Median of Two Sorted Arrays

Problem Statement

Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays.

The overall run time complexity should be O(log (m+n)).

Solution

Python3 Solution:

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# this function will handle cases where array indices are out of range
def get_value_at_index(arr, i):
    if i >= 0:
        if i < len(arr):
            return arr[i]
        else:
            return float("inf")
    else:
        return -float("inf")


class Solution:
    def median_binary_search(self, nums1, nums2):
        t = len(nums1) + len(nums2)
        half = t // 2

        start, end = 0, len(nums1) - 1

        # since there will be a median value we can directly return the value
        # hence keeping this while condition True
        while True:
            i = (start + end) // 2
            j = half - (i + 1) - 1

            if get_value_at_index(nums1, i) > get_value_at_index(nums2, j + 1):
                end = i - 1
            elif get_value_at_index(nums2, j) > get_value_at_index(nums1, i + 1):
                start = i + 1
            else:
                if t % 2:
                    return min(
                        get_value_at_index(nums1, i + 1),
                        get_value_at_index(nums2, j + 1),
                    )
                else:
                    return (
                        max(get_value_at_index(nums1, i), get_value_at_index(nums2, j))
                        + min(
                            get_value_at_index(nums1, i + 1),
                            get_value_at_index(nums2, j + 1),
                        )
                    ) / 2

    def findMedianSortedArrays(self, nums1: List[int], nums2: List[int]) -> float:
        return self.median_binary_search(nums1, nums2)

Test Cases

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[1,3]
[2]
[1, 2, 3]
[3, 5, 6, 10]
[0, 19]
[1, 2]
[1, 2, 3, 4]
[3, 5, 6, 10]
[1, 2, 3, 4]
[3]
[1, 2, 3, 4]
[3, 4]
[1, 2, 10, 11]
[]
[]
[1]
[1, 2]
[]
[1, 2, 3]
[2]
[1, 3, 5, 5]
[4]