用Python合并排序

我找不到任何可用的Python3.3合并排序算法代码，所以我自己做了一个。有没有办法加快速度？它在大约0.3-0.5秒内对20000个数字进行排序

def msort(x):
    result = []
    if len(x) < 2:
        return x
    mid = int(len(x)/2)
    y = msort(x[:mid])
    z = msort(x[mid:])
    while (len(y) > 0) or (len(z) > 0):
        if len(y) > 0 and len(z) > 0:
            if y[0] > z[0]:
                result.append(z[0])
                z.pop(0)
            else:
                result.append(y[0])
                y.pop(0)
        elif len(z) > 0:
            for i in z:
                result.append(i)
                z.pop(0)
        else:
            for i in y:
                result.append(i)
                y.pop(0)
    return result

def msort（x）：
结果=[]
如果len（x）<2：
返回x
mid=int（len（x）/2）
y=msort（x[：mid]）
z=msort（x[mid:]
而（len（y）>0）或（len（z）>0）：
如果len（y）>0且len（z）>0：
如果y[0]>z[0]：
result.append（z[0]）
z、 流行音乐（0）
其他：
结果.追加（y[0]）
y、 流行音乐（0）
elif len（z）>0:
对于z中的i：
结果.追加（i）
z、 流行音乐（0）
其他：
对于y中的i：
结果.追加（i）
y、 流行音乐（0）
返回结果

这样的循环可能会加速：

for i in z:
    result.append(i)
    z.pop(0)

相反，只需这样做：

result.extend(z)

---

请注意，无需清理

z

的内容，因为您无论如何都不会使用它。

您可以在mergesort的顶级调用中初始化整个结果列表：

result = [0]*len(x)   # replace 0 with a suitable default element if necessary. 
                      # or just copy x (result = x[:])

然后，对于递归调用，您可以使用一个helper函数，向该函数传递的不是子列表，而是索引到

x

。底层调用从

x

读取它们的值，并直接写入

result

---

通过这种方式，您可以避免所有应该提高性能的

pop

ing和

append

ing。

第一个改进是简化主循环中的三种情况：与其在某些序列有元素时迭代，不如在两个序列都有元素时迭代。离开循环时，其中一个将为空，我们不知道是哪个，但我们不在乎：我们将它们附加到结果的末尾

def msort2(x):
    if len(x) < 2:
        return x
    result = []          # moved!
    mid = int(len(x) / 2)
    y = msort2(x[:mid])
    z = msort2(x[mid:])
    while (len(y) > 0) and (len(z) > 0):
        if y[0] > z[0]:
            result.append(z[0])
            z.pop(0)
        else:
            result.append(y[0])
            y.pop(0)
    result += y
    result += z
    return result

最后一个改进是使用非递归算法对短序列进行排序。在这种情况下，我使用内置的

sorted

功能，并在输入大小小于20时使用它：

def msort4(x):
    if len(x) < 20:
        return sorted(x)
    result = []
    mid = int(len(x) / 2)
    y = msort4(x[:mid])
    z = msort4(x[mid:])
    i = 0
    j = 0
    while i < len(y) and j < len(z):
        if y[i] > z[j]:
            result.append(z[j])
            j += 1
        else:
            result.append(y[i])
            i += 1
    result += y[i:]
    result += z[j:]
    return result

def msort4（x）：
如果len（x）<20：
返回排序（x）
结果=[]
mid=int（len（x）/2）
y=msort4（x[：中间]）
z=msort4（x[mid:]
i=0
j=0
而iz[j]：
result.append（z[j]）
j+=1
其他：
结果.追加（y[i]）
i+=1
结果+=y[i:]
结果+=z[j:]
返回结果

---

我对100000个整数的随机列表进行排序的测量结果是，原始版本为2.46秒，msort2为2.33秒，msort3为0.60秒，msort4为0.40秒。作为参考，使用

