python - Problems with the pseudocode in CLRS -

i'm using clrs introduction algorithms. trying implement algorithm written in pseudocode in book, in python. however, i'm having problems because book starts indexing 1. how implemented merge sort, doesn't work correctly:

def mergesort(a, start, end):     if(start < end):         middle = math.floor((start + end)/2)         mergesort(a, start, middle)         mergesort(a, middle + 1, end)         merge(a, start, middle, end)  def merge(a, start, middle, end):     n1 = middle - start + 1     n2 = end - middle     l = [0] * n1     r = [0] * n2     in range(0, n1):         l[i] = a[start + - 1]     j in range(0, n2):         r[j] = a[middle + j]     = 0     j = 0     k in range(start, end):         if(i >= n1):             a[k] = r[j]             j += 1         elif(j >= n2):              a[k] = l[i]              += 1         elif(l[i] <= r[j]):             a[k] = l[i]             += 1         else:             a[k] = r[j]             j += 1 

how should convert pseudocode python code without having these (off-by-one?) errors ?

there small error easy on , indices in line of merge function

a[start + - 1] should start + i

because begin looping 0 , value of start can 0 makes start + -1
, iteration

start == == 0

your index becomes -1 last element of list in python

and in final loop of merge function range should

for k in range(start, end+1) because has iterated start until end inclusive

this should run fine

import math def mergesort(a, start, end):     if(start < end):         middle = math.floor((start + end)/2)         mergesort(a, start, middle)         mergesort(a, middle + 1, end)         merge(a, start, middle, end)  def merge(a, start, middle, end):     n1 = middle - start + 1     n2 = end - middle     l = [0] * n1     r = [0] * n2     in range(0, n1):         l[i] = a[start + ]     j in range(0, n2):         r[j] = a[middle + j+1]     = 0     j = 0     k in range(start, end+1):         if(i >= n1):             a[k] = r[j]             j += 1         elif(j >= n2):              a[k] = l[i]              += 1         elif(l[i] <= r[j]):             a[k] = l[i]             += 1         else:             a[k] = r[j]             j += 1   arr=[4,8,5,6,9,8,1] mergesort(arr,0,len(arr)-1) print(arr)