# 28.Search a 2D Matrix

## 1.Description(Easy)

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**

Consider the following matrix:

```
[
    [1, 3, 5, 7],
    [10, 11, 16, 20],
    [23, 30, 34, 50]
]
```

Given`target = 3`, return`true`.

[**Challenge**](http://lintcode.com/en/problem/search-a-2d-matrix/#challenge)

O(log(n) + log(m)) time

## 2.Code

把他们变成一维的来做，注意矩阵的表示方法。

```
public boolean searchMatrix(int[][] matrix, int target) {
      if(matrix==null || matrix.length==0){
            return false;
        }
        if(matrix[0]==null || matrix[0].length==0){
            return false;
        }
        int row=matrix.length;
        int column=matrix[0].length;
        int start=0;
        int end=row*column-1;
        while(start+1<end){
            int mid=start+(end-start)/2;
            if(matrix[mid/column][mid%column]==target){
                return true;
            }
            else if(matrix[mid/column][mid%column]>target){
                end=mid;
            }
            else{
                start=mid;
            }
        }
        if(matrix[start/column][start%column]==target){
            return true;
        }
        if(matrix[end/column][end%column]==target){
            return true;
        }
        return false;        
    }
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://junnie.gitbook.io/nine-chapter/1.binary-search/28search-a-2d-matrix.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.