排序的
对所有列表进行排序需要0.03秒。
一个较长的列表，用于计算倒数并遵循
排序的
界面。修改它，使其成为一个适当排序的对象的方法，这很简单

import operator

class MergeSorted:

    def __init__(self):
        self.inversions = 0

    def __call__(self, l, key=None, reverse=False):

        self.inversions = 0

        if key is None:
            self.key = lambda x: x
        else:
            self.key = key

        if reverse:
            self.compare = operator.gt
        else:
            self.compare = operator.lt

        dest = list(l)
        working = [0] * len(l)
        self.inversions = self._merge_sort(dest, working, 0, len(dest))
        return dest

    def _merge_sort(self, dest, working, low, high):
        if low < high - 1:
            mid = (low + high) // 2
            x = self._merge_sort(dest, working, low, mid)
            y = self._merge_sort(dest, working, mid, high)
            z = self._merge(dest, working, low, mid, high)
            return (x + y + z)
        else:
            return 0

    def _merge(self, dest, working, low, mid, high):
        i = 0
        j = 0
        inversions = 0

        while (low + i < mid) and (mid + j < high):
            if self.compare(self.key(dest[low + i]), self.key(dest[mid + j])):
                working[low + i + j] = dest[low + i]
                i += 1
            else:
                working[low + i + j] = dest[mid + j]
                inversions += (mid - (low + i))
                j += 1

        while low + i < mid:
            working[low + i + j] = dest[low + i]
            i += 1

        while mid + j < high:
            working[low + i + j] = dest[mid + j]
            j += 1

        for k in range(low, high):
            dest[k] = working[k]

        return inversions


msorted = MergeSorted()

这是另一个解决方案

class MergeSort(object):
    def _merge(self,left, right):
        nl = len(left)
        nr = len(right)
        result = [0]*(nl+nr)
        i=0
        j=0
        for k in range(len(result)):
            if nl>i and nr>j:
                if left[i] <= right[j]:
                    result[k]=left[i]
                    i+=1
                else:
                    result[k]=right[j]
                    j+=1
            elif nl==i:
                result[k] = right[j]
                j+=1
            else: #nr>j:
                result[k] = left[i]
                i+=1
        return result

    def sort(self,arr):
        n = len(arr)
        if n<=1:
            return arr 
        left = self.sort(arr[:n/2])
        right = self.sort(arr[n/2:] )
        return self._merge(left, right)
def main():
    import random
    a= range(100000)
    random.shuffle(a)
    mr_clss = MergeSort()
    result = mr_clss.sort(a)
    #print result

if __name__ == '__main__':
    main()

def合并（l1、l2、out=[]）：
如果l1=[]：返回+l2
如果l2=[]：返回+l1
如果l1[0]
def merge_sort（x）：
如果len（x）<2：返回x
结果，mid=[]，int（len（x）/2）
y=合并\排序（x[：中间]）
z=合并\排序（x[mid:]）
而（len（y）>0）和（len（z）>0）：
如果y[0]>z[0]：result.append（z.pop（0））
else:result.append（y.pop（0））
结果.扩展（y+z）
返回结果
接受我的实现

def merge_sort(sequence):
    """
    Sequence of numbers is taken as input, and is split into two halves, following which they are recursively sorted.
    """
    if len(sequence) < 2:
        return sequence

    mid = len(sequence) // 2     # note: 7//2 = 3, whereas 7/2 = 3.5

    left_sequence = merge_sort(sequence[:mid])
    right_sequence = merge_sort(sequence[mid:])

    return merge(left_sequence, right_sequence)

def merge(left, right):
    """
    Traverse both sorted sub-arrays (left and right), and populate the result array
    """
    result = []
    i = j = 0
    while i < len(left) and j < len(right):
        if left[i] < right[j]:
            result.append(left[i])
            i += 1
        else:
            result.append(right[j])
            j += 1
    result += left[i:]
    result += right[j:]

    return result

# Print the sorted list.
print(merge_sort([5, 2, 6, 8, 5, 8, 1]))

def merge_排序（顺序）：
"""
数字序列作为输入，被分成两半，然后递归排序。
"""
如果len（序列）<2：
返回序列
mid=len（序列）//2#注：7//2=3，而7/2=3.5
左\序列=合并\排序（序列[：中间]）
右\序列=合并\排序（序列[mid:]）
返回合并（左\u序列、右\u序列）
def合并（左、右）：
"""
遍历已排序的两个子数组（左侧和右侧），并填充结果数组
"""
结果=[]
i=j=0
而i
试试这个递归版本

def mergeList(l1,l2):
    l3=[]
    Tlen=len(l1)+len(l2)
    inf= float("inf")
    for i in range(Tlen):
        print   "l1= ",l1[0]," l2= ",l2[0]
        if l1[0]<=l2[0]:
            l3.append(l1[0])
            del l1[0]
            l1.append(inf)
        else:
            l3.append(l2[0])
            del l2[0]
            l2.append(inf)
    return l3

def main():
    l1=[2,10,7,6,8]
    print mergeSort(breaklist(l1))

