Combination Sum 3
Application of Backtracking

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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 rocksolid 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:
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Don't forget to take indepth 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:
 Letter Case Permutation
 Power Set
 All Paths Between Two Nodes
 Word Search
 Sudoku
 NQueens
 Word Square
 Generate Parentheses
The above content is written by:
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
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