[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;
}