def breaklist(rawlist):
    newlist=[]
    for atom in rawlist:
        print atom
        list_atom=[atom]
        newlist.append(list_atom)
    return newlist

def mergeSort(inputList):
    listlen=len(inputList)
    if listlen ==1:
        return inputList
    else:
        newlist=[]
        if listlen % 2==0:
            for i in range(listlen/2):
                newlist.append(mergeList(inputList[2*i],inputList[2*i+1]))
        else:
            for i in range((listlen+1)/2):
                if 2*i+1<listlen:
                    newlist.append(mergeList(inputList[2*i],inputList[2*i+1]))
                else:
                    newlist.append(inputList[2*i])
        return  mergeSort(newlist)

if __name__ == '__main__':
    main()

def合并列表（l1、l2）：
l3=[]
Tlen=len（l1）+len（l2）
inf=浮动（“inf”）
对于范围内的i（Tlen）：
打印“l1=”，l1[0]，“l2=”，l2[0]
如果l1[0]如前所述，
l.pop（0）
是一个O（len（l））操作并且必须避免，则上述msort函数是O（n**2）。如果效率重要的话，索引更好，但也有成本。l中x的
更快，但对于mergesort不容易实现：
iter
可以在这里使用。最后，检查
i
两次，因为在访问元素时再次测试：异常机制（try-except）更好，最后改进了30%

def msort(l):
    if len(l)>1:
        t=len(l)//2
        it1=iter(msort(l[:t]));x1=next(it1)
        it2=iter(msort(l[t:]));x2=next(it2)
        l=[]
        try:
            while True:
                if x1<=x2: l.append(x1);x1=next(it1)
                else     : l.append(x2);x2=next(it2)
        except:
            if x1<=x2: l.append(x2);l.extend(it2)
            else:      l.append(x1);l.extend(it1)
    return l

def msort（l）：
如果len（l）>1：
t=len（l）//2
it1=国际热核实验堆（msort（l[：t]）；x1=下一个（it1）
it2=国际热核实验堆（msort（l[t:]）；x2=下一个（it2）
l=[]
尝试：
尽管如此：
如果x1代码来自麻省理工学院课程。（与通用合作伙伴一起）

import operator


def merge(left, right, compare):
    result = []
    i, j = 0, 0
    while i < len(left) and j < len(right):
        if compare(left[i], right[j]):
            result.append(left[i])
            i += 1
        else:
            result.append(right[j])
            j += 1
    while i < len(left):
        result.append(left[i])
        i += 1
    while j < len(right):
        result.append(right[j])
        j += 1
    return result


def mergeSort(L, compare=operator.lt):
    if len(L) < 2:
        return L[:]
    else:
        middle = int(len(L) / 2)
        left = mergeSort(L[:middle], compare)
        right = mergeSort(L[middle:], compare)
        return merge(left, right, compare)

导入操作符
def合并（左、右、比较）：
结果=[]
i、 j=0，0
而i
晚会有点晚了，但我想我会放弃我的梦想
def merge_sort(x):

    if len(x) < 2:return x

    result,mid = [],int(len(x)/2)

    y = merge_sort(x[:mid])
    z = merge_sort(x[mid:])

    while (len(y) > 0) and (len(z) > 0):
            if y[0] > z[0]:result.append(z.pop(0))   
            else:result.append(y.pop(0))

    result.extend(y+z)
    return result

def merge_sort(sequence):
    """
    Sequence of numbers is taken as input, and is split into two halves, following which they are recursively sorted.
    """
    if len(sequence) < 2:
        return sequence

    mid = len(sequence) // 2     # note: 7//2 = 3, whereas 7/2 = 3.5

    left_sequence = merge_sort(sequence[:mid])
    right_sequence = merge_sort(sequence[mid:])

    return merge(left_sequence, right_sequence)

def merge(left, right):
    """
    Traverse both sorted sub-arrays (left and right), and populate the result array
    """
    result = []
    i = j = 0
    while i < len(left) and j < len(right):
        if left[i] < right[j]:
            result.append(left[i])
            i += 1
        else:
            result.append(right[j])
            j += 1
    result += left[i:]
    result += right[j:]

    return result

# Print the sorted list.
print(merge_sort([5, 2, 6, 8, 5, 8, 1]))

def mergeList(l1,l2):
    l3=[]
    Tlen=len(l1)+len(l2)
    inf= float("inf")
    for i in range(Tlen):
        print   "l1= ",l1[0]," l2= ",l2[0]
        if l1[0]<=l2[0]:
            l3.append(l1[0])
            del l1[0]
            l1.append(inf)
        else:
            l3.append(l2[0])
            del l2[0]
            l2.append(inf)
    return l3

