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def binary_search(self, A, target):
    '''
    二分查找法
    '''
    # 检查输入
    if len(A) < 1 or target < A[0] or target > A[-1]:
        return -1

    l, r = 0, len(A)-1
    while l < r:                #退出条件，注意不要用l == r判断
        m = (l + （ r - l )) >> 1  #计算二分点, 要防止溢出
        if A[m] == target:      #find
            return m
        elif target < A[m]:     # l....target....m............r
            r = m               # 右边界直接移动
        else:
            l = m + 1           # 左边界移动时要+1
    return -1

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pub fn interpolation_search(
    arr: &[i32],
    target: &i32,
) -> Result<usize, usize> {
    // 1. Handle empty sequence.
    if arr.is_empty() {
        return Err(0)
    }

    // 2. Setup variable storing iteration informaion.
    let mut hi = arr.len() - 1;
    let mut lo = 0_usize;

    let mut interpolant = 0_usize;

    // 3. Main loop to calculate the interpolant.
    loop {
        let lo_val = arr[lo];
        let hi_val = arr[hi];

        // 3.1. Three condition to exit the loop
        if hi <= lo || *target < lo_val || *target > hi_val {
            break
        }

        // 3.2. The linear interpolation part
        let offset = (*target - lo_val) * (hi - lo) as i32 / (hi_val - lo_val);
        interpolant = lo + offset as usize;

        let mid_val = arr[interpolant];

        // 3.3. Comparison between the interpolant and targert value.
        if mid_val > *target {
            hi = interpolant - 1;
        } else if mid_val < *target {
            lo = interpolant + 1;
        } else {
            break
        }
    }

    // 4. Determine whether the returning interpolant are equal to target value.
    if *target > arr[hi] {
        Err(hi + 1)
    } else if *target < arr[lo] {
        Err(lo)
    } else {
        Ok(interpolant)
    }
}

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use crate::searching::binary_search;

pub fn exponential_search<T>(arr: &[T], target: &T) -> Result<usize, usize>
    where T: PartialOrd
{
    // 1. Handle empty scenario.
    let size = arr.len();
    if size == 0 {
        return Err(0);
    }

    // 2. Determine searching boundaries.
    let mut hi = 1_usize; // Upper bound.
    while hi < size && arr[hi] < *target {
        hi <<= 1;
    }
    let lo = hi >> 1; // Lower bound.

    // 3. Do binary search.
    binary_search(&arr[lo..size.min(hi + 1)], target)
        .map(|index| lo + index)
        .map_err(|index| lo + index)
}