add combination-sum solution

Author: jongwanra

combination-sum/jongwanra.py

@@ -0,0 +1,100 @@
+"""
+[Problem]
+https://leetcode.com/problems/combination-sum/
+
+candidates: unique array of integers
+return a list of all unique combinations of candidates == target
+any order
+
+하나의 숫자는 candidates에서 무제한으로 선택할 수 있다.
+두 조합이 서로 다르다고 간주되는 조건은, 선택된 숫자 중 적어도 하나의 개수가 다를 때이다.
+[Brainstorming]
+DFS를 이용해서 Combination을 만든다.
+종료조건: target == sum || target > sum
+
+[Plan]
+1. candidates를 오름차순 정렬
+2. DFS
+
+[Complexity]
+N -> candidates.length
+M -> approximately target divided by the smallest candidate. -> target / min(candidates)
+Time: O(N^M)
+Space: O(N + M)
+  - 재귀 호출 스택: 깊이는 최대 target / min(candidates)
+  - chosen: 재귀 스택 깊이 만큼 공간 차지
+  - cache: 최악의 경우 answer와 같은 개수의 조합 저장 -> O(number of combinations)
+"""
+
+from typing import List
+
+
+class Solution:
+    def combinationSum1(self, candidates: List[int], target: int) -> List[List[int]]:
+        cache = set()
+        answer = []
+        chosen = []
+
+        def dfs(sum: int) -> None:
+            nonlocal target, candidates, cache, answer, chosen
+            print(chosen)
+            if sum > target:
+                return
+            if sum == target:
+                copied_chosen = chosen[:]
+                copied_chosen.sort()
+
+                cache_key = tuple(copied_chosen)
+                if cache_key in cache:
+                    # print(f"already exists {cache_key} in cache")
+                    return
+                cache.add(cache_key)
+                answer.append(copied_chosen)
+
+            for candidate in candidates:
+                chosen.append(candidate)
+                dfs(sum + candidate)
+                chosen.pop()
+
+        dfs(0)
+        return answer
+
+    """
+    중복 조합 방지 another solution
+    ref: https://www.algodale.com/problems/combination-sum/
+
+    [Complexity]
+    N -> candidates.length
+    M -> target / min(candidates)
+    Time: O(N^M)
+    Space: O(M)
+    """
+
+    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
+        answer = []
+        combi = []
+
+        def dfs(sum: int, start: int) -> None:
+            nonlocal target, answer, combi, candidates
+
+            if sum > target:
+                return
+            if sum == target:
+                answer.append(combi[:])
+                return
+
+            for index in range(start, len(candidates)):
+                candidate = candidates[index]
+                combi.append(candidate)
+                dfs(sum + candidate, index)
+                combi.pop()
+
+        dfs(0, 0)
+        return answer
+
+
+sol = Solution()
+# print(sol.combinationSum([2,3,6,7], 7))
+print(sol.combinationSum([2, 3, 5], 8))
+# print(sol.combinationSum([2], 1))
+