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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 rock-solid understanding.

Algorithm:

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Java Code:

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Python Code:

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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:

• Letter Case Permutation
• Power Set
• All Paths Between Two Nodes
• Word Search
• Sudoku
• N-Queens
• Word Square
• Generate Parentheses

Instructor: