diff options
Diffstat (limited to 'math/piLegendre.cpp')
| -rw-r--r-- | math/piLegendre.cpp | 23 |
1 files changed, 23 insertions, 0 deletions
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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