// Binary Search Twice
public class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if (matrix == null || matrix.length == 0) {
            return false;
        }
        if (matrix[0] == null || matrix[0].length == 0) {
            return false;
        }

        int row = matrix.length;
        int column = matrix[0].length;

        // find the row index, the last number <= target
        int start = 0, end = row - 1;
        while (start + 1 < end) {
            int mid = start + (end - start) / 2;
            if (matrix[mid][0] == target) {
                return true;
            } else if (matrix[mid][0] < target) {
                start = mid;
            } else {
                end = mid;
            }
        }
        if (matrix[end][0] <= target) {
            row = end;
        } else if (matrix[start][0] <= target) {
            row = start;
        } else {
            return false;
        }

        // find the column index, the number equal to target
        start = 0;
        end = column - 1;
        while (start + 1 < end) {
            int mid = start + (end - start) / 2;
            if (matrix[row][mid] == target) {
                return true;
            } else if (matrix[row][mid] < target) {
                start = mid;
            } else {
                end = mid;
            }
        }
        if (matrix[row][start] == target) {
            return true;
        } else if (matrix[row][end] == target) {
            return true;
        }
        return false;
    }
}

// Binary Search Once
public class Solution {
    /**
     * @param matrix, a list of lists of integers
     * @param target, an integer
     * @return a boolean, indicate whether matrix contains target
     */
    public boolean searchMatrix(int[][] matrix, int target) {
        // write your code here
        if(matrix == null || matrix.length == 0){
            return false;
        }

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

        int row = matrix.length;
        int column = matrix[0].length;

        int start = 0, end = row * column - 1;
        while(start <= end){
            int mid = start + (end - start) / 2;
            int number = matrix[mid / column][mid % column];
            if(number == target){
                return true;
            }else if(number > target){
                end = mid - 1;
            }else{
                start = mid + 1;
            }
        }

        return false;

    }
}