Add Binary Coded Decimal algorithm to bit manipulation (#966)

Author: AliAlimohammadi

DIRECTORY.md

@@ -2,7 +2,7 @@
 
 ## Src
   * Backtracking
-    * [All Combination Of Size K](https://github.com/TheAlgorithms/Rust/blob/master/src/backtracking/all_combination_of_size_k.rs)
+    * [All Combinations of Size K](https://github.com/TheAlgorithms/Rust/blob/master/src/backtracking/all_combination_of_size_k.rs)
     * [Graph Coloring](https://github.com/TheAlgorithms/Rust/blob/master/src/backtracking/graph_coloring.rs)
     * [Hamiltonian Cycle](https://github.com/TheAlgorithms/Rust/blob/master/src/backtracking/hamiltonian_cycle.rs)
     * [Knight Tour](https://github.com/TheAlgorithms/Rust/blob/master/src/backtracking/knight_tour.rs)
@@ -17,6 +17,7 @@
     * [Multiply](https://github.com/TheAlgorithms/Rust/blob/master/src/big_integer/multiply.rs)
     * [Poly1305](https://github.com/TheAlgorithms/Rust/blob/master/src/big_integer/poly1305.rs)
   * Bit Manipulation
+    * [Binary Coded Decimal](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/binary_coded_decimal.rs)
     * [Counting Bits](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/counting_bits.rs)
     * [Highest Set Bit](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/highest_set_bit.rs)
     * [N Bits Gray Code](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/n_bits_gray_code.rs)
@@ -104,7 +105,7 @@
     * [Maximal Square](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/maximal_square.rs)
     * [Maximum Subarray](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/maximum_subarray.rs)
     * [Minimum Cost Path](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/minimum_cost_path.rs)
-    * [Optimal Bst](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/optimal_bst.rs)
+    * [Optimal BST](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/optimal_bst.rs)
     * [Rod Cutting](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/rod_cutting.rs)
     * [Smith-Waterman](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/smith_waterman.rs)
     * [Snail](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/snail.rs)

src/bit_manipulation/binary_coded_decimal.rs

@@ -0,0 +1,129 @@
+//! Binary Coded Decimal (BCD) conversion
+//!
+//! This module provides a function to convert decimal integers to Binary Coded Decimal (BCD) format.
+//! In BCD, each decimal digit is represented by its 4-bit binary equivalent.
+//!
+//! # Examples
+//!
+//! ```
+//! use the_algorithms_rust::bit_manipulation::binary_coded_decimal;
+//!
+//! assert_eq!(binary_coded_decimal(12), "0b00010010");
+//! assert_eq!(binary_coded_decimal(987), "0b100110000111");
+//! ```
+
+use std::fmt::Write;
+
+/// Converts a decimal integer to Binary Coded Decimal (BCD) format.
+///
+/// Each digit of the input number is represented by a 4-bit binary value.
+/// Negative numbers are treated as 0.
+///
+/// # Arguments
+///
+/// * `number` - An integer to be converted to BCD format
+///
+/// # Returns
+///
+/// A `String` representing the BCD encoding with "0b" prefix
+///
+/// # Examples
+///
+/// ```
+/// use the_algorithms_rust::bit_manipulation::binary_coded_decimal;
+///
+/// assert_eq!(binary_coded_decimal(0), "0b0000");
+/// assert_eq!(binary_coded_decimal(3), "0b0011");
+/// assert_eq!(binary_coded_decimal(12), "0b00010010");
+/// assert_eq!(binary_coded_decimal(987), "0b100110000111");
+/// assert_eq!(binary_coded_decimal(-5), "0b0000");
+/// ```
+///
+/// # Algorithm
+///
+/// 1. Convert the number to its absolute value (negative numbers become 0)
+/// 2. For each decimal digit:
+///    - Convert the digit to binary
+///    - Pad to 4 bits with leading zeros
+///    - Concatenate to the result
+/// 3. Prepend "0b" to the final binary string
+pub fn binary_coded_decimal(number: i32) -> String {
+    // Handle negative numbers by converting to 0
+    let num = if number < 0 { 0 } else { number };
+
+    // Convert to string to process each digit
+    let digits = num.to_string();
+
+    // Build the BCD string using fold for efficiency
+    let bcd = digits.chars().fold(String::new(), |mut acc, digit| {
+        // Convert char to digit value and format as 4-bit binary
+        let digit_value = digit.to_digit(10).unwrap();
+        write!(acc, "{digit_value:04b}").unwrap();
+        acc
+    });
+
+    format!("0b{bcd}")
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_zero() {
+        assert_eq!(binary_coded_decimal(0), "0b0000");
+    }
+
+    #[test]
+    fn test_single_digit() {
+        assert_eq!(binary_coded_decimal(1), "0b0001");
+        assert_eq!(binary_coded_decimal(2), "0b0010");
+        assert_eq!(binary_coded_decimal(3), "0b0011");
+        assert_eq!(binary_coded_decimal(4), "0b0100");
+        assert_eq!(binary_coded_decimal(5), "0b0101");
+        assert_eq!(binary_coded_decimal(6), "0b0110");
+        assert_eq!(binary_coded_decimal(7), "0b0111");
+        assert_eq!(binary_coded_decimal(8), "0b1000");
+        assert_eq!(binary_coded_decimal(9), "0b1001");
+    }
+
+    #[test]
+    fn test_two_digits() {
+        assert_eq!(binary_coded_decimal(10), "0b00010000");
+        assert_eq!(binary_coded_decimal(12), "0b00010010");
+        assert_eq!(binary_coded_decimal(25), "0b00100101");
+        assert_eq!(binary_coded_decimal(99), "0b10011001");
+    }
+
+    #[test]
+    fn test_three_digits() {
+        assert_eq!(binary_coded_decimal(100), "0b000100000000");
+        assert_eq!(binary_coded_decimal(123), "0b000100100011");
+        assert_eq!(binary_coded_decimal(456), "0b010001010110");
+        assert_eq!(binary_coded_decimal(987), "0b100110000111");
+    }
+
+    #[test]
+    fn test_large_numbers() {
+        assert_eq!(binary_coded_decimal(1234), "0b0001001000110100");
+        assert_eq!(binary_coded_decimal(9999), "0b1001100110011001");
+    }
+
+    #[test]
+    fn test_negative_numbers() {
+        // Negative numbers should be treated as 0
+        assert_eq!(binary_coded_decimal(-1), "0b0000");
+        assert_eq!(binary_coded_decimal(-2), "0b0000");
+        assert_eq!(binary_coded_decimal(-100), "0b0000");
+    }
+
+    #[test]
+    fn test_each_digit_encoding() {
+        // Verify that each digit is encoded correctly in a multi-digit number
+        // 67 should be: 6 (0110) and 7 (0111)
+        assert_eq!(binary_coded_decimal(67), "0b01100111");
+
+        // 305 should be: 3 (0011), 0 (0000), 5 (0101)
+        assert_eq!(binary_coded_decimal(305), "0b001100000101");
+    }
+}

src/bit_manipulation/mod.rs

@@ -1,10 +1,12 @@
+mod binary_coded_decimal;
 mod counting_bits;
 mod highest_set_bit;
 mod n_bits_gray_code;
 mod reverse_bits;
 mod sum_of_two_integers;
 mod swap_odd_even_bits;
 
+pub use binary_coded_decimal::binary_coded_decimal;
 pub use counting_bits::count_set_bits;
 pub use highest_set_bit::find_highest_set_bit;
 pub use n_bits_gray_code::generate_gray_code;