Nearly every one have used the . 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 = 5Output: Explanation: The Multiplication Table:1	2	32	4	63	6	9The 5-th smallest number is 3 (1, 2, 2, 3, 3).

 

Example 2:

Input: m = 2, n = 3, k = 6Output: Explanation: The Multiplication Table:1	2	32	4	6The 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]

 

Approach: #1 Bianry Serach

class Solution {public:    int findKthNumber(int m, int n, int k) {        int l = 1, r = m * n;        while (l < r) {            int mid = l + (r - l) / 2;            if (!bignums(mid, m, n, k)) l = mid + 1;            else r = mid;        }        return l;    }private:    bool bignums(int x, int m, int n, int k) {        int count = 0;        for (int i = 1; i <= m; ++i) {            count += min(x/i, n);        }        return count >= k;    }};

Runtime: 24 ms, faster than 12.44% of C++ online submissions for Kth Smallest Number in Multiplication Table. 

 

Analysis:

for (int i = 1; i <= m; ++i) {            count += min(x/i, n);        }

we use this code to find the numbers of elements less than k , in the row of i  the elements are i, 2*i, 3*i, 4*i, 5*i ........ the largest number is k * i <= x, so the numbers of elements which is less than or equal to x is k = x / i;