LeetCode[Array]: Search a 2D Matrix

最新推荐文章于 2020-07-03 09:27:28 发布

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最新推荐文章于 2020-07-03 09:27:28 发布

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分类专栏： LeetCode LeetCode 文章标签： LeetCode Array matrix 二分查找算法

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本文介绍了一种高效的矩阵搜索算法，该算法适用于每一行和每一列都按递增顺序排列的矩阵。文章提供了一个C++实现的例子，并详细解释了如何将矩阵转换为一维数组进行二分查找。

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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.

这个题目实际上考查的是二分查找，通过下标操作可以将矩阵变成一个一维升序数组，我的C++实现代码如下：

bool searchMatrix(vector<vector<int> > &matrix, int target) {
    int row = matrix.size(), col = matrix[0].size();

    int low = 0, high = row * col - 1;
    while (low <= high) {
        int middle = (low + high) >> 1;
        int midVal = matrix[middle / col][middle % col];
        if (midVal == target) return true;
        else if (midVal > target) high = middle - 1;
        else low = middle + 1;
    }

    return false;
}