4. Median of Two Sorted Arrays

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

Follow up: 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 == m
  • nums2.length == n
  • 0 <= m <= 1000
  • 0 <= n <= 1000
  • 1 <= m + n <= 2000
  • -106 <= nums1[i], nums2[i] <= 106

Rust Solution

struct Solution;

impl Solution {
    fn find_median_sorted_arrays(nums1: Vec<i32>, nums2: Vec<i32>) -> f64 {
        let n1 = nums1.len();
        let n2 = nums2.len();
        if n1 < n2 {
            return Self::find_median_sorted_arrays(nums2, nums1);
        }
        let mut lo = 0;
        let mut hi = n2 * 2;
        while lo <= hi {
            let mid2 = (lo + hi) / 2;
            let mid1 = n1 + n2 - mid2;
            let l1 = if mid1 == 0 {
                std::i32::MIN
            } else {
                nums1[(mid1 - 1) / 2]
            };
            let l2 = if mid2 == 0 {
                std::i32::MIN
            } else {
                nums2[(mid2 - 1) / 2]
            };
            let r1 = if mid1 == n1 * 2 {
                std::i32::MAX
            } else {
                nums1[mid1 / 2]
            };
            let r2 = if mid2 == n2 * 2 {
                std::i32::MAX
            } else {
                nums2[mid2 / 2]
            };

            if l1 > r2 {
                lo = mid2 + 1;
            } else if l2 > r1 {
                hi = mid2 - 1;
            } else {
                return (l1.max(l2) + r1.min(r2)) as f64 / 2.0;
            }
        }
        panic!()
    }
}

#[test]
fn test() {
    use assert_approx_eq::assert_approx_eq;
    let nums1 = vec![1, 3];
    let nums2 = vec![2];
    let res = 2.0;
    assert_approx_eq!(Solution::find_median_sorted_arrays(nums1, nums2), res);
    let nums1 = vec![1, 2];
    let nums2 = vec![3, 4];
    let res = 2.5;
    assert_approx_eq!(Solution::find_median_sorted_arrays(nums1, nums2), res);
    let nums1 = vec![1];
    let nums2 = vec![2, 3];
    let res = 2.0;
    assert_approx_eq!(Solution::find_median_sorted_arrays(nums1, nums2), res);
}

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