668. Kth Smallest Number in Multiplication Table

Question

Nearly every one have used the Multiplication Table. But could you find out the k-th smallest number quickly from the multiplication table?

Given the height m and the length n of a m * n Multiplication Table, and a positive integer k, you need to return the k-th smallest number in this table.

Example 1:
Input: m = 3, n = 3, k = 5
Output:
Explanation:
The Multiplication Table:
1	2	3
2	4	6
3	6	9

The 5-th smallest number is 3 (1, 2, 2, 3, 3).
Example 2:
Input: m = 2, n = 3, k = 6
Output:
Explanation:
The Multiplication Table:
1	2	3
2	4	6

The 6-th smallest number is 6 (1, 2, 2, 3, 4, 6).

Note:

  1. The m and n will be in the range [1, 30000].
  2. The k will be in the range [1, m * n]

Solution

  • Method 1: binary search 
    class Solution {
    public int findKthNumber(int m, int n, int k) {
       int low = 1, high = m * n;
        while(low <= high){
            int mid = low + (high - low) / 2;
            int count = getLowerNum(m, n, mid);
            if(count < k) low = mid + 1;
            else high = mid - 1;
        }
        return low;
    }
    private int getLowerNum(int m, int n, int target){
        int row = m - 1, col = 0;
        int res = 0;
        while(row >= 0 && col < n){
            if((row + 1) * (col + 1) > target) row--;
            else{
                res += row + 1;
                col++;
            }
        }
        return res;
    }
}