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78 lines
2.2 KiB
78 lines
2.2 KiB
# 二分搜索
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![alt text][binary-image]
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From [Wikipedia][binary-wiki]: 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.
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__Properties__
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* Worst case performance O(log n)
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* Best case performance O(1)
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* Average case performance O(log n)
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* Worst case space complexity O(1)
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```rust
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use std::cmp::Ordering;
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pub fn binary_search<T: Ord>(item: &T, arr: &[T]) -> Option<usize> {
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let mut left = 0;
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let mut right = arr.len();
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while left < right {
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let mid = left + (right - left) / 2;
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match item.cmp(&arr[mid]) {
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Ordering::Less => right = mid,
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Ordering::Equal => return Some(mid),
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Ordering::Greater => left = mid + 1,
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}
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}
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None
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn empty() {
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let index = binary_search(&"a", &vec![]);
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assert_eq!(index, None);
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}
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#[test]
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fn one_item() {
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let index = binary_search(&"a", &vec!["a"]);
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assert_eq!(index, Some(0));
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}
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#[test]
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fn search_strings() {
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let index = binary_search(&"a", &vec!["a", "b", "c", "d", "google", "zoo"]);
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assert_eq!(index, Some(0));
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}
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#[test]
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fn search_ints() {
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let index = binary_search(&4, &vec![1, 2, 3, 4]);
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assert_eq!(index, Some(3));
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let index = binary_search(&3, &vec![1, 2, 3, 4]);
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assert_eq!(index, Some(2));
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let index = binary_search(&2, &vec![1, 2, 3, 4]);
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assert_eq!(index, Some(1));
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let index = binary_search(&1, &vec![1, 2, 3, 4]);
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assert_eq!(index, Some(0));
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}
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#[test]
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fn not_found() {
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let index = binary_search(&5, &vec![1, 2, 3, 4]);
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assert_eq!(index, None);
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}
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}
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```
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[binary-wiki]: https://en.wikipedia.org/wiki/Binary_search_algorithm
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[binary-image]: https://upload.wikimedia.org/wikipedia/commons/f/f7/Binary_search_into_array.png |