median of two sorted array - what's wrong with the following code?

Question

I have spent hours debugging the following code, but I still cannot figure out where really breaks it. I feel the case ai+bi<=k is causing the error, but I don't know how to fix it. Can someone help?

Here is my code:

class Solution:
    def findMedianSortedArrays(self, nums1: List[int], nums2: List[int]) -> float:
        m, n = len(nums1), len(nums2)
        mid1 = (m+n+1)//2
        mid2 = (m+n+2)//2
        return (self.getKth(nums1, nums2, mid1)+self.getKth(nums1, nums2, mid2))/2

    # k one-indexed
    def getKth(self, a, b, k):
        if not a:
            return b[k-1]
        if not b:
            return a[k-1]
        ai, bi = (len(a)+1)//2, (len(b)+1)//2
        ae, be = a[ai-1], b[bi-1]

        if ai+bi<=k:
            if ae<be:
                return self.getKth(a[ai:], b, k-ai)
            else:
                return self.getKth(a, b[bi:], k-bi)
        else:
            if ae<be:
                return self.getKth(a, b[:bi], k)
            else:
                return self.getKth(a[:ai], b, k)

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

Similar Solution(k is zero-based): https://leetcode.com/problems/median-of-two-sorted-arrays/discuss/2511/Intuitive-Python-O(log-(m%2Bn))-solution-by-kth-smallest-in-the-two-sorted-arrays-252ms

When arrays are [1,3] and [2], it keeps iterating when a=[3], b=[2] and k=1. — Lusha Li
– Lusha Li, Commented Sep 3, 2019 at 3:46
I would try to perform the algorithm by hand for a small example to understand where it breakls (and compare what you do with what the debugger does). — MrSmith42
– MrSmith42, Commented Sep 3, 2019 at 6:09

Yola · Accepted Answer · 2019-09-03 06:37:02Z

1

The bug is in else clause. It should be like this:

        if ae<be:
            return self.getKth(a, b[:bi-1], k)
        else:
            return self.getKth(a[:ai-1], b, k)

You need to use the same indices you use in the following line:

    ae, be = a[ai-1], b[bi-1]

answered Sep 3, 2019 at 6:37

Yola

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