feat: add count distinct primes from binary string algorithm

bit_manipulation/count_distinct_primes_from_binary_string.cpp

@@ -0,0 +1,107 @@
+/**
+ * @file count_distinct_primes_from_binary_string.cpp
+ * @brief Count distinct primes formed from binary strings using allowed operations.
+ * 
+ * @author Rudraksh Tank
+ * @date July 2025
+ *
+ * @details
+ * Given a binary string, the task is to count how many distinct prime decimal numbers
+ * can be formed by:
+ * - Swapping any two characters (makes position irrelevant)
+ * - Changing any '1' to '0' (not the reverse)
+ *
+ * Efficient solution using bit manipulation and Sieve of Eratosthenes.
+ *
+ * Tags: Bit Manipulation, Prime Numbers, Combinatorics, Greedy, Bitmask
+ */
+
+#include <cstdint>      ///< For uint32_t 
+#include <iostream>     ///< For input/output stream handling (std::cin, std::cout)
+#include <vector>       ///< For dynamic array storage (std::vector)
+#include <unordered_set>///< For storing distinct primes without duplicates (std::unordered_set)
+#include <algorithm>    ///< For algorithms like std::count
+#include <cassert>      ///< For assert-based testing
+
+const uint32_t MAX = 1e6;  ///< Upper bound for prime sieve
+static std::vector<bool> is_prime;
+
+/**
+ * @namespace bit_manipulation
+ * @brief Bit manipulation algorithms
+ */
+namespace bit_manipulation {
+
+    /**
+     * @brief Precomputes all prime numbers up to MAX using Sieve of Eratosthenes.
+     */
+    void precomputePrimes() {
+        is_prime.assign(MAX + 1, true);
+        is_prime[0] = is_prime[1] = false;
+        for (uint32_t i = 2; i * i <= MAX; i++) {
+            if (is_prime[i]) {
+                for (uint32_t j = i * i; j <= MAX; j += i) {
+                    is_prime[j] = false;
+                }
+            }
+        }
+    }
+
+    int popcount(uint32_t x) {
+        int count = 0;
+        while (x) {
+            count += x & 1;
+            x >>= 1;
+        }
+        return count;
+    }
+    /**
+     * @brief Counts distinct prime numbers that can be formed from the given binary string.
+     * @param s Binary string input
+     * @return Number of distinct primes possible after allowed transformations
+     */
+    int countPrimeBinaryStrings(const std::string &s) {
+        int n = s.length();
+        int k = std::count(s.begin(), s.end(), '1');
+        int cnt = 0;
+        int limit = 1 << n;
+
+        std::unordered_set<int> seen;
+
+        for (uint32_t i = 2; i < limit; i++) {
+            if (popcount(i) <= k && is_prime[i]) {
+                if (!seen.count(i)) {
+                    cnt++;
+                    seen.insert(i);
+                }
+            }
+        }
+
+        return cnt;
+    }
+
+} // namespace bit_manipulation
+
+/**
+ * @brief Static test function using assertions instead of I/O.
+ */
+static void tests() {
+    using namespace bit_manipulation;
+
+    precomputePrimes();
+
+    // Example test cases
+    assert(countPrimeBinaryStrings("1") == 0);     // Only "1" -> not prime
+    assert(countPrimeBinaryStrings("11") == 2);     // Should form primes like 3
+    assert(countPrimeBinaryStrings("101") == 3);    // Can form primes like 5
+    assert(countPrimeBinaryStrings("000") == 0);   // No 1s -> no primes possible
+}
+
+/**
+ * @brief Main function to run tests.
+ * @returns 0 on successful exit
+ */
+int main() {
+    tests();
+    return 0;
+}