Add is power of two implementation

Author: AliAlimohammadi

DIRECTORY.md

@@ -20,6 +20,7 @@
     * [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)
+    * [Highest Set Bit](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/is_power_of_two.rs)
     * [N Bits Gray Code](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/n_bits_gray_code.rs)
     * [Previous Power of Two](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/find_previous_power_of_two.rs)
     * [Reverse Bits](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/reverse_bits.rs)

src/bit_manipulation/is_power_of_two.rs

@@ -0,0 +1,242 @@
+//! Power of Two Check
+//!
+//! This module provides a function to determine if a given positive integer is a power of two
+//! using efficient bit manipulation.
+//!
+//! # Algorithm
+//!
+//! The algorithm uses the property that powers of two have exactly one bit set in their
+//! binary representation. When we subtract 1 from a power of two, all bits after the single
+//! set bit become 1, and the set bit becomes 0:
+//!
+//! ```text
+//! n     = 0..100..00  (power of 2)
+//! n - 1 = 0..011..11
+//! n & (n - 1) = 0     (no intersections)
+//! ```
+//!
+//! For example:
+//! - 8 in binary:  1000
+//! - 7 in binary:  0111
+//! - 8 & 7 = 0000 = 0 ✓
+//!
+//! Author: Alexander Pantyukhin
+//! Date: November 1, 2022
+
+/// Determines if a given number is a power of two.
+///
+/// This function uses bit manipulation to efficiently check if a number is a power of two.
+/// A number is a power of two if it has exactly one bit set in its binary representation.
+/// The check `number & (number - 1) == 0` leverages this property.
+///
+/// # Arguments
+///
+/// * `number` - An integer to check (must be non-negative)
+///
+/// # Returns
+///
+/// A `Result` containing:
+/// - `Ok(true)` - If the number is a power of two (including 0 and 1)
+/// - `Ok(false)` - If the number is not a power of two
+/// - `Err(String)` - If the number is negative
+///
+/// # Examples
+///
+/// ```
+/// use the_algorithms_rust::bit_manipulation::is_power_of_two;
+///
+/// assert_eq!(is_power_of_two(0).unwrap(), true);
+/// assert_eq!(is_power_of_two(1).unwrap(), true);
+/// assert_eq!(is_power_of_two(2).unwrap(), true);
+/// assert_eq!(is_power_of_two(4).unwrap(), true);
+/// assert_eq!(is_power_of_two(8).unwrap(), true);
+/// assert_eq!(is_power_of_two(16).unwrap(), true);
+///
+/// assert_eq!(is_power_of_two(3).unwrap(), false);
+/// assert_eq!(is_power_of_two(6).unwrap(), false);
+/// assert_eq!(is_power_of_two(17).unwrap(), false);
+///
+/// // Negative numbers return an error
+/// assert!(is_power_of_two(-1).is_err());
+/// ```
+///
+/// # Errors
+///
+/// Returns an error if the input number is negative.
+///
+/// # Time Complexity
+///
+/// O(1) - The function performs a constant number of operations regardless of input size.
+pub fn is_power_of_two(number: i32) -> Result<bool, String> {
+    if number < 0 {
+        return Err("number must not be negative".to_string());
+    }
+
+    // Convert to u32 for safe bit operations
+    let num = number as u32;
+
+    // Check if number & (number - 1) == 0
+    // For powers of 2, this will always be true
+    Ok(num & num.wrapping_sub(1) == 0)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_zero() {
+        // 0 is considered a power of 2 by the algorithm (2^(-∞) interpretation)
