二分搜索

From Wikipedia: Binary search, also known as half-interval search or logarithmic search, is a search algorithm that finds the position of a target value within a sorted array. It compares the target value to the middle element of the array; if they are unequal, the half in which the target cannot lie is eliminated and the search continues on the remaining half until it is successful.

Properties

• Worst case performance O(log n)
• Best case performance O(1)
• Average case performance O(log n)
• Worst case space complexity O(1)

use std::cmp::Ordering;
pub fn binary_search<T: Ord>(item: &T, arr: &[T]) -> Option<usize> {
    let mut left = 0;
    let mut right = arr.len();
    while left < right {
        let mid = left + (right - left) / 2;
        match item.cmp(&arr[mid]) {
            Ordering::Less => right = mid,
            Ordering::Equal => return Some(mid),
            Ordering::Greater => left = mid + 1,
        }
    }
    None
}
#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn empty() {
        let index = binary_search(&"a", &vec![]);
        assert_eq!(index, None);
    }
    #[test]
    fn one_item() {
        let index = binary_search(&"a", &vec!["a"]);
        assert_eq!(index, Some(0));
    }
    #[test]
    fn search_strings() {
        let index = binary_search(&"a", &vec!["a", "b", "c", "d", "google", "zoo"]);
        assert_eq!(index, Some(0));
    }
    #[test]
    fn search_ints() {
        let index = binary_search(&4, &vec![1, 2, 3, 4]);
        assert_eq!(index, Some(3));
        let index = binary_search(&3, &vec![1, 2, 3, 4]);
        assert_eq!(index, Some(2));
        let index = binary_search(&2, &vec![1, 2, 3, 4]);
        assert_eq!(index, Some(1));
        let index = binary_search(&1, &vec![1, 2, 3, 4]);
        assert_eq!(index, Some(0));
    }
    #[test]
    fn not_found() {
        let index = binary_search(&5, &vec![1, 2, 3, 4]);
        assert_eq!(index, None);
    }
}