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4. Median of Two Sorted Arrays 👍

  • Time: $O(\log\min(m, n))$
  • Space: $O(1)$
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class Solution {
 public:
  double findMedianSortedArrays(vector<int>& nums1, vector<int>& nums2) {
    const int n1 = nums1.size();
    const int n2 = nums2.size();
    if (n1 > n2)
      return findMedianSortedArrays(nums2, nums1);

    int l = 0;
    int r = n1;

    while (l <= r) {
      const int partition1 = (l + r) / 2;
      const int partition2 = (n1 + n2 + 1) / 2 - partition1;
      const int maxLeft1 = partition1 == 0 ? INT_MIN : nums1[partition1 - 1];
      const int maxLeft2 = partition2 == 0 ? INT_MIN : nums2[partition2 - 1];
      const int minRight1 = partition1 == n1 ? INT_MAX : nums1[partition1];
      const int minRight2 = partition2 == n2 ? INT_MAX : nums2[partition2];
      if (maxLeft1 <= minRight2 && maxLeft2 <= minRight1)
        return (n1 + n2) % 2 == 0
                   ? (max(maxLeft1, maxLeft2) + min(minRight1, minRight2)) * 0.5
                   : max(maxLeft1, maxLeft2);
      else if (maxLeft1 > minRight2)
        r = partition1 - 1;
      else
        l = partition1 + 1;
    }

    throw;
  }
};

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class Solution {
  public double findMedianSortedArrays(int[] nums1, int[] nums2) {
    final int n1 = nums1.length;
    final int n2 = nums2.length;
    if (n1 > n2)
      return findMedianSortedArrays(nums2, nums1);

    int l = 0;
    int r = n1;

    while (l <= r) {
      final int partition1 = (l + r) / 2;
      final int partition2 = (n1 + n2 + 1) / 2 - partition1;
      final int maxLeft1 = partition1 == 0 ? Integer.MIN_VALUE : nums1[partition1 - 1];
      final int maxLeft2 = partition2 == 0 ? Integer.MIN_VALUE : nums2[partition2 - 1];
      final int minRight1 = partition1 == n1 ? Integer.MAX_VALUE : nums1[partition1];
      final int minRight2 = partition2 == n2 ? Integer.MAX_VALUE : nums2[partition2];
      if (maxLeft1 <= minRight2 && maxLeft2 <= minRight1)
        return (n1 + n2) % 2 == 0
            ? (Math.max(maxLeft1, maxLeft2) + Math.min(minRight1, minRight2)) * 0.5
            : Math.max(maxLeft1, maxLeft2);
      else if (maxLeft1 > minRight2)
        r = partition1 - 1;
      else
        l = partition1 + 1;
    }

    throw new IllegalArgumentException();
  }
}

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class Solution:
  def findMedianSortedArrays(self, nums1: list[int], nums2: list[int]) -> float:
    n1 = len(nums1)
    n2 = len(nums2)
    if n1 > n2:
      return self.findMedianSortedArrays(nums2, nums1)

    l = 0
    r = n1

    while l <= r:
      partition1 = (l + r) // 2
      partition2 = (n1 + n2 + 1) // 2 - partition1
      maxLeft1 = -2**31 if partition1 == 0 else nums1[partition1 - 1]
      maxLeft2 = -2**31 if partition2 == 0 else nums2[partition2 - 1]
      minRight1 = 2**31 - 1 if partition1 == n1 else nums1[partition1]
      minRight2 = 2**31 - 1 if partition2 == n2 else nums2[partition2]
      if maxLeft1 <= minRight2 and maxLeft2 <= minRight1:
        return (max(maxLeft1, maxLeft2) + min(minRight1, minRight2)) * 0.5 if (n1 + n2) % 2 == 0 else max(maxLeft1, maxLeft2)
      elif maxLeft1 > minRight2:
        r = partition1 - 1
      else:
        l = partition1 + 1