+        assert_eq!(is_power_of_two(0).unwrap(), true);
+    }
+
+    #[test]
+    fn test_one() {
+        // 1 = 2^0
+        assert_eq!(is_power_of_two(1).unwrap(), true);
+    }
+
+    #[test]
+    fn test_powers_of_two() {
+        assert_eq!(is_power_of_two(2).unwrap(), true); // 2^1
+        assert_eq!(is_power_of_two(4).unwrap(), true); // 2^2
+        assert_eq!(is_power_of_two(8).unwrap(), true); // 2^3
+        assert_eq!(is_power_of_two(16).unwrap(), true); // 2^4
+        assert_eq!(is_power_of_two(32).unwrap(), true); // 2^5
+        assert_eq!(is_power_of_two(64).unwrap(), true); // 2^6
+        assert_eq!(is_power_of_two(128).unwrap(), true); // 2^7
+        assert_eq!(is_power_of_two(256).unwrap(), true); // 2^8
+        assert_eq!(is_power_of_two(512).unwrap(), true); // 2^9
+        assert_eq!(is_power_of_two(1024).unwrap(), true); // 2^10
+        assert_eq!(is_power_of_two(2048).unwrap(), true); // 2^11
+        assert_eq!(is_power_of_two(4096).unwrap(), true); // 2^12
+        assert_eq!(is_power_of_two(8192).unwrap(), true); // 2^13
+        assert_eq!(is_power_of_two(16384).unwrap(), true); // 2^14
+        assert_eq!(is_power_of_two(32768).unwrap(), true); // 2^15
+        assert_eq!(is_power_of_two(65536).unwrap(), true); // 2^16
+    }
+
+    #[test]
+    fn test_non_powers_of_two() {
+        assert_eq!(is_power_of_two(3).unwrap(), false);
+        assert_eq!(is_power_of_two(5).unwrap(), false);
+        assert_eq!(is_power_of_two(6).unwrap(), false);
+        assert_eq!(is_power_of_two(7).unwrap(), false);
+        assert_eq!(is_power_of_two(9).unwrap(), false);
+        assert_eq!(is_power_of_two(10).unwrap(), false);
+        assert_eq!(is_power_of_two(11).unwrap(), false);
+        assert_eq!(is_power_of_two(12).unwrap(), false);
+        assert_eq!(is_power_of_two(13).unwrap(), false);
+        assert_eq!(is_power_of_two(14).unwrap(), false);
+        assert_eq!(is_power_of_two(15).unwrap(), false);
+        assert_eq!(is_power_of_two(17).unwrap(), false);
+        assert_eq!(is_power_of_two(18).unwrap(), false);
+    }
+
+    #[test]
+    fn test_specific_non_powers() {
+        assert_eq!(is_power_of_two(6).unwrap(), false);
+        assert_eq!(is_power_of_two(17).unwrap(), false);
+        assert_eq!(is_power_of_two(100).unwrap(), false);
+        assert_eq!(is_power_of_two(1000).unwrap(), false);
+    }
+
+    #[test]
+    fn test_large_powers_of_two() {
+        assert_eq!(is_power_of_two(131072).unwrap(), true); // 2^17
+        assert_eq!(is_power_of_two(262144).unwrap(), true); // 2^18
+        assert_eq!(is_power_of_two(524288).unwrap(), true); // 2^19
+        assert_eq!(is_power_of_two(1048576).unwrap(), true); // 2^20
+    }
+
+    #[test]
+    fn test_numbers_near_powers_of_two() {
+        // One less than powers of 2
+        assert_eq!(is_power_of_two(3).unwrap(), false); // 2^2 - 1
+        assert_eq!(is_power_of_two(7).unwrap(), false); // 2^3 - 1
+        assert_eq!(is_power_of_two(15).unwrap(), false); // 2^4 - 1
+        assert_eq!(is_power_of_two(31).unwrap(), false); // 2^5 - 1
+        assert_eq!(is_power_of_two(63).unwrap(), false); // 2^6 - 1
+        assert_eq!(is_power_of_two(127).unwrap(), false); // 2^7 - 1
+        assert_eq!(is_power_of_two(255).unwrap(), false); // 2^8 - 1
+
+        // One more than powers of 2
