[算法][LeetCode]Search a 2D Matrix——二维数组的二分查找

题目要求

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.

  分析

  一开始写的时候把他拆分成了两个二分查找，先纵向找，再横向找。纵向的二分查找比较复杂，要确定是在某个坐标上，或者在两个坐标之间。

  后来找到一个更好的方法，就是把二维数组的坐标转化成一位数组，整体进行二分查找，程序更简单，复杂度也更低了。

  Java代码

  public boolean searchMatrix(int[][] matrix, int target) {if (matrix.length == 0 || matrix[0].length == 0) {return false;}int xLength = matrix[0].length;int min = 0;int max = matrix[0].length * matrix.length - 1;int x, y, current;while (min <= max) {current = (min + max) / 2;y = current / xLength;x = current % xLength;if (matrix[y][x] == target) {return  true;} else if (target < matrix[y][x]) {max = current - 1;} else {min = current + 1;}}return false;}