goldbachs_conjecture.cpp

puzzles/interviews/training/goldbachs_conjecture.cpp

@@ -0,0 +1,79 @@
+#include <vector>
+#include <unordered_set>
+#include <iostream>
+#include <cmath>
+#include <algorithm>
+
+using namespace std;
+
+static std::vector<int> GetPrimes(const size_t n) {
+    std::vector<int> primes;
+    std::vector<int> lp(n + 1, 0);
+
+for (auto i = 2u; i <= n; ++i) {
+    if (lp[i] == 0) {
+        lp[i] = i;
+        primes.push_back(i);
+    }
+    for (auto j = 0u; j < primes.size() && primes[j] <= lp[i] && i * primes[j] <= n; ++j)
+        lp[i * primes[j]] = primes[j];
+}
+return primes;
+
+}
+
+inline bool is_prime( int n, const vector<int>& primes ){
+    int sqrt_n = floor(sqrt(double(n)));
+    for ( int i = 0; i < primes.size() && primes[i] <= sqrt_n; ++i ){
+        if ( n % primes[i] == 0 ) {
+            return false;
+        }
+    }
+    return true;
+}
+
+vector<int> primesum(int A) {
+
+    vector<int> primes;
+
+#if 0
+    for ( int i = 2; i < A; ++i){
+        if ( is_prime(i,primes) ){
+            primes.push_back(i);
+        }
+    }
+#endif
+
+    primes = GetPrimes(A);
+
+#if 1
+    unordered_set<int> primes_set(primes.begin(),primes.end());
+    for ( int i = 0; i < primes.size(); ++i ){
+        if ( primes_set.find(A-primes[i]) != primes_set.end() ) {
+            return {primes[i], A-primes[i]};
+        }
+    }
+#else
+    for ( int i = 0; i < primes.size(); ++i ) {
+        auto it = std::lower_bound(primes.begin(), primes.end(), A - primes[i]);
+        if ( it != primes.end() && *it == A-primes[i] ) {
+            return {primes[i], A-primes[i]};
+        }
+    }
+#endif
+
+    return {}; 
+}
+
+void solve_and_print(int A){
+    auto r = primesum(A);
+    std::cout << r[0] << ' ' << r[1] << std::endl;
+}
+
+int main()
+{
+    solve_and_print(4);
+    solve_and_print(10);
+
+    solve_and_print(16777214);
+}

puzzles/interviews/training/permutation.py

@@ -1,7 +1,7 @@
-#
-#   Prints all permutations.
-#
 def permutation(s, b, e):
+    """
+      Prints all permutations.
+    """
     if b+1 == e:
         print(s)
     else:
@@ -16,12 +16,13 @@ def permutation(s, b, e):
         s[b] = s[e-1]
         s[e-1] = c
 
-#
+
-#   Prints all permutations. But in addition doesn't print
-#   multiple instances of same value.
-#   e.g. abb bab bba  ( doesn't print two abb )
-#
 def permutation2(s):
+    """
+      Prints all permutations. But in addition doesn't print
+      multiple instances of same value.
+      e.g. abb bab bba  ( doesn't print two abb )
+    """
     print(s)
     l = len(s)
 
@@ -41,6 +42,7 @@ def permutation2(s):
             if i == 0:
                 return
 
+
 if __name__ == "__main__":
     s = ['a', 'b', 'c', 'd', 'e', 'e']
     permutation(s, 0, len(s))