searching in 2d array as O(n) with unsorted rows

Question

I need to write a method that takes 2d array \'int [][] m\' and a value \'val\' and check if val is in the array in the complexity of O(n) while n defined as the num

Answer 1

your solution is here. i made a function that do binary search for first column. if the val find in the first column the function return true, else last period of 'l' and 'r' are benefit for us. 'r' and 'l' are always equal of have only one distance(r=l or abs(r-l)=1 ). lower bound of 'r' and 'l' are expected row that the val maybe exist in it. so we should search this row.
O(n) for binary search is Log(n) and for row search is n. so the final O(n) will be n.code is here:

static boolean binarySearch(int arr[][], int l, int r, int x)
{
    if (r>=l)
    {
        int mid = l + (r - l)/2;

        // If the element is present at the 
        // middle itself
        if (arr[mid][0] == x)
           return true;

        // If element is smaller than mid, then 
        // it can only be present in left subarray
        if (arr[mid][0] > x)
           return binarySearch(arr, l, mid-1, x);

        // Else the element can only be present
        // in right subarray
        return binarySearch(arr, mid+1, r, x);
    }

    // We reach here when element is not present
    //  in array

    int row = Math.min(l,r);
    for(int i=0; i