def main():
    l1=[2,10,7,6,8]
    print mergeSort(breaklist(l1))

def breaklist(rawlist):
    newlist=[]
    for atom in rawlist:
        print atom
        list_atom=[atom]
        newlist.append(list_atom)
    return newlist

def mergeSort(inputList):
    listlen=len(inputList)
    if listlen ==1:
        return inputList
    else:
        newlist=[]
        if listlen % 2==0:
            for i in range(listlen/2):
                newlist.append(mergeList(inputList[2*i],inputList[2*i+1]))
        else:
            for i in range((listlen+1)/2):
                if 2*i+1<listlen:
                    newlist.append(mergeList(inputList[2*i],inputList[2*i+1]))
                else:
                    newlist.append(inputList[2*i])
        return  mergeSort(newlist)

if __name__ == '__main__':
    main()

def msort(l):
    if len(l)>1:
        t=len(l)//2
        it1=iter(msort(l[:t]));x1=next(it1)
        it2=iter(msort(l[t:]));x2=next(it2)
        l=[]
        try:
            while True:
                if x1<=x2: l.append(x1);x1=next(it1)
                else     : l.append(x2);x2=next(it2)
        except:
            if x1<=x2: l.append(x2);l.extend(it2)
            else:      l.append(x1);l.extend(it1)
    return l

import operator


def merge(left, right, compare):
    result = []
    i, j = 0, 0
    while i < len(left) and j < len(right):
        if compare(left[i], right[j]):
            result.append(left[i])
            i += 1
        else:
            result.append(right[j])
            j += 1
    while i < len(left):
        result.append(left[i])
        i += 1
    while j < len(right):
        result.append(right[j])
        j += 1
    return result


def mergeSort(L, compare=operator.lt):
    if len(L) < 2:
        return L[:]
    else:
        middle = int(len(L) / 2)
        left = mergeSort(L[:middle], compare)
        right = mergeSort(L[middle:], compare)
        return merge(left, right, compare)

# [Python 3]
def merge_sort(arr):
    if len(arr) < 2:
        return arr
    half = len(arr) // 2
    left = merge_sort(arr[:half])
    right = merge_sort(arr[half:])
    out = []
    li = ri = 0  # index of next element from left, right halves
    while True:
        if li >= len(left):  # left half is exhausted
            out.extend(right[ri:])
            break
        if ri >= len(right): # right half is exhausted
            out.extend(left[li:])
            break
        if left[li] < right[ri]:
            out.append(left[li])
            li += 1
        else:
            out.append(right[ri])
            ri += 1
    return out

merge sort: 1.03605 seconds
Python sort: 0.045 seconds
Ratio merge / Python sort: 23.0229

def merge(arr, p, q, r):
    n1 = q - p + 1
    n2 = r - q
    right, left = [], []
    for i in range(n1):
        left.append(arr[p + i])
    for j in range(n2):
        right.append(arr[q + j + 1])
    left.append(float('inf'))
    right.append(float('inf'))
    i = j = 0
    for k in range(p, r + 1):
        if left[i] <= right[j]:
            arr[k] = left[i]
            i += 1
        else:
            arr[k] = right[j]
            j += 1


def merge_sort(arr, p, r):
    if p < r:
        q = (p + r) // 2
        merge_sort(arr, p, q)
        merge_sort(arr, q + 1, r)
        merge(arr, p, q, r)


if __name__ == '__main__':
    test = [5, 2, 4, 7, 1, 3, 2, 6]
    merge_sort(test, 0, len(test) - 1)
    print test

[1, 2, 2, 3, 4, 5, 6, 7]

def merge(x):
    if len(x) == 1:
        return x
    else:
        mid = int(len(x) / 2)
        l = merge(x[:mid])
        r = merge(x[mid:])
    i = j = 0
    result = []
    while i < len(l) and j < len(r):
        if l[i] < r[j]:
            result.append(l[i])
            i += 1
        else:
            result.append(r[j])
            j += 1
    result += l[i:]
    result += r[j:]
    return result

def mergeSort(alist):
    print("Splitting ",alist)
    if len(alist)>1:
        mid = len(alist)//2
        lefthalf = alist[:mid]
        righthalf = alist[mid:]

        mergeSort(lefthalf)
        mergeSort(righthalf)

