Why subtracr one from median. Python binary search example

Question

Hello folks. I'm solving leetcode question related to binary search everything went smoothly. Until the last line where arr[len(arr)//2-1

I'm trying to access the median of an even array. Why tho subtracted instead of the regular law of median

Median = number at the middle + add one to get th3 number after/2

class Solution(object):
def findMedianSortedArrays(self, nums1, nums2):
"""
:type nums1: List[int]
:type nums2: List[int]
:rtype: float
"""
arr = nums1 + nums2
arr.sort()
if len(arr) % 2 != 0:
return arr[len(arr)//2]
else:
return (arr[len(arr)//2] + arr[len(arr)//2-1])*1.00/2

Here's the link of the question ineetcoze

https://leetcode.com/problems/median-of-two-sorted-arrays/description/

Any tips?

Answer 1

The "regular law of median"
https://en.m.wikipedia.org/wiki/Median

If the number of elements is odd, the median is the element at the center.
_ _ X _ _
Example: len(arr)=5 then median is the 3rd element, which in Python is arr[2]
The integer division // works here because it rounds down.

If the number of elements is even, the median is the average of the two central elements.
_ _ X|X _ _
Example: len(arr)=6 then the elements at the center are the 3rd and 4th element, with index of 2 and 3.
If we do the math, 6//2=3 so this is the higher index, the other element is at the previous index.
So we take the average of arr[len(arr)//2] and arr[len(arr)//2-1]
The same is expressed in the code.