[leetcode]74. Search a 2D Matrix二维矩阵查找

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

 

题意：

给定2D Matrix, 从左至右，从上到下升序排列,  问2D Matrix中是否含有target

 

思路:  Binary Search

题干说明了input有从左至右，从上到下升序排列，强暗示需要用Binary Search

需要注意：

int midValue = matrix[mid / n][mid % n];

mid/n

可以得出mid在第几个n上，即Matrix的row

mid%n

可以得出mid在n的第几位上，即Matrix的col

 

代码

class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if (matrix.length == 0) return false;
        final int rowLen = matrix.length;
        final int colLen = matrix[0].length;

        int l = 0;
        int r = rowLen * colLen -1 ;

        while (l <= r) {
            int mid = l + (r - l) / 2;
            int midValue = matrix[mid / colLen][mid % colLen];

            if (midValue == target){
                return true;
            } else if (midValue < target) {
                l = mid + 1;
            } else{
                r = mid -1;
            }
        }
        return false;
    }
}