Find Peak Element II

There is an integer matrix which has the following features:

• The numbers in adjacent positions are different.
• The matrix has n rows and m columns.
• For all i < m, A[0][i] < A[1][i] && A[n - 2][i] > A[n - 1][i].
• For all j < n, A[j][0] < A[j][1] && A[j][m - 2] > A[j][m - 1].

We define a position P is a peek if:

A[j][i] > A[j+1][i] && A[j][i] > A[j-1][i] && A[j][i] > A[j][i+1] && A[j][i] > A[j][i-1]

Given a matrix:

[
  [1 ,2 ,3 ,6 ,5],
  [16,41,23,22,6],
  [15,17,24,21,7],
  [14,18,19,20,10],
  [13,14,11,10,9]
]

return index of 41 (which is [1,1]) or index of 24 (which is [2,2])

思路是先上下二分，后左右二分．复杂度为T(n) = O(n)+O(n/2)+T(n/2) ...T(n) = O(n)+O(n/2)+O(n/2)+O(n/4) ... = 3*(O(n/2)+O(n/4)+...)=O(n)

class Solution:
    #@param A: An list of list integer 
    #@return: The index of position is a list of integer, for example [2,2]
    def findPeakII(self, A):
        if not A:
            return [-1,-1]
        l = 1
        r = len(A[0]) - 2
        up = 1
        down = len(A) - 2
        import sys
        while l + 1 < r and up + 1 < down:
            midRow = (up + down)/2
            rowMax = - sys.maxint - 1  #max value in the middle row
            for i in xrange(l, r + 1): #find the max value in the middle row
                if A[midRow][i] > rowMax:
                    index1 = i
                    rowMax = A[midRow][i]
            if A[midRow - 1][index1] < rowMax and A[midRow + 1][index1] < rowMax:
                return [midRow, index1]
            else:
                if A[midRow - 1][index1] > rowMax:
                    down = midRow
                else:
                    up = midRow
            colMax = -sys.maxint - 1

            for j in xrange(up, down + 1):
                if A[j][index1] > colMax:
                    index2 = j
                    colMax = A[j][index1]
            if A[index2][index1 - 1] < colMax and A[index2][index1 + 1] < colMax:
                return [index2, index1]
            else:
                if A[index2][index1 -1 ] > colMax:
                    r = index1
                else:
                    l = index1
       
        if A[up][l] > A[down][l] or A[up][r] > A[down][r]:
            first = up
        else:
            first = down
        if A[first][l] > A[first][r]:
            second = l
        else:
            second = r
        return [first, second]