Median of Two Sorted Arrays -- leetcode -- Python

最新推荐文章于 2023-06-12 16:30:30 发布

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本文介绍了一种高效算法，用于找到两个已排序数组的中位数，其运行时间为O(log(m+n))。算法通过递归查找第k小的元素来实现。

Problem：

　　　There are two sorted arrays A and B of size m and n respectively. Find the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)).

MyCode:

class Solution:

	# @return a float
	def findMedianSortedArrays(self, A, B):
		m = len(A); n = len(B)
		if m == 0 or n == 0:
			if n == 0:
				B = A; n = m
			if n % 2 == 1:
				return B[n/2]
			else:
				return (B[n/2] + B[n/2-1])/2.0
		mn = m + n;
		if mn % 2 == 1:
			return float(self.KthNum(A, B, mn / 2 + 1))
		else:
			return (self.KthNum(A, B, mn / 2 + 1) + self.KthNum(A, B, mn / 2)) / 2.0

	def KthNum(self, A, B, k):
		m = len(A); n = len(B)
		l = 0; r = min(m, k) - 1
		B.append(1000000000); B.append(-1000000000)
		while l <= r:
			mid = l + (r - l) / 2
			bk = k - (mid + 1) - 1
			#print l, r, A[l], A[r], m, bk, A[m], B[bk], B[bk+1]
			#print A[mid], mid, bk, n, l, r
			if bk >= n:
				l = mid + 1
			else:
				if A[mid] >= B[bk] and A[mid] <= B[bk+1]:
					B.pop(); B.pop()
					return A[mid]
				if A[mid] > B[bk+1]:
					r = mid - 1
				elif A[mid] < B[bk]:
					l = mid + 1
		B.pop(); B.pop()
		return self.KthNum(B, A, k)

if __name__=='__main__':
	print Solution().findMedianSortedArrays([1,2], [1, 2, 3])

参考: http://blog.youkuaiyun.com/yutianzuijin/article/details/11499917/

Code:

class Solution:

	# @return a float
	def findMedianSortedArrays(self, A, B):
		def findKthNum(a, b, k):
			if len(a) > len(b):
				return findKthNum(b, a, k)
			m = len(a); n = len(b)
			if m == 0:
				return b[k-1]
			if k == 1:
				return min(a[0], b[0])
			pa = min(k/2, m); pb = k - pa
			if a[pa-1] == b[pb-1]:
				return a[pa-1]
			elif a[pa-1] > b[pb-1]:
				return findKthNum(a, b[pb:], k-pb)
			else:
				return findKthNum(a[pa:], b, k-pa)

		mn = len(A) + len(B)
		if mn % 2 == 1:
			return float(findKthNum(A, B, mn / 2 + 1))
		else:
			return (findKthNum(A, B, mn / 2) + findKthNum(A, B, mn / 2 + 1)) / 2.0

if __name__=='__main__':
	print Solution().findMedianSortedArrays([4,5], [1,2,3,6])