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/**

* 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.

*

* Example 1:

* Input:

* matrix = [

* [1, 3, 5, 7],

* [10, 11, 16, 20],

* [23, 30, 34, 50]

* ]

* target = 3

* Output: true

*

* Example 2:

* Input:

* matrix = [

* [1, 3, 5, 7],

* [10, 11, 16, 20],

* [23, 30, 34, 50]

* ]

* target = 13

* Output: false

*/

public class SearchA2DMatrix74 {

public boolean searchMatrix(int[][] matrix, int target) {

if (matrix == null || matrix.length == 0 || matrix[0].length == 0) return false;

int start = 0;

int end = matrix.length - 1;

while (start < end) {

int mid = start + (end - start + 1) / 2;

if (matrix[mid][0] == target) return true;

if (matrix[mid][0] < target) {

start = mid;

} else {

end = mid - 1;;

}

}

int row = start;

start = 0;

end = matrix[0].length - 1;

while (start < end) {

int mid = start + (end - start) / 2;

if (matrix[row][mid] == target) return true;

if (matrix[row][mid] > target) {

end = mid - 1;

} else {

start = mid + 1;

}

}

return matrix[row][start] == target;

}

public boolean searchMatrix2(int[][] matrix, int target) {

if (matrix == null || matrix.length == 0 || matrix[0].length == 0) return false;

int start = 0;

int end = matrix.length - 1;

while (start + 1 < end) {

int mid = start + (end - start) / 2;

if (matrix[mid][0] == target) return true;

if (matrix[mid][0] < target) {

start = mid;

} else {

end = mid - 1;;

}

}

int row = target >= matrix[end][0] ? end : start;

start = 0;

end = matrix[0].length - 1;

while (start < end) {

int mid = start + (end - start) / 2;

if (matrix[row][mid] == target) return true;

if (matrix[row][mid] > target) {

end = mid - 1;

} else {

start = mid + 1;

}

}

return matrix[row][start] == target;

}

public boolean searchMatrix3(int[][] matrix, int target) {

if (matrix == null || matrix.length == 0 || matrix[0].length == 0) return false;

int M = matrix.length;

int N = matrix[0].length;

int start = 0;

int end = M * N - 1;

while (start < end) {

int mid = start + (end - start) / 2;

int midVal = matrix[mid / N][mid % N];

if (midVal == target) return true;

if (midVal < target) {

start = mid + 1;

} else {

end = mid - 1;

}

}

return matrix[start / N][start % N] == target;

}

}