[LeetCode] 240. Search a 2D Matrix II 搜索一个二维矩阵之二

 

Write an efficient algorithm that searches for a target value in an m x n integer matrix. The 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.

 

Example 1:

Input: 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]], target = 5
Output: true

Example 2:

Input: 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]], target = 20
Output: false

 

Constraints:

  • m == matrix.length
  • n == matrix[i].length
  • 1 <= n, m <= 300
  • -109 <= matix[i][j] <= 109
  • All the integers in each row are sorted in ascending order.
  • All the integers in each column are sorted in ascending order.
  • -109 <= target <= 109

 

突然发现 LeetCode 很喜欢从 LintCode 上盗题,这是逼我去刷 LintCode 的节奏么?! 这道题让我们在一个二维数组中快速的搜索的一个数字,这个二维数组各行各列都是按递增顺序排列的,是之前那道 Search a 2D Matrix 的延伸,那道题的不同在于每行的第一个数字比上一行的最后一个数字大,是一个整体蛇形递增的数组。所以那道题可以将二维数组展开成一个一位数组用一次二查搜索。而这道题没法那么做,这道题有它自己的特点。如果我们观察题目中给的那个例子,可以发现有两个位置的数字很有特点,左下角和右上角的数。左下角的 18,往上所有的数变小,往右所有数增加,那么就可以和目标数相比较,如果目标数大,就往右搜,如果目标数小,就往上搜。这样就可以判断目标数是否存在。当然也可以把起始数放在右上角,往左和下搜,停止条件设置正确就行。代码如下:

 

class Solution {
public:
    bool searchMatrix(vector<vector<int> > &matrix, int target) {
        if (matrix.empty() || matrix[0].empty()) return false;
        if (target < matrix[0][0] || target > matrix.back().back()) return false;
        int x = matrix.size() - 1, y = 0;
        while (true) {
            if (matrix[x][y] > target) --x;
            else if (matrix[x][y] < target) ++y;
            else return true;
            if (x < 0 || y >= matrix[0].size()) break;
        }
        return false;
    }
};

 

Github 同步地址:

https://github.com/grandyang/leetcode/issues/240

 

类似题目:

Search a 2D Matrix

 

参考资料:

https://leetcode.com/problems/search-a-2d-matrix-ii/

https://leetcode.com/problems/search-a-2d-matrix-ii/discuss/66139/C%2B%2B-search-from-top-right

https://leetcode.com/problems/search-a-2d-matrix-ii/discuss/66140/My-concise-O(m%2Bn)-Java-solution 

 

LeetCode All in One 题目讲解汇总(持续更新中...)

posted @ 2015-07-23 00:58  Grandyang  阅读(19493)  评论(6编辑  收藏  举报
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