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Count square and non-square numbers before n in C++
We are given a number N. The goal is to find ordered pairs of positive numbers such that the sum of their cubes is N.
Naive Approach
Traverse all numbers from 1 to N and check if it is a perfect square. If floor(sqrt(i))==ceil(sqrt(i)).
Then the number is a perfect square.
Efficient Approach
Perfect squares below N can be found using formula: floor(sqrt(N)).
Let’s understand with examples.
Input
N=20
Output
Count of square numbers: 4 Count of non-square numbers: 16
Explanation
Square numbers are 1, 4, 9 and 16. Rest all are non-squares and less than 20.
Input
N=40
Output
Count of square numbers: 6 Count of non-square numbers: 34
Explanation
Square numbers are 1, 4, 9, 16, 25, 36. Rest all are non-squares and less than 40.
Naive Approach
Approach used in the below program is as follows
We take integer N.
Function squareNums(int n) takes n and returns the count of numbers below n that are perfect squares or non-squares.
Take the initial variable count as 0.
Traverse using for loop from i=1 to i<=n
If floor(sqrt(i))==ceil(sqrt(i)), then the number is a perfect square so increment count.
At the end of all loops count will have a total number that are perfect squares.
N-squares will be numbers that are non squares
Example
#include <bits/stdc++.h>
#include <math.h>
using namespace std;
int squareNums(int n){
int count = 0;
for (int i = 1; i <= n; i++){
if(floor(sqrt(i))==ceil(sqrt(i)))
{ count++; }
}
return count;
}
int main(){
int N = 40;
int squares=squareNums(N);
cout <<endl<<"Count of squares numbers: "<<squares;
cout <<endl<<"Count of non-squares numbers: "<<N-squares;
return 0;
}Output
If we run the above code it will generate the following output −
Count of squares numbers: 6 Count of non-squares numbers: 34
Efficient Approach
Approach used in the below program is as follows
We take integer N.
Take variable squares = floor(sqrt(N)).
Variable squares will have a number of perfect squares below N.
N-squares will be the number of non-squares below N.
Example
#include <bits/stdc++.h>
#include <math.h>
using namespace std;
int main(){
int N = 40;
int squares=floor(sqrt(N));
cout <<endl<<"Count of squares numbers: "<<squares;
cout <<endl<<"Count of non-squares numbers: "<<N-squares;
return 0;
}Output
If we run the above code it will generate the following output −
Count of squares numbers: 6 Count of non-squares numbers: 34
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