How do I proceed with a question like this? [closed] - c++

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Good Evening everyone. I am not really sure as to whether it is against the rules to ask questions like these on this platform (If it is, kindly tell me). The question is of a "practice competition". I could complete 5 of 10 test cases but I am not sure what is wrong in this. Please suggest any correction/logic/hint... And Time Complexity must be less than O(n^2) (According to the input given)
The approach I tried is:
int main() {
/* Enter your code here. Read input from STDIN. Print output to STDOUT */
signed long int t, n;
scanf("%d", &t);
for (int i = 1; i <= t; i++) {
int count = 0;
scanf("%d", &n);
if (n <= 10)
count = n;
else {
// count = 9;
string s;
s = to_string(n);
int len = s.length();
int x = n / (pow(10, len - 2));
int h = x / 11;
string y = to_string(x);
if (y.length() <= 2)
x = 0;
count = (9 * (len - 1)) + x + h;
}
printf("%d\n", count);
}
return 0;
}
Please suggest whatever you feel is helpful. Thank you so much.

Answer 1

For the problem, given that the work area you are dealing with is relatively small (the number of beautiful numbers less than 10^9 can be reasonably handled with a table of those values), here is a version of a solution that uses a pre-generated table of all of the beautiful numbers in sorted order.
Once the table is set up, it is just a matter of doing a binary search to determine the number of beautiful numbers there are that occur before the input value. The position of the closest beautiful number in the table is the number of beautiful numbers we need.
The binary search is done by utilizing the <algorithm> function std::upper_bound. This function will return an iterator to the item that is greater than the search item. Then to get the position, std::distance is used (we subtract 1, since std::upper_bound will give us the item that is greater than the searched item).
The generation of the table can be done at compile-time (by hand, just initializing an array), or if you're lazy, generated at runtime with a simple loop. Here is one such solution:
#include <algorithm>
#include <vector>
#include <iostream>
std::vector<int> values;
int generate_value(int digit, int numTimes)
{
int total = 0;
for (int i = 0; i < numTimes; ++i)
total = 10 * total + digit;
return total;
}
// I'm lazy, so let the program generate the table for me
void generate_values()
{
size_t curIdx = 0;
values.push_back(0);
for (int i = 1; i <= 9; ++i)
{
for (int j = 1; j <= 9; ++j)
values.push_back(generate_value(j, i));
}
values.push_back(1111111111);
}
// does a binary search and returns the position of the beautiful number
int beautiful(int num)
{
if (num == 0)
return 1;
// get iterator to closest number equaling the beautiful number
auto iter = std::upper_bound(values.begin(), values.end(), num);
// get distance from beginning of vector
return std::distance(values.begin(), iter) - 1;
}
int main()
{
generate_values();
std::cout << beautiful(18) << "\n";;
std::cout << beautiful(1) << "\n";;
std::cout << beautiful(9) << "\n";;
std::cout << beautiful(100500) << "\n";;
std::cout << beautiful(33) << "\n";;
std::cout << beautiful(1000000000) << "\n";;
}
Output:
10
1
9
45
12
81
The size of the table is in total, 83 entries, thus a binary search of this table will take no more than log(83) checks to find the value, which is at most 7 probes in the table.

Answer 2

This is not a complex problem.
Assuming your input is correct so we don’t have to do any checking we observe:
If number n is single digit the number of beautiful numbers is b = n.
If number n is double digit and the first digit is f, then the number of beautiful numbers b = 9 + x, where x is a number of all beautiful double digit numbers smaller than n,
If number n is triple digit and the first digit is f, then the number of beautiful numbers b = 2 x 9 + x, where x is a number of all beautiful triple digit numbers smaller than n.
And so on and on
Thus we can extrapolate: If number n has d digits, than the number of beautiful numbers
s = (d-1) * 9 + x,
where x is a number of beautiful d-digit numbers smaller than or equal to n.
So your problem was reduced to finding x. And this can be reduced even further. Take for instance number n = 44437. The important number here is first digit f. It is trivial to see that all 5 digit beautiful numbers that begin where single digits are less then f are ok. In our example 11111, 22222, 33333 are ok, while 444444 and larger are not.
So all you need to do is to check if beautiful number fffff is smaller than or equal to n. And this can be done with simple traversal of input string.
So your solution would be:
s = (d-1) * 9 + (f-1) + supersecretsauce,
where:
s - solution
n – your input number of age
d – number of digits, assuming your input is always correct is length(n)
f – first digit of your number n
supersecretsauce – 1 if fff…f is smaller or equal than n, 0 if bigger.
And even the traversal of input string can be optimized, but I leave that to you.
Oh yeah... and the time complexity of this solution O(n) = length(n) = log10(n).

Answer 3

A couple of things about the early set up.
1) From the input example you gave, it appears the t and each n need to be input sequentially, but your code prints the number of beautiful numbers before the next input is received. I would suggest reading in t first, then looping through an array of size t to get all the inputs first.
2) The constraints aren't tested. I would test the t and each value in the array mentioned before that the constraints are met, and either have the user try again if they aren't, or simply abort.