LEETCODE: Search a 2D Matrix

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于 2014-12-25 21:38:15 发布

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文章标签： LEETCODE 算法二分法

本文链接：https://blog.youkuaiyun.com/anyicheng2015/article/details/42153805

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本文介绍了一种高效的搜索算法，用于在一特殊性质的二维矩阵中查找特定值。该矩阵的每一行从左到右递增排序，并且每行的第一个元素大于前一行的最后一个元素。文章通过一个具体的例子展示了如何使用二分法进行搜索。

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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.

二分法！

class Solution {
public:
    bool searchMatrix(vector<vector<int> > &matrix, int target) {
        int up = 0;
        int down = matrix.size() - 1;
        while(up <= down) {
            int mid = (up + down) / 2;
            
            if(matrix[mid][0] == target) return true;
            
            if(matrix[mid][0]  > target) {
                down = mid - 1;
            }
            else if(matrix[mid][matrix[0].size() - 1] < target){
                up = mid + 1;
            } 
            else {
                int left = 0;
                int right = matrix[0].size() - 1;
                while(left <= right) {
                    int nmid = (left + right) / 2;
                    if(matrix[mid][nmid] == target) return true;
                    
                    if(matrix[mid][nmid] > target) {
                        right = nmid - 1;
                    }
                    else {
                        left = nmid + 1;
                    }
                }
                return false;
            }
        }
        return false;
    }
};