Given a positive integer n, the task is to generate all possible unique ways to represent n as sum of positive integers.
2 1 1
1 1 1 1
1 1 1
Approach: We have already discussed the implementation of generating unique partitions in this post. This post contains another and far more intuitive implementation for the above problem using recursion.
The idea is simple and is kind of same approach as used here. We have to move recursively from n to 1 and keep on appending the numbers used to form sum in the array. When the sum becomes equal to n then we print the array and return. The base cases considered in the implementation are: remSum == 0: Required n is formed so print the array.
Then we have started forming required sum using the max value number used in the previous partition. If that number becomes greater than n we ignore it else we append that number to the array and move recursively to next iteration to form sum = (remSum – i) and where max value
number that could be used is i or less than i. This way we can generate the required unique partitions.
Below is the implementation of the above approach:
4 3 1 2 2 2 1 1 1 1 1 1
- Generate all unique partitions of an integer
- Find ways an Integer can be expressed as sum of n-th power of unique natural numbers
- Given a string, print all possible palindromic partitions
- Sum of elements of all partitions of number such that no element is less than K
- Generate all passwords from given character set
- All unique combinations whose sum equals to K
- Generate all the binary strings of N bits
- Recursive program to generate power set
- Generate all binary strings without consecutive 1's
- Generate N integers satisfying the given conditions
- Number of Unique BST with a given key | Dynamic Programming
- Unique paths in a Grid with Obstacles
- Generate array with minimum sum which can be deleted in P steps
- Generate all possible strings such that char at index i is either str1[i] or str2[i]
- Count unique numbers that can be generated from N by adding one and removing trailing zeros
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 Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.