+        assert_eq!(is_power_of_two(3).unwrap(), false); // 2^1 + 1
+        assert_eq!(is_power_of_two(5).unwrap(), false); // 2^2 + 1
+        assert_eq!(is_power_of_two(9).unwrap(), false); // 2^3 + 1
+        assert_eq!(is_power_of_two(17).unwrap(), false); // 2^4 + 1
+        assert_eq!(is_power_of_two(33).unwrap(), false); // 2^5 + 1
+        assert_eq!(is_power_of_two(65).unwrap(), false); // 2^6 + 1
+        assert_eq!(is_power_of_two(129).unwrap(), false); // 2^7 + 1
+    }
+
+    #[test]
+    fn test_negative_number_returns_error() {
+        let result = is_power_of_two(-1);
+        assert!(result.is_err());
+        assert_eq!(result.unwrap_err(), "number must not be negative");
+    }
+
+    #[test]
+    fn test_multiple_negative_numbers() {
+        assert!(is_power_of_two(-1).is_err());
+        assert!(is_power_of_two(-2).is_err());
+        assert!(is_power_of_two(-4).is_err());
+        assert!(is_power_of_two(-8).is_err());
+        assert!(is_power_of_two(-100).is_err());
+    }
+
+    #[test]
+    fn test_all_powers_of_two_up_to_30() {
+        // Test 2^0 through 2^30
+        for i in 0..=30 {
+            let power = 1u32 << i; // 2^i
+            assert_eq!(
+                is_power_of_two(power as i32).unwrap(),
+                true,
+                "2^{i} = {power} should be a power of 2"
+            );
+        }
+    }
+
+    #[test]
+    fn test_range_verification() {
+        // Test that between consecutive powers of 2, only the powers return true
+        for i in 1..10 {
+            let power = 1 << i; // 2^i
+            assert_eq!(is_power_of_two(power).unwrap(), true);
+
+            // Check numbers between this power and the next
+            let next_power = 1 << (i + 1);
+            for num in (power + 1)..next_power {
+                assert_eq!(
+                    is_power_of_two(num).unwrap(),
+                    false,
+                    "{num} should not be a power of 2"
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn test_bit_manipulation_correctness() {
+        // Verify the bit manipulation logic for specific examples
+        // For 8: 1000 & 0111 = 0000 ✓
+        assert_eq!(8 & 7, 0);
+        assert_eq!(is_power_of_two(8).unwrap(), true);
+
+        // For 16: 10000 & 01111 = 00000 ✓
+        assert_eq!(16 & 15, 0);
+        assert_eq!(is_power_of_two(16).unwrap(), true);
+
+        // For 6: 110 & 101 = 100 ✗
+        assert_ne!(6 & 5, 0);
+        assert_eq!(is_power_of_two(6).unwrap(), false);
+    }
+
+    #[test]
+    fn test_edge_case_max_i32_power_of_two() {
+        // Largest power of 2 that fits in i32: 2^30 = 1073741824
+        assert_eq!(is_power_of_two(1073741824).unwrap(), true);
+    }
+}

src/bit_manipulation/mod.rs

@@ -2,6 +2,7 @@ mod binary_coded_decimal;
 mod counting_bits;
 mod find_previous_power_of_two;
 mod highest_set_bit;
+mod is_power_of_two;
 mod n_bits_gray_code;
 mod reverse_bits;
 mod sum_of_two_integers;
@@ -12,6 +13,7 @@ pub use self::binary_coded_decimal::binary_coded_decimal;
 pub use self::counting_bits::count_set_bits;
 pub use self::find_previous_power_of_two::find_previous_power_of_two;
 pub use self::highest_set_bit::find_highest_set_bit;
+pub use self::is_power_of_two::is_power_of_two;
 pub use self::n_bits_gray_code::generate_gray_code;
 pub use self::reverse_bits::reverse_bits;
 pub use self::sum_of_two_integers::add_two_integers;