LeetCode-in-All
4. Median of Two Sorted Arrays
Hard
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)).
Example 1:
Input: nums1 = [1,3], nums2 = [2]
Output: 2.00000
Explanation: merged array = [1,2,3] and median is 2.
Example 2:
Input: nums1 = [1,2], nums2 = [3,4]
Output: 2.50000
Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5.
Example 3:
Input: nums1 = [0,0], nums2 = [0,0]
Output: 0.00000
Example 4:
Input: nums1 = [], nums2 = [1]
Output: 1.00000
Example 5:
Input: nums1 = [2], nums2 = []
Output: 2.00000
Constraints:
nums1.length == mnums2.length == n0 <= m <= 10000 <= n <= 10001 <= m + n <= 2000-106 <= nums1[i], nums2[i] <= 106
Solution
(define/contract (find-median-sorted-arrays nums1 nums2)
(-> (listof exact-integer?) (listof exact-integer?) flonum?)
(define (find-kth-smallest k nums1 nums2)
(cond
[(empty? nums1) (list-ref nums2 k)]
[(empty? nums2) (list-ref nums1 k)]
[(= k 0) (min (car nums1) (car nums2))]
[else
(let* ([mid1 (min (length nums1) (quotient (+ k 1) 2))]
[mid2 (min (length nums2) (quotient (+ k 1) 2))]
[median1 (list-ref nums1 (sub1 mid1))]
[median2 (list-ref nums2 (sub1 mid2))])
(cond
[(< median1 median2)
(find-kth-smallest (- k mid1) (drop nums1 mid1) nums2)]
[else
(find-kth-smallest (- k mid2) nums1 (drop nums2 mid2))]))]))
(define (find-median)
(let* ([m (length nums1)]
[n (length nums2)]
[total-length (+ m n)]
[half-length (quotient total-length 2)])
(if (even? total-length)
(/ (+ (exact->inexact (find-kth-smallest half-length nums1 nums2))
(exact->inexact (find-kth-smallest (sub1 half-length) nums1 nums2)))
2.0)
(exact->inexact (find-kth-smallest half-length nums1 nums2)))))
(find-median))