I can't figure out a sum and numbers solution - c++

Question

I am not that skilled or advanced in C++ and I have trouble solving a problem.
I know how to do it mathematically but I can't write the source code, my algorithm is wrong and messy.
So, the problem is that I have to write a code that reads a number ( n ) from the keyboard and then it has to find a sum that is equal to n squared ( n ^ 2 ) and the number of sum's elements has to be equal to n.
For example 3^2 = 9, 3^2 = 2 + 3 + 4, 3 elements and 3^2 is 9 = 2 + 3 + 4.
I had several attempts but none of them were successful.
I know I'm borderline stupid but at least I tried.
If anyone has the time to look over this problem and is willing to help me I'd be very thankful.
1
#include <iostream>
#include <list>
#include <algorithm>
using namespace std;
int main()
{
//1,3,5,7,9,11,13,15,17,19,21,23,25,27..
int n;
list<int> l;
cin >> n;
if ( n % 2 == 0 ){
cout << "Wrong." << endl;
}
for ( int i = 1; i <= 99;i+=2){
l.push_back(i);
}
//List is full with 1,3,5,7,9,11,13,15,17,19,21,23,25,27..
list<int>::iterator it = find(begin(l),end(l), n);
}
2
#include <iostream>
#include <bits/stdc++.h>
using namespace std;
int main()
{
// 3^2 = 2 + 3 + 4
// 7^2 = 4 + 5 + 6 + 7 + 8 + 9 + 10
int n;
int numbers[100];
for (int i = 0; i <= 100; i++){
numbers[i] = i;
}
cin >> n;
int requiredSum;
requiredSum = n * n;
//while(sum < requiredSum){
// for(int i = 1; i < requiredSum; i++){
// sum += i;
// sumnums.push_back(sum);
// }
//}
int sum = 0;
std::vector<int> sumnums;
while(sum < requiredSum){
for(int i = 1; i < requiredSum; i++){
sum += i;
sumnums.push_back(sum);
}
}
for(int i=0; i<sumnums.size(); ++i)
std::cout << sumnums[i] << ' ';
}
Update:
The numbers of the sum have to be consecutive numbers.Like 3 * 3 has to be equal to 2 + 3 + 4 not 3 + 3 + 3.
So, my first try was that I found a rule for each sum.
Like 3 * 3 = 2 + 3 + 4, 5 * 5 = 3 + 4 + 5 + 6 + 7, 7 * 7 = 4 + 5 + 6 + 7 + 8 + 9 + 10.
Every sum starts with the second element of the previous sum and continues for a number of elements equal to n - 1, like 3 * 3 = 2 + 3 + 4, 5 * 5 , the sum for 5 * 5 starts with 3 + another 4 elements.
And another algorithm would be #molbdnilo 's, like 3 * 3 = 3 + 3 + 3 = 3 + 3 + 3 - 1 + 1, 3 * 3 = ( 3 - 1 ) + 3 + ( 3 + 1 ), but then 5 * 5 = (5 - 2) + ( 5 - 1 ) + 5 + 5 + 1 + 5 + 2

Answer 1

Let's do a few special cases by hand.
(The division here is integer division.)
3^2: 9
2 + 3 + 4 = 9
x-1 x x+1
1 is 3/2
5: 25
3 + 4 + 5 + 6 + 7 = 25
x-2 x-1 x x+1 x+2
2 is 5/2
7: 49
4 + 5 + 6 + 7 + 8 + 9 + 10
x-3 x-2 x-1 x x+1 x+2 x+3
3 is 7/2
It appears that we're looking for the sequence from n - n / 2 to n + n / 2.
(Or, equivalently, n / 2 + 1 to n / 2 + n, but I like symmetry.)
Assuming that this is correct (the proof left as an exercise ;-):
int main()
{
int n = 0;
std::cin >> n;
if (n % 2 == 0)
{
std::cout << "Must be odd\n";
return -1;
}
int delta = n / 2;
for (int i = n - delta; i <= n + delta; i++)
{
std::cout << i << " ";
}
std::cout << std::endl;
}

Answer 2

If there is not constraints on what are the elements forming the sum, the simplest solution is just to sum up the number n, n times, which is always n^2.
int main()
{
int n;
cout<<"Enter n: ";
cin >> n;
for(int i=0; i<n-1; i++){
cout<<n<<"+";
}
cout<<n<<"="<<(n*n);
return 0;
}

Answer 3

Firstly, better use std::vector<> than std::list<>, at least while you have less than ~million elements (it will be faster, because of inside structure of the containers).
Secondly, prefer ++i usage, instead of, i++. Specially in situation like that
...for(int i = 1; i < requiredSum; i++)...
Take a look over here
Finally,
the only error you had that you were simply pushing new numbers inside container (std::list, std::vector, etc.) instead of summing them, so
while(sum < requiredSum){
for(int i = 1; i < requiredSum; i++){
sum += i;
sumnums.push_back(sum);
}
change to
// will count our numbers
amountOfNumbers = 1;
while(sum < requiredSum && amountOfNumber < n)
{
sum += amountOfNumbers;
++amountOfNumbers;
}
// we should make -1 to our amount
--amountOfNumber;
// now let's check our requirements...
if(sum == requiredSum && amountOfNumbers == n)
{
cout << "Got it!";
// you can easily cout them, if you wish, because you have amountOfNumbers.
// implementation of that I am leaving for you, because it is not hard ;)
}
else
{
cout << "Damn it!;
}
I assumed that you need sequential sum of numbers that starts from 1 and equals to n*n and their amount equils to n.
If something wrong or need explanation, please, do not hesitate to contact me.
Upd. amountOfNumber < n intead <=
Also, regarding "not starting from 1". You said that you know how do it on paper, than could you provide your algorithm, then we can better understand your problem.
Upd.#2: Correct and simple answer.
Sorry for such a long answer. I came up with a great and simple solution.
Your condition requires this equation x+(x+1)+(x+2)+... = n*n to be true then we can easily find a solution.
nx+ArPrg = nn, where is
ArPrg - Arithmetic progression (ArPrg = ((n-1)*(1+n-1))/2)
After some manipulation with only unknown variable x, our final equation will be
#include <iostream>
int main()
{
int n;
std::cout << "Enter x: ";
std::cin >> n;
auto squareOfN = n * n;
if (n % 2 == 0)
{
std::cout << "Can't count this.\n";
}
auto x = n - (n - 1) / 2;
std::cout << "Our numbers: ";
for (int i = 0; i < n; ++i)
std::cout << x + i << " ";
return 0;
}
Math is cool :)