Question - Java: Pyramid layers

Question

The top of the pyramid contains one brick.
2nd layer has 1 + 2 = 3 bricks.
3rd layer has 1 + 2 + 3 = 6 bricksh.
….
nth layer has 1 + 2 + … + n bricks.
Given the number of bricks you have, calculate the maximum number of layers you can build.
My code:
static void calculateHeight(long n) {
double layers = 0, part1, part2, part3;
double k = 0;

k = (162 * n) / (2 * Math.sqrt(27));
part1 = (Math.sqrt(3) * Math.abs(k) / (3 * k));
part2 = Math.cbrt(Math.abs(k) + Math.sqrt((k * k) - 1));
part3 = Math.cbrt(Math.abs(k) - Math.sqrt((k * k) - 1));
layers = part1 * (part2 + part3) - 1;
System.out.print((long) layers + " ");
}
Problem: When I enter 658, the correct output would be 14 (14.826), but when I enter 286 it shows 10 (10.9999), not 11 (correct output). So if I use Math.round the other answers would be incorrect, so how can I fix that?

Answer 1

For this reason you have to solve a cubic equation.

Answer 2

An idea will be to rewrite the code in Javas high-precision arithmetic with BigDecimal etc.

Answer 3

I tried it with BigDecimal out. For the above mentioned examples it worked.

Answer 4

I have found in web Newton solver for cubic equations and the results are similar to this.

Answer 5

Another example which works without BigDecimal. How about this:

https://code.sololearn.com/cpjl45JXECnh/?ref=app

Answer 6

Lily ,
As you have already written the solutions for the equation are scattered on both sides to the results you expect.

Therefore, I think that the outputs must then be inserted into the equation, and tested what number of bricks is really needed. This can be determined with a simple algorithm similar to the one in my first code.

I don't see any other approach that can get around this.

Could you please give us feedback what is the current status here?

Answer 7

Can you add your logic for calculations..?
Round, ceil, floor none works for that.

Answer 8

I did it but it gave me the problem above

Answer 9

There is a hint for that problem brick=(n*(n+1)*(n+2))/6 with n is layer. From that I have 6*brick=n^3+3n^2+2n and solve n to find layer

Answer 10

https://code.sololearn.com/c8x3fGqnc43A/?ref=app
It is quite new to me. Would you mind demonstrating it on my code, please?

Answer 11

The task description says about sum of n numbers.
The hint is about sum of squires of n numbers. And your calculations for part1, part2, part3 are unknown to me..
So sry, question and answers are unknown to me.. Can you add the calculations details.?.