2018-08-08 swift_Binary Search

Binary Search是二分查找，将目标分成两部分来进行查找，相比顺序查找效率要高一些，例如在书店中，20本书里有一本书没有被消磁，按照顺序可能会查到最后第20本才会找到，但是如果分成两部分一次就可以排除10本书，效率提高很多。

func binarySearch(_ a: [T], key: T, range: Range) -> Int? {
    if range.lowerBound >= range.upperBound {
        // If we get here, then the search key is not present in the array.
        return nil
        
    } else {
        // Calculate where to split the array.
        let midIndex = range.lowerBound + (range.upperBound - range.lowerBound) / 2
        
        // Is the search key in the left half?
        if a[midIndex] > key {
            return binarySearch(a, key: key, range: range.lowerBound ..< midIndex)
            
            // Is the search key in the right half?
        } else if a[midIndex] < key {
            return binarySearch(a, key: key, range: midIndex + 1 ..< range.upperBound)
            
            // If we get here, then we've found the search key!
        } else {
            return midIndex
        }
    }
}

let numbers = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67]

binarySearch(numbers, key: 43, range: 0 ..< numbers.count)

在分四次之后找到了43
需要注意的是二分查找的元素是按照顺序排列的