(cache * cache, vector<ll>(cache));
+
+ll pi(ll n);
+
+ll phi(ll n, ll k) {
+	if (n <= 1 || k < 0) return 0;
+	if (n <= primes[k]) return n - 1;
+	if (n < N && primes[k] * primes[k] > n) return n - pi(n) + k;
+	bool ok = n < cache * cache;
+	if (ok && memo[n][k] > 0) return memo[n][k];
+	ll res = n/primes[k] - phi(n/primes[k], k - 1) + phi(n, k - 1);
+	if (ok) memo[n][k] = res;
+	return res;
+}
+
+ll pi(ll n) {
+	if (n < N) { // implement this as O(1) lookup for speedup!
+		return distance(primes.begin(), upper_bound(primes.begin(), primes.end(), n));
+	} else {
+		ll k = pi(sqrtl(n) + 1);
+		return n - phi(n, k) + k;
+}}
-- 
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