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Author: NinePiece2

Solutions/0216-combination-sum-iii/README.md

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+<p>Find all valid combinations of <code>k</code> numbers that sum up to <code>n</code> such that the following conditions are true:</p>
+
+<ul>
+	<li>Only numbers <code>1</code> through <code>9</code> are used.</li>
+	<li>Each number is used <strong>at most once</strong>.</li>
+</ul>
+
+<p>Return <em>a list of all possible valid combinations</em>. The list must not contain the same combination twice, and the combinations may be returned in any order.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> k = 3, n = 7
+<strong>Output:</strong> [[1,2,4]]
+<strong>Explanation:</strong>
+1 + 2 + 4 = 7
+There are no other valid combinations.</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> k = 3, n = 9
+<strong>Output:</strong> [[1,2,6],[1,3,5],[2,3,4]]
+<strong>Explanation:</strong>
+1 + 2 + 6 = 9
+1 + 3 + 5 = 9
+2 + 3 + 4 = 9
+There are no other valid combinations.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<pre>
+<strong>Input:</strong> k = 4, n = 1
+<strong>Output:</strong> []
+<strong>Explanation:</strong> 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>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>2 &lt;= k &lt;= 9</code></li>
+	<li><code>1 &lt;= n &lt;= 60</code></li>
+</ul>

Solutions/0216-combination-sum-iii/solution.py

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+class Solution:
+    def combinationSum3(self, k: int, n: int) -> List[List[int]]:
+        result, temp = [], []
+
+        def dfs(i: int, j: int):
+            if j == 0:
+                if len(temp) == k:
+                    result.append(temp[:])
+                return
+            
+            if i > 9 or i > j or len(temp) > k:
+                return
+            
+            temp.append(i)
+            dfs(i + 1, j - i)
+            temp.pop()
+            dfs(i + 1, j)
+
+        dfs(1, n)
+        return result