基于拉格朗日中值的二分查找

/*
1、拉格朗日中值:减少比较次数

left                     mid       data                right
------------------------------------------------------------
一般求mid:mid=(left+right)/2
 可以转换为：
mid = left + (right-left)/2
mid = left + (right-left) * 1/2
如果待查找的值的下标为 data
mid = left + (right-left) *  (data-left)/(right-left) (比例)

 */

func bin_searchMid(arr []int,data int) int  {
    low := 0
    high := len(arr)-1
    i := 0
    for low<= high{
        i++
        fmt.Println("第N次",i)

        leftv := float64(data-arr[low]) // 大段
        allv := float64(arr[high]-arr[low])//整段
        diff := float64(high-low) // 比例
        mid := int(float64(low)+leftv/allv*diff) //计算中间的值
        //mid := (low+high)/2

        if mid <0 || mid >= len(arr){
            return -1
        }

        if arr[mid] > data {
            high = mid -1
        }else if arr[mid] < data{
            low = mid +1
        }else {
            return mid
        }
    }
    return -1
}