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| 1 | +/// Finds the missing number in a slice of consecutive integers. |
| 2 | +/// |
| 3 | +/// This function uses XOR bitwise operation to find the missing number. |
| 4 | +/// It XORs all expected numbers in the range [min, max] with the actual |
| 5 | +/// numbers present in the array. Since XOR has the property that `a ^ a = 0`, |
| 6 | +/// all present numbers cancel out, leaving only the missing number. |
| 7 | +/// |
| 8 | +/// # Arguments |
| 9 | +/// |
| 10 | +/// * `nums` - A slice of integers forming a sequence with one missing number |
| 11 | +/// |
| 12 | +/// # Returns |
| 13 | +/// |
| 14 | +/// * `Ok(i32)` - The missing number in the sequence |
| 15 | +/// * `Err(String)` - An error message if the input is invalid |
| 16 | +/// |
| 17 | +/// # Examples |
| 18 | +/// |
| 19 | +/// ``` |
| 20 | +/// # use the_algorithms_rust::bit_manipulation::find_missing_number; |
| 21 | +/// assert_eq!(find_missing_number(&[0, 1, 3, 4]).unwrap(), 2); |
| 22 | +/// assert_eq!(find_missing_number(&[4, 3, 1, 0]).unwrap(), 2); |
| 23 | +/// assert_eq!(find_missing_number(&[-4, -3, -1, 0]).unwrap(), -2); |
| 24 | +/// assert_eq!(find_missing_number(&[-2, 2, 1, 3, 0]).unwrap(), -1); |
| 25 | +/// assert_eq!(find_missing_number(&[1, 3, 4, 5, 6]).unwrap(), 2); |
| 26 | +/// ``` |
| 27 | +pub fn find_missing_number(nums: &[i32]) -> Result<i32, String> { |
| 28 | + if nums.is_empty() { |
| 29 | + return Err("input array must not be empty".to_string()); |
| 30 | + } |
| 31 | + |
| 32 | + if nums.len() == 1 { |
| 33 | + return Err("array must have at least 2 elements to find a missing number".to_string()); |
| 34 | + } |
| 35 | + |
| 36 | + let low = *nums.iter().min().unwrap(); |
| 37 | + let high = *nums.iter().max().unwrap(); |
| 38 | + |
| 39 | + let mut missing_number = high; |
| 40 | + |
| 41 | + for i in low..high { |
| 42 | + let index = (i - low) as usize; |
| 43 | + missing_number ^= i ^ nums[index]; |
| 44 | + } |
| 45 | + |
| 46 | + Ok(missing_number) |
| 47 | +} |
| 48 | + |
| 49 | +#[cfg(test)] |
| 50 | +mod tests { |
| 51 | + use super::*; |
| 52 | + |
| 53 | + #[test] |
| 54 | + fn test_missing_in_middle() { |
| 55 | + assert_eq!(find_missing_number(&[0, 1, 3, 4]).unwrap(), 2); |
| 56 | + } |
| 57 | + |
| 58 | + #[test] |
| 59 | + fn test_unordered_array() { |
| 60 | + assert_eq!(find_missing_number(&[4, 3, 1, 0]).unwrap(), 2); |
| 61 | + } |
| 62 | + |
| 63 | + #[test] |
| 64 | + fn test_negative_numbers() { |
| 65 | + assert_eq!(find_missing_number(&[-4, -3, -1, 0]).unwrap(), -2); |
| 66 | + } |
| 67 | + |
| 68 | + #[test] |
| 69 | + fn test_negative_and_positive() { |
| 70 | + assert_eq!(find_missing_number(&[-2, 2, 1, 3, 0]).unwrap(), -1); |
| 71 | + } |
| 72 | + |
| 73 | + #[test] |
| 74 | + fn test_missing_at_start() { |
| 75 | + assert_eq!(find_missing_number(&[1, 3, 4, 5, 6]).unwrap(), 2); |
| 76 | + } |
| 77 | + |
| 78 | + #[test] |
| 79 | + fn test_unordered_missing_middle() { |
| 80 | + assert_eq!(find_missing_number(&[6, 5, 4, 2, 1]).unwrap(), 3); |
| 81 | + } |
| 82 | + |
| 83 | + #[test] |
| 84 | + fn test_another_unordered() { |
| 85 | + assert_eq!(find_missing_number(&[6, 1, 5, 3, 4]).unwrap(), 2); |
| 86 | + } |
| 87 | + |
| 88 | + #[test] |
| 89 | + fn test_empty_array() { |
| 90 | + assert!(find_missing_number(&[]).is_err()); |
| 91 | + assert_eq!( |
| 92 | + find_missing_number(&[]).unwrap_err(), |
| 93 | + "input array must not be empty" |
| 94 | + ); |
| 95 | + } |
| 96 | + |
| 97 | + #[test] |
| 98 | + fn test_single_element() { |
| 99 | + assert!(find_missing_number(&[5]).is_err()); |
| 100 | + assert_eq!( |
| 101 | + find_missing_number(&[5]).unwrap_err(), |
| 102 | + "array must have at least 2 elements to find a missing number" |
| 103 | + ); |
| 104 | + } |
| 105 | + |
| 106 | + #[test] |
| 107 | + fn test_two_elements() { |
| 108 | + assert_eq!(find_missing_number(&[0, 2]).unwrap(), 1); |
| 109 | + assert_eq!(find_missing_number(&[2, 0]).unwrap(), 1); |
| 110 | + } |
| 111 | + |
| 112 | + #[test] |
| 113 | + fn test_large_range() { |
| 114 | + assert_eq!(find_missing_number(&[100, 101, 103, 104]).unwrap(), 102); |
| 115 | + } |
| 116 | + |
| 117 | + #[test] |
| 118 | + fn test_missing_at_boundaries() { |
| 119 | + // Missing is the second to last element |
| 120 | + assert_eq!(find_missing_number(&[1, 2, 3, 5]).unwrap(), 4); |
| 121 | + } |
| 122 | +} |
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