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
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 very simple. For every distinct pair (x, y) formed by numbers less than the n1/3, if their sum (x3 + y3) is equal to given number, we store them in a hash table using sum as a key. If pairs with sum equal to given number appears again, we simply print both pairs.
1) Create an empty hash map, say s. 2) cubeRoot = n1/3 3) for (int x = 1; x < cubeRoot; x++) for (int y = x + 1; y <= cubeRoot; y++) int sum = x3 + y3; if (sum != n) continue; if sum exists in s, we found two pairs with sum, print the pairs else insert pair(x, y) in s using sum as key
Below is C++ implementation of above idea –
(2, 24) and (18, 20)
Time Complexity of above solution is O(n2/3) which is much less than O(n).
Can we solve the above problem in O(n1/3) time? We will be discussing that in next post.
This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Find Cube Pairs | Set 2 (A n^(1/3) Solution)
- Find the diagonal of the Cube
- 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
- Given GCD G and LCM L, find number of possible pairs (a, b)
- Find the maximum possible value of a[i] % a[j] over all pairs of i and j
- Find the number of pairs such that their gcd is equals to 1
- Find the sum of all possible pairs in an array of N elements
- Find unique pairs such that each element is less than or equal to N
- Find number of magical pairs of string of length L
- Find the number of distinct pairs of vertices which have a distance of exactly k in a tree
- Ways to form n/2 pairs such that difference of pairs is minimum
- Centered cube number
- N-th number which is both a square and a cube
- Largest right circular cylinder within a cube