Search a 2D Matrix

Description

Write an efficient algorithm that searches for a value in an mxn 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.

Example

Consider the following matrix:

[
    [1, 3, 5, 7],
    [10, 11, 16, 20],
    [23, 30, 34, 50]
]

Given

target = 3, returntrue.

Challenge

O(log(n) + log(m)) time

Related problems

Search in Rotated Sorted Array

Search a 2D Matrix II

Implementation

Link: http://lintcode.com/en/problem/search-a-2d-matrix/

class Solution {
public:
    /**
     * @param matrix, a list of lists of integers
     * @param target, an integer
     * @return a boolean, indicate whether matrix contains target
     */
    bool searchMatrix(vector<vector<int> > &matrix, int target) {
        // write your code here
        if(matrix.size() == 0 || matrix[0].size() == 0) return false;

        int m = matrix.size();
        int n = matrix[0].size();
        int start = 0;
        int end = m * n - 1;

        while(start + 1 < end){
            int mid = start + (end - start)/2;
            if(matrix[mid / n][mid % n] == target){
                return true;
            }else if(matrix[mid / n][mid % n] > target){
                end = mid;
            }else{
                start = mid;
            }
        }

        if(matrix[start / n][start % n] == target){
            return true;
        }

        if(matrix[end / n][end % n] == target){
            return true;
        }

        return false;
    }
};