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kth smallest number in a multiplication table
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/*
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:
The m and n will be in the range [1, 30000].
The k will be in the range [1, m * n]
*/
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 = enough(mid,m,n,k);
if(count < k){
low = mid+1;
}
else high=mid-1;
}
return low;
}
int enough(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;
}
};