combination-sum-iii

Combination Sum III

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combinationSum3

Find all valid combinations of <code>k</code> numbers that sum up to <code>n</code> such that the following conditions are true:

<ul>
	<li>Only numbers <code>1</code> through <code>9</code> are used.</li>
	<li>Each number is used at most once.</li>
</ul>

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.

&nbsp;
Example 1:

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

Example 2:

<pre>
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.
</pre>

Example 3:

<pre>
Input: k = 4, n = 1
Output: []
Explanation: There are no valid combinations.
Using 4 different numbers in the range [1,9], the smallest sum we can get is 1+2+3+4 = 10 and since 10 &gt; 1, there are no valid combination.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= k &lt;= 9</code></li>
	<li><code>1 &lt;= n &lt;= 60</code></li>
</ul>

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