114. Flatten Binary Tree to Linked List

Description

Given a binary tree, flatten it to a linked list in-place.
For example, given the following tree:
1
/
2 5
/ \
3 4 6
The flattened tree should look like:

1

2

3

4

5

6

Hints

If you notice carefully in the flattened tree, each node’s right child points to the next node of a pre-order traversal.

Method

非递归的先序遍历，使用栈临时存储节点，先存右子节点，再存左子节点

4. Median of Two Sorted Arrays

There are two sorted arrays nums1 and nums2 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))$.

You may assume nums1 and nums2 cannot be both empty.

Method

cut A and B into two parts:

there is two conditions we should make sure:

• len(left_part) == len(right_part)
• max(left_part) <= min(right_part)

so, for the aboving condition, the equivalent should be：

$i + j = m - i + n - j \quad and \quad m \leq n \\ B[j -1] \leq A[i] \quad and \quad A[i - 1] \leq B[j]$

the condition $m \leq n$ means $j \geq 0$。

then the median of two arrays is:

median = (max(left_part) + min(right_part)) / 2    // when m + n is even
median = max(A[i-1], B[j-1])                       // when m + n is odd

the mission can be solved by the following steps:

• find min(len(array1), len(array2)) and set it to m
• searching i in [0, m] to find the ‘i’ that:
  • B[j - 1] <= A[i] and A[i -1] <= B[j] where j = (m + n + 1)/2 - i

if the time complexity is $ O(log (min(m+n)))$,we should use binary search to find the ‘i’

Pseudo-code

<1> Set imin = 0, imax = m, then start searching in [imin, imax]
<2> Set i = (imin + imax)/2, j = (m + n + 1)/2 - i
<3> Now we have len(left_part)==len(right_part). And there are only 3 situations
     that we may encounter:
     <a> B[j-1] <= A[i] and A[i-1] <= B[j]
         means we have found the object 'i', stop searching
     <b> B[j-1] > A[i]
         means A[i] is too small, 'i' should be increased, so set:
         imin = i + 1;
         go to <2>
     <c> A[i-1] > B[j]
         means A[i-1] is too big, 'i' should be decreased, so set:
         imax = i - 1;
         go to <2>

when it comes to eadge values i=0,i=m,j=0,j=n, where** A[i-1],B[j-1],A[i],B[j]** may not exist.