Given a number n, find two pairs that can represent the number as sum of two cubes. In other words, find two pairs (a, b) and (c, d) such that given number n can be expressed as
n = a^3 + b^3 = c^3 + d^3
where a, b, c and d are four distinct numbers.
Input: n = 1729 Output: (1, 12) and (9, 10) Explanation: 1729 = 1^3 + 12^3 = 9^3 + 10^3 Input: n = 4104 Output: (2, 16) and (9, 15) Explanation: 4104 = 2^3 + 16^3 = 9^3 + 15^3 Input: n = 13832 Output: (2, 24) and (18, 20) Explanation: 13832 = 2^3 + 24^3 = 18^3 + 20^3
We have discussed a O(n2/3) solution in below set 1.
In this post, a O(n1/3) solution is discussed.
Any number n that satisfies the constraint will have two distinct pairs (a, b) and (c, d) such that a, b, c and d are all less than n1/3. The idea is to create an auxiliary array of size n1/3. Each index i in the array will store value equal to cube of that index i.e. arr[i] = i^3. Now the problem reduces to finding pair of elements in an sorted array whose sum is equal to given number n. The problem is discussed in detail here.
Below is the implementation of above idea :
(10, 27) (19, 24)
Time Complexity of above solution is O(n^(1/3)).
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- Find Cube Pairs | Set 1 (A n^(2/3) Solution)
- Find initial integral solution of Linear Diophantine equation if finite solution exists
- Count of pairs in an Array whose sum is a Perfect Cube
- Find the diagonal of the Cube
- Find Cube root of a number using Log function
- Find the concentration of a solution using given Mass and Volume
- Find the Largest Cube formed by Deleting minimum Digits from a number
- Percentage increase in volume of the cube if a side of cube is increased by a given percentage
- Find the maximum possible value of a[i] % a[j] over all pairs of i and j
- Given GCD G and LCM L, find number of possible pairs (a, b)
- Find all Pairs possible from the given Array
- Find the count of even odd pairs in a given Array
- Find number of pairs (x, y) in an Array such that x^y > y^x | Set 2
- Find minimum GCD of all pairs in an array
- Find the GCD of LCM of all unique pairs in an Array
- Find the sum of all possible pairs in an array of N elements
- Find the number of pairs such that their gcd is equals to 1
- Find unique pairs such that each element is less than or equal to N
- Find the number of ordered pairs such that a * p + b * q = N, where p and q are primes
- Find the minimum value of the given expression over all pairs of the array