        i=0
        j=0
        k=0
        while i < len(lefthalf) and j < len(righthalf):
            if lefthalf[i] < righthalf[j]:
                alist[k]=lefthalf[i]
                i=i+1
            else:
                alist[k]=righthalf[j]
                j=j+1
            k=k+1

        while i < len(lefthalf):
            alist[k]=lefthalf[i]
            i=i+1
            k=k+1

        while j < len(righthalf):
            alist[k]=righthalf[j]
            j=j+1
            k=k+1
    print("Merging ",alist)

alist = [54,26,93,17,77,31,44,55,20]
mergeSort(alist)
print(alist)

    def merge(a,low,mid,high):
        l=a[low:mid+1]
        r=a[mid+1:high+1]
        #print(l,r)
        k=0;i=0;j=0;
        c=[0 for i in range(low,high+1)]
        while(i<len(l) and j<len(r)):
            if(l[i]<=r[j]):

                c[k]=(l[i])
                k+=1

                i+=1
            else:
                c[k]=(r[j])
                j+=1
                k+=1
        while(i<len(l)):
            c[k]=(l[i])
            k+=1
            i+=1

        while(j<len(r)):
            c[k]=(r[j])
            k+=1
            j+=1
        #print(c)  
        a[low:high+1]=c  

    def mergesort(a,low,high):
        if(high>low):
            mid=(low+high)//2


            mergesort(a,low,mid)
            mergesort(a,mid+1,high)
            merge(a,low,mid,high)

    a=[12,8,3,2,9,0]
    mergesort(a,0,len(a)-1)
    print(a)

def merge_sort(arr):
    if len(arr) < 2:
        return arr[:]
    middle_of_arr = len(arr) / 2
    left = arr[0:middle_of_arr]
    right = arr[middle_of_arr:]
    left_side = merge_sort(left)
    right_side = merge_sort(right)
    return merge(left_side, right_side)

def merge(left_side, right_side):
    result = []
    while len(left_side) > 0 or len(right_side) > 0:
        if len(left_side) > 0 and len(right_side) > 0:
            if left_side[0] <= right_side[0]:
                result.append(left_side.pop(0))
            else:
                result.append(right_side.pop(0))
        elif len(left_side) > 0:
            result.append(left_side.pop(0))
        elif len(right_side) > 0:
            result.append(right_side.pop(0))
    return result

arr = [6, 5, 4, 3, 2, 1]
# print merge_sort(arr)
# [1, 2, 3, 4, 5, 6]

def mergesort(lis):
    if len(lis) > 1:
        left, right = map(lambda l: list(reversed(mergesort(l))), (lis[::2], lis[1::2]))
        lis.clear()
        while left and right:
            lis.append(left.pop() if left[-1] < right[-1] else right.pop())
        lis.extend(left[::-1])
        lis.extend(right[::-1])
    return lis

def merge(left,right):
    result=[] 
    i,j=0,0
    while i<len(left) and j<len(right):
        if left[i] < right[j]:
            result.append(left[i])
            i+=1
        else:
            result.append(right[j])
            j+=1
    result.extend(left[i:]) # since we want to add each element and not the object list
    result.extend(right[j:])
    return result

def merge_sort(data):
    if len(data)==1:
        return data
    middle=len(data)//2
    left_data=merge_sort(data[:middle])
    right_data=merge_sort(data[middle:])
    return merge(left_data,right_data)


data=[100,5,200,3,100,4,8,9] 
print(merge_sort(data))

def merge_sort(array):
    n = len(array)
    if n > 1:
        mid = n//2
        left = array[0:mid]
        right = array[mid:n]
        print(mid, left, right, array)
        merge_sort(left)
        merge_sort(right)
        merge(left, right, array)

def merge(left, right, array):
    array_length = len(array)
    right_length = len(right)
    left_length = len(left)
    left_index = right_index = 0
    for array_index in range(0, array_length):
        if right_index == right_length:
            array[array_index:array_length] = left[left_index:left_length]
            break
        elif left_index == left_length:
            array[array_index:array_length] = right[right_index:right_length]
            break
        elif left[left_index] <= right[right_index]:
                array[array_index] = left[left_index]
                left_index += 1
        else:
            array[array_index] = right[right_index]
            right_index += 1

array = [99,2,3,3,12,4,5]
arr_len = len(array)
merge_sort(array)
print(array)
assert len(array) == arr_len

import math

def merge_array(ar1, ar2):
    c, i, j= [], 0, 0

    while i < len(ar1) and j < len(ar2):
        if  ar1[i] < ar2[j]:
            c.append(ar1[i])
            i+=1
        else:
            c.append(ar2[j])
            j+=1     
    return c + ar1[i:] + ar2[j:]

def mergesort(array):
    n = len(array)
    if n == 1:
        return array
    half_n =  math.floor(n/2)  
    ar1, ar2 = mergesort(array[:half_n]), mergesort(array[half_n:])
    return merge_array(ar1, ar2)

