寻找两个正序数组的中位数

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给定两个大小分别为 m 和 n 的正序(从小到大)数组 nums1 和 nums2。请你找出并返回这两个正序数组的 中位数 。

算法的时间复杂度应该为 O(log (m+n)) 。

 

示例 1:

输入:nums1 = [1,3], nums2 = [2] 输出:2.00000 解释:合并数组 = [1,2,3] ,中位数 2 示例 2:

输入:nums1 = [1,2], nums2 = [3,4] 输出:2.50000 解释:合并数组 = [1,2,3,4] ,中位数 (2 + 3) / 2 = 2.5

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上代码

``func findMedianSortedArrays(_ nums1: [Int], _ nums2: [Int]) -> Double {

    let totalLength = nums1.count+nums2.count

    if totalLength%2==1 {

        return Double(findMedianSortedArrays(nums1, startIndex1: 0, nums2, startIndex2: 0, targetIndex: totalLength/2+1))

    }else{

        return (Double(findMedianSortedArrays(nums1, startIndex1: 0, nums2, startIndex2: 0, targetIndex: totalLength/2+1))+Double(findMedianSortedArrays(nums1, startIndex1: 0, nums2, startIndex2: 0, targetIndex: totalLength/2)))/2

    }

}

\

func findMedianSortedArrays(_ nums1: [Int],startIndex1:Int, _ nums2: [Int],startIndex2:Int,targetIndex:Int)->Int {

    let length1 = nums1.count-startIndex1

    let length2 = nums2.count-startIndex2

    if length1>length2 {

    return    findMedianSortedArrays(nums2, startIndex1: startIndex2, nums1, startIndex2: startIndex1, targetIndex: targetIndex)

    }

    if length1==0 {

        return nums2[startIndex2+targetIndex-1]

    }

    if targetIndex == 1 {

        return min(nums1[startIndex1], nums2[startIndex2])

    }

    let newstart1 = startIndex1+min(length1, targetIndex/2)-1

    let newstart2 = startIndex2+min(length2, targetIndex/2)-1

\

    if nums1[newstart1]<nums2[newstart2] {

      return  findMedianSortedArrays(nums1, startIndex1: newstart1+1, nums2, startIndex2: startIndex2, targetIndex: targetIndex-(newstart1-startIndex1+1))

    }else{

      return  findMedianSortedArrays(nums1, startIndex1: startIndex1, nums2, startIndex2: newstart2+1, targetIndex: targetIndex-(newstart2-startIndex2+1))

    }

}``