Search in a matrix sorted by rows and columns

Problem:
Search in a row wise and column wise sorted matrix

Solution:
Assuming both sorted in strictly increasing order:

M[row][column] < M[row+1][column] and M[row][column] < M[row][column+1]

Start from the top-right corner of the matrix. If the matrix element is larger than the target, move to the column on the left; if smaller, move to the row below.

Complexity if O(#rows + #columns)

public Position searchSortedMatrix(int x, int[][] M) {
 if (M.length==0 || M[0].length==0) return Position(-1,-1);
 int row = 0, column = M[0].length-1, curVal;
 while (row<M.length && column>=0) {
  curVal = M[row][column];
  if (curVal == x) return Position(row,column);
  if (curVal > x) column--;
  else row++;
 }
 return Position(-1,-1);
}

Note that binary search won't work because the element being searched can be located virtually anywhere, so we can't choose the "right" row or column beforehand.


There's also a divide and conqure solution exist:
1) Find the middle element.
2) If middle element is same as key return.
3) If middle element is lesser than key then
….3a) search submatrix on lower side of middle element
….3b) Search submatrix on right hand side.of middle element
4) If middle element is greater than key then
….4a) search vertical submatrix on left side of middle element
….4b) search submatrix on right hand side.

If given a n x n matrix, the time complexity of the divide and conqure solution is O(n^1.58) (follows from a recurrence: T(n) = 3T(n/2) + O(1), see geeksforgeeks link for details).

Complexity:

time - O(n)
space - O(1)

Links and credits:
http://www.careercup.com/question?id=6448780970819584
http://www.geeksforgeeks.org/divide-conquer-set-6-search-row-wise-column-wise-sorted-2d-array/