240 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.

Solution

class Solution {
public:
    bool helpSearch(vector<vector<int>>& matrix, int is, int ie, int js, int je, int target ) {
        if ( ie < is or je < js ) return false;
        if ( is == ie and js == je ) return ( target == matrix[is][js] );
        int m = matrix.size();
        int n = matrix[0].size();
        int center = matrix[(is+ie)/2][(js+je)/2];
        if ( target == center ) return true;
        if ( target < center ) {
            if ( helpSearch(matrix, is, (is+ie)/2-1, js, je, target) ) return true;
            if ( helpSearch(matrix, (is+ie)/2, ie, js, (js+je)/2-1, target) ) return true;
        }
        else {
            if ( helpSearch(matrix, (is+ie)/2+1, ie, js, je, target) ) return true;
            if ( helpSearch(matrix, is, (is+ie)/2, (js+je)/2+1, je, target) ) return true;
        }
        return false;
    }
    bool searchMatrix(vector<vector<int>>& matrix, int target) {
        int m = matrix.size();
        if ( m == 0 ) return false;
        int n = matrix[0].size();
        if ( n == 0 ) return false;
        return helpSearch(matrix, 0, m-1, 0, n-1, target);
    }
};

Notes