Search a 2D Matrix

Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:

• Integers in each row are sorted from left to right.
• The first integer of each row is greater than the last integer of the previous row.

For example,

Consider the following matrix:

[
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]

Given target = 3, return true.

Solution:  binary search

Because of the matrix's special features, the matrix can be considered as a sorted array. Your goal is to find one element in this sorted array by using binary search. 

midValue 的位置： 行数是position/columns，而列数是position%columns.

Run time complexity is O(logn), constant space.

public class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if(matrix == null || matrix.length == 0 || matrix[0].length == 0)
            return false;
        
        int i = matrix[0].length;
        int j = matrix.length;
        
        int start = 0, end = i * j -1;
        while(start <= end) {
            int mid = (end + start) / 2;
            int midValue = matrix[mid/i][mid%i];
            if(target == midValue)
                return true;
            if(target < midValue)
                end = mid - 1;
            else
                start = mid + 1;
        }
        return false;
    }
}