Given a number N, at every step, subtract the largest perfect cube( ≤ N) from N. Repeat this step while N > 0. The task is to count the number of steps that can be performed.
Input: N = 100
First step, 100 – (4 * 4 * 4) = 100 – 64 = 36
Second step, 36 – (3 * 3 * 3) = 36 – 27 = 9
Third step, 9 – (2 * 2 * 2) = 9 – 8 = 1
Fourth step, 1 – (1 * 1 * 1) = 1 – 1 = 0
Input: N = 150
First step, 150 – (5 * 5 * 5) = 150 – 125 = 25
Second step, 25 – (2 * 2 * 2) = 25 – 8 = 17
Third step, 17 – (2 * 2 * 2) = 17 – 8 = 9
Fourth step, 9 – (2 * 2 * 2) = 9 – 8 = 1
Fifth step, 1 – (1 * 1 * 1) = 1 – 1 = 0
- Get the number from which the largest perfect cube has to be reduced.
- Find the cube root of the number and convert the result as an integer. The cube root of the number might contain some fraction part after the decimal, which needs to be avoided.
- Subtract the cube of the integer found in the previous step. This would remove the largest possible perfect cube from the number in the above step.
N = N - ((int) ∛N)3
- Repeat the above two steps with the reduced number, till it is greater than 0.
- Print the number of times a perfect cube has been reduced from N. This is the final result.
Below is the implementation of the above approach:
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- Largest cube that can be inscribed within the sphere
- Largest sphere that can be inscribed inside a cube
- Largest cone that can be inscribed within a cube
- Largest cube that can be inscribed within a right circular cone
- Largest right circular cylinder that can be inscribed within a cone which is in turn inscribed within a cube
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- Largest sphere that can be inscribed within a cube which is in turn inscribed within a right circular cone
- Perfect cube greater than a given number
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