[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;
}