#here is my answer using two function one for merge and another for divide and 
 #conquer 
l=int(input('enter range len'))      
c=list(range(l,0,-1))
print('list before sorting is',c)
def mergesort1(c,l,r):    
    i,j,k=0,0,0
    while (i<len(l))&(j<len(r)):
        if l[i]<r[j]:
            c[k]=l[i]
            i +=1            
        else:
            c[k]=r[j]
            j +=1
        k +=1
    while i<len(l):
        c[k]=l[i]
        i+=1
        k+=1
    while j<len(r):
        c[k]=r[j]
        j+=1
        k+=1
    return c   
def mergesort(c):
    if len(c)<2:
        return c
    else:
        l=c[0:(len(c)//2)]
        r=c[len(c)//2:len(c)]
        mergesort(l)
        mergesort(r)
    return    mergesort1(c,l,r)   

[1, 2, 3, 4, 5]

from run_time import run_time
from random_arr import make_arr

def merge(arr1: list, arr2: list):
    temp = []
    x, y = 0, 0
    while len(arr1) and len(arr2):
        if arr1[0] < arr2[0]:
            temp.append(arr1[0])
            x += 1
            arr1 = arr1[x:]
        elif arr1[0] > arr2[0]:
            temp.append(arr2[0])
            y += 1
            arr2 = arr2[y:]
        else:
            temp.append(arr1[0])
            temp.append(arr2[0])
            x += 1
            y += 1
            arr1 = arr1[x:]
            arr2 = arr2[y:]

    if len(arr1) > 0:
        temp += arr1
    if len(arr2) > 0:
        temp += arr2
    return temp

@run_time
def merge_sort(arr: list):
    total = len(arr)
    step = 2
    while True:
        for i in range(0, total, step):
            arr[i:i + step] = merge(arr[i:i + step//2], arr[i + step//2:i + step])
        step *= 2
        if step > 2 * total:
            return arr

arr = make_arr(20000)
merge_sort(arr)
# run_time is 0.10300588607788086

def merge_sort(S):
    temp = []

    if len(S) < 2:
        return S

    split = len(S) // 2
    left = merge_sort(S[:split])
    right = merge_sort(S[split:])

    finale = temp + merge(left, right)

    return finale


def merge(left, right):

    holder = []

    while len(left) > 0 and len(right) > 0:

        if left[0] < right[0]:

            holder.append(left[0])
            del left[0]

        elif left[0] > right[0]:

            holder.append(right[0])
            del right[0]

    if len(left) > 0:

        holder.extend(left)

    elif len(right) > 0:

        holder.extend(right)

    return holder


def splitArray(s):
    return s[:len(s)//2], s[len(s)//2:]

# the idea here is i+j should sum to n as you increment i and j, 
# but once out of bound, the next item of a or b is infinity 
# therefore, the comparison will always switch to the other array
def merge(a, b, n):
    result = [0] * n
    a = a + [float('inf')]
    b = b + [float('inf')]
    result = [0] * n
    i, j = 0, 0
    for k in range(0, n):
        if a[i] < b[j]:
            result[k] = a[i]
            i+=1
        else:
            result[k] = b[j]
            j+=1
    return result

def mergeSort(items):
    n = len(items)
    baseCase = []
    if n == 0:
        return baseCase
    if n == 1:
        baseCase.append(items[0])
        return baseCase
    if n == 2:
        if items[0] < items[1]:
            baseCase.append(items[0])
            baseCase.append(items[1])
            return baseCase
        else:
            baseCase.append(items[1])
            baseCase.append(items[0])
            return baseCase
    left, right = splitArray(items)
    sortedLeft = mergeSort(left)
    sortedRight = mergeSort(right)
    return merge(sortedLeft,sortedRight,n)

# Driver code to test above
arr = [12, 11, 13, 5, 6, 7]
n = len(arr)
print ("Given array is")
for i in range(n):
    print ("%d" %arr[i]),

arr = mergeSort(arr)
print ("\n\nSorted array is")
for i in range(n):
    print ("%d" %arr[i]),