[算法] 求无序数组元素最小差值

通过排序后，依次遍历前后两值求差即可，所以实质上的核心问题是排序；

通过经典的比较排序算法复杂度在O(nlogn)，而如果数据波动不大，则可通过桶排序将复杂度降到O(n)；

 

array = (5, 2, 4, 9, 0, 6)

# quick sort
# O(nlogn)
def split(list, start, end):
    middle = list[end]
    index = start -1
    for i in range(start, end+1):
        if list[i] <= middle:
            index += 1
            temp = list[i]
            list[i] = list[index]
            list[index] = temp

    return index

def quick_sort(list, start, end):
    if (start < end):
        index = split(list, start, end)
        quick_sort(list, start, index-1)
        quick_sort(list, index+1, end)

# bucket sort
def bucket_sort(list):
    max_e = list[0]
    min_e = list[0]

    # max & min element
    for i in list:
        if i > max_e:
            max_e = i
        if i < min_e:
            min_e = i

    bucket_v = max_e - min_e + 1
    B = []
    for i in range(bucket_v):
        B.append(0)
    for i in list:
        B[i - min_e] += 1
    return B

def min_diff():
    l = list(array)

    # sort
    B = bucket_sort(l)
    first = True
    diff = -1
    for i in range(len(B)):
        if B[i] >= 2:
            diff = 0
            break
        elif B[i] == 1 and first:
            low = i
            first = False
        elif B[i] == 1: # ! first
            high = i
            tmp_diff = high - low
            if (diff < 0 or tmp_diff < diff):
                diff = tmp_diff
            low = i
        # else B[i] == 0, ignore

    print "min diff from bucket sort:", diff

    # qsort
    quick_sort(l, 0, len(l)-1)
    first = True
    diff = -1
    for i in l:
        if first:
            low = i
            first = False
        else:
            high = i
            tmp_diff = high - low
            if (diff < 0 or tmp_diff < diff):
                diff = tmp_diff
            low = i

    print "min diff from quick sort:", diff

if __name__ == "__main__":
    print array
    min_diff()