• Customer Support: admin@thealgorists.com
  • Feedback: We are listening to your every feedback, and taking action to constantly improve your learning experience. If you have any feedback, please use this form: https://thealgorists.com/Feedback.
  • If you are a student, email to admin@thealgorists.com to get special student discount.



Problem Statement:


Find all valid combinations of k numbers that sum up to n such that the following conditions are true:
  • Only numbers 1 through 9 are used.
  • Each number is used at most once.

Return a list of all possible valid combinations. The list must not contain the same combination twice, and the combinations may be returned in any order.

Example 1:
Input: k = 3, n = 7
Output: [[1,2,4]]
Explanation:
1 + 2 + 4 = 7
There are no other valid combinations.

Example 2:
Input: k = 3, n = 9
Output: [[1,2,6],[1,3,5],[2,3,4]]
Explanation:
1 + 2 + 6 = 9
1 + 3 + 5 = 9
2 + 3 + 4 = 9
There are no other valid combinations.

Example 3:
Input: k = 4, n = 1
Output: []
Explanation: There are no valid combinations. [1,2,1] is not valid because 1 is used twice.

Example 4:
Input: k = 3, n = 2
Output: []
Explanation: There are no valid combinations.

Example 5:
Input: k = 9, n = 45
Output: [[1,2,3,4,5,6,7,8,9]]
Explanation:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
​​​​​​​There are no other valid combinations.

Solution:


  • NOTE: I highly recommend going through the Backtracking chapters in the order they are given in the Index page to get the most out of it and be able to build a rock-solid understanding.


If you have already followed Combination Sum and Combination Sum 2, then there is not much to add here.

The solution for this problem is very similar to that of Combination Sum 2. We have just handled the additional constraint k here, as you would see in the code below:



This is a Premium content. Please subscribe to access the code.
After subscribing please come back and refresh this page.




Don't forget to take in-depth look at the other backtracking problems because that is what would make you comfortable with using the backtracking template and master the art of Backtracking:


The above content is written by:

Abhishek Dey

Abhishek Dey

A Visionary Software Engineer With A Mission To Empower Every Person & Every Organization On The Planet To Achieve More

Microsoft | University of Florida

View LinkedIn profile


If you have any feedback, please use this form: https://thealgorists.com/Feedback.




Subscribe to Our Youtube Channel

Follow Us On LinkedIn
wave