【LeetCode】240. Search a 2D Matrix II

Search a 2D Matrix II

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.

 

递归，每层排除中心元素左上角或者右下角的1/4

class Solution {
public:
    bool searchMatrix(vector<vector<int>>& matrix, int target) {
        if(matrix.empty() || matrix[0].empty())
            return false;
        int m = matrix.size();
        int n = matrix[0].size();
        return Helper(matrix, 0, m-1, 0, n-1, target);
    }
    bool Helper(vector<vector<int>>& matrix, int rlow, int rhigh, int clow, int chigh, int target)
    {
        if(rlow > rhigh || clow > chigh)
            return false;
        if(rlow == rhigh && clow == chigh)
            return matrix[rlow][clow] == target;
        int rmid = (rlow + rhigh) / 2;
        int cmid = (clow + chigh) / 2;
        int val = matrix[rmid][cmid];
        if(val == target)
            return true;
        else if(val > target)
            return Helper(matrix, rlow, rmid-1, clow, chigh, target)
                || Helper(matrix, rmid, rhigh, clow, cmid-1, target);
        else
            return Helper(matrix, rmid+1, rhigh, clow, chigh, target)
                || Helper(matrix, rlow, rmid, cmid+1, chigh, target);
    }
};