2019-11-02 12:07:41 +08:00
|
|
|
|
# 4. 二维数组中的查找
|
|
|
|
|
|
|
2019-11-02 14:18:29 +08:00
|
|
|
|
## 题目链接
|
|
|
|
|
|
|
|
|
|
|
|
[牛客网](https://www.nowcoder.com/practice/abc3fe2ce8e146608e868a70efebf62e?tpId=13&tqId=11154&tPage=1&rp=1&ru=/ta/coding-interviews&qru=/ta/coding-interviews/question-ranking&from=cyc_github)
|
2019-11-02 12:07:41 +08:00
|
|
|
|
|
|
|
|
|
|
## 题目描述
|
|
|
|
|
|
|
|
|
|
|
|
给定一个二维数组，其每一行从左到右递增排序，从上到下也是递增排序。给定一个数，判断这个数是否在该二维数组中。
|
|
|
|
|
|
|
|
|
|
|
|
```html
|
|
|
|
|
|
Consider the following matrix:
|
|
|
|
|
|
[
|
|
|
|
|
|
[1, 4, 7, 11, 15],
|
|
|
|
|
|
[2, 5, 8, 12, 19],
|
|
|
|
|
|
[3, 6, 9, 16, 22],
|
|
|
|
|
|
[10, 13, 14, 17, 24],
|
|
|
|
|
|
[18, 21, 23, 26, 30]
|
|
|
|
|
|
]
|
|
|
|
|
|
|
|
|
|
|
|
Given target = 5, return true.
|
|
|
|
|
|
Given target = 20, return false.
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
## 解题思路
|
|
|
|
|
|
|
|
|
|
|
|
要求时间复杂度 O(M + N)，空间复杂度 O(1)。其中 M 为行数，N 为 列数。
|
|
|
|
|
|
|
|
|
|
|
|
该二维数组中的一个数，小于它的数一定在其左边，大于它的数一定在其下边。因此，从右上角开始查找，就可以根据 target 和当前元素的大小关系来缩小查找区间，当前元素的查找区间为左下角的所有元素。
|
|
|
|
|
|
|
2019-11-02 14:39:13 +08:00
|
|
|
|
<div align="center"> <img src="https://cs-notes-1256109796.cos.ap-guangzhou.myqcloud.com/35a8c711-0dc0-4613-95f3-be96c6c6e104.gif" width="400px"> </div><br>
|
2019-11-02 12:07:41 +08:00
|
|
|
|
|
|
|
|
|
|
```java
|
|
|
|
|
|
public boolean Find(int target, int[][] matrix) {
|
|
|
|
|
|
if (matrix == null || matrix.length == 0 || matrix[0].length == 0)
|
|
|
|
|
|
return false;
|
|
|
|
|
|
int rows = matrix.length, cols = matrix[0].length;
|
|
|
|
|
|
int r = 0, c = cols - 1; // 从右上角开始
|
|
|
|
|
|
while (r <= rows - 1 && c >= 0) {
|
|
|
|
|
|
if (target == matrix[r][c])
|
|
|
|
|
|
return true;
|
|
|
|
|
|
else if (target > matrix[r][c])
|
|
|
|
|
|
r++;
|
|
|
|
|
|
else
|
|
|
|
|
|
c--;
|
|
|
|
|
|
}
|
|
|
|
|
|
return false;
|
|
|
|
|
|
}
|
|
|
|
|
|
```
|
2019-11-02 14:39:13 +08:00
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2019-11-02 17:33:10 +08:00
|
|
|
|
<div align="center"><img width="320px" src="https://cs-notes-1256109796.cos.ap-guangzhou.myqcloud.com/githubio/公众号二维码-2.png"></img></div>
|
