240. Search a 2D Matrix II

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#算法分析与设计 #leetcode

本文介绍了一种高效的矩阵搜索算法，该算法能在排序的二维矩阵中查找指定的目标值。矩阵的每一行从左到右递增排序，每一列从上到下递增排序。文章通过示例演示了如何使用逐行扫描结合二分查找的方法来实现这一目标。

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 in ascending from left to right.
Integers in each column are sorted in ascending from top to bottom.

For example,

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.

//算法思想: 逐行扫描matrix,对每一行进行二分查找
class Solution {
public:
    bool binarySearch(vector<int>& vec,int target){
        int front=0;
        int rear=vec.size()-1;
        int mid=0;
        while(front<=rear){
            mid=(front+rear)/2;
            if(target<vec[mid]) rear=mid-1;
            else if(target>vec[mid]) front=mid+1;
            else return true;
        }//while
        return false;
    }
    bool searchMatrix(vector<vector<int>>& matrix, int target) {
        for(vector<vector<int>>::size_type i=0;i!=matrix.size();++i)
            if(binarySearch(matrix[i],target)) return true;
    	return false;
    }
};