Given the size of array N, the task is to construct an array of size N with positive integer elements such that the cube sum of all elements of this array is a perfect square.
Note: Repititions of integers are allowed.
Input: N = 1
Explanation: Cube of 4 is 64, and 64 is perfect square.
Input: N = 6
Output: 5 10 5 10 5 5
Explanation: Cubic sum of array element is (5)3 + (10)3 + (5)3 + (10)3 + (5)3 + (5)3 = 2500, and 2500 is perfect square.
Approach: The idea is to construct array of size, N which contain first N natural number. If closely observed,
cubic sum of first N natural number: (1)3 + (2)3 + (3)3 + (4)3 + …….(N)3 is always perfect square.
Below is the implementation of the above approach.
1, 2, 3, 4, 5, 6,
Time Complexity: O(N) where N is the size of the Array.
Space Complexity: O(1)
- Construct an Array of size N whose sum of cube of all elements is a perfect square
- Count numbers upto N which are both perfect square and perfect cube
- Find smallest perfect square number A such that N + A is also a perfect square number
- Check if a number is a perfect square having all its digits as a perfect square
- Print N numbers such that their sum is a Perfect Cube
- Previous perfect square and cube number smaller than number N
- Count all triplets whose sum is equal to a perfect cube
- Smallest perfect Cube divisible by all elements of an array
- Smallest N digit number whose sum of square of digits is a Perfect Square
- Print N numbers such that their product is a Perfect Cube
- Count of pairs in an Array whose sum is a Perfect Cube
- Percentage increase in volume of the cube if a side of cube is increased by a given percentage
- Count of subarrays having sum as a perfect cube
- Permutation of numbers such that sum of two consecutive numbers is a perfect square
- Print n numbers such that their sum is a perfect square
- Check if a number is perfect square without finding square root
- Largest number in an array that is not a perfect cube
- Largest perfect cube number in an Array
- Smallest perfect cube in an array
- Sum of all perfect square divisors of numbers from 1 to N
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