歸併排序的python實現：遞歸與非遞歸

遞歸

原理比較簡單，就是有序數組的合併。

def merge(a, b):
    c = []
    i = j = 0
    while i < len(a) and j < len(b):
        if a[i] < b[j]:
            c.append(a[i])
            i += 1
        else:
            c.append(b[j])
            j += 1
    while i < len(a):
        c.append(a[i])
        i += 1
    while j < len(b):
        c.append(b[j])
        j += 1
    return c

def merge_sort(lists):
    if len(lists) <= 1:
        return lists
    middle = len(lists) // 2
    left = merge_sort(lists[:middle])
    right = merge_sort(lists[middle:])
    return merge(left, right)

 

非遞歸版本

非遞歸版本不需要額外的空間。直接在原數組上進行切割合併

def merge(seq, low, mid, high):
    left = seq[low: mid]
    right = seq[mid: high]
    k = 0 
    j = 0
    result = []
    while k < len(left) and j < len(right):
        if left[k] <= right[j]:
            result.append(left[k])
            k += 1
        else:
            result.append(right[j])
            j += 1
    result += left[k:]
    result += right[j:]
    seq[low: high] = result

def merge_sort(seq):
    i = 1 # i是步長
    while i < len(seq):
        low = 0
        while low < len(seq):
            mid = low + i #mid前後均爲有序
            high = min(low+2*i,len(seq))
            if mid < high: 
                merge(seq, low, mid, high)
            low += 2*i
        i *= 2