668. Kth Smallest Number in Multiplication Table

• Difficulty: Hard

• Topics: Binary Search

• Similar Questions:

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  • Find K-th Smallest Pair Distance

  • K-th Smallest Prime Fraction

Problem:

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:

Solutions:

class Solution {
public:
    int findKthNumber(int m, int n, int k) {
        int left = 1; 
        int right = m * n;

        while (left < right) {
            int mid = left + (right - left) / 2;

            int count = countSmallerNum(m, n, mid);
            if (count >= k) {
                right =  mid;
            } else {
                left = mid + 1;
            }
        }

        return left;
    }

private:
    int countSmallerNum(int m, int n, int num) {
        int row = m - 1;
        int col = 0;

        int count = 0;
        while (row >= 0 && col < n) {
            int product = (row + 1) * (col + 1);
            if (product <= num) {
                count += row + 1;
                ++col;
            } else if (product > num) {
                --row;
            } 
        }

        return count;
    }

};