From f572d2c9e05391a7523545f651bdd260e6dd02e4 Mon Sep 17 00:00:00 2001
From: Sainnhe Park <i@sainnhe.dev>
Date: Thu, 2 Feb 2023 10:40:18 +0800
Subject: [PATCH] s0039

---
 include/s0039_combination_sum.hpp |  3 ---
 notes/src/combinations.md         |  4 +--
 src/s0039_combination_sum.cpp     | 42 +++++++++++++++++--------------
 3 files changed, 25 insertions(+), 24 deletions(-)

diff --git a/include/s0039_combination_sum.hpp b/include/s0039_combination_sum.hpp
index 45b83f4..f16dd73 100644
--- a/include/s0039_combination_sum.hpp
+++ b/include/s0039_combination_sum.hpp
@@ -2,7 +2,6 @@
 #define S0039_COMBINATION_SUM_HPP
 
 #include <algorithm>
-#include <iterator>
 #include <vector>
 
 using namespace std;
@@ -10,8 +9,6 @@ using namespace std;
 class S0039 {
  public:
   vector<vector<int>> combinationSum(vector<int>& candidates, int target);
-  void dfs(vector<int>& candidates, int target, vector<vector<int>>& ans,
-           vector<int>& combine, int idx);
 };
 
 #endif
diff --git a/notes/src/combinations.md b/notes/src/combinations.md
index db26057..c51c7a3 100644
--- a/notes/src/combinations.md
+++ b/notes/src/combinations.md
@@ -69,6 +69,6 @@ void combineDFS(int n, int k, int begin, vector<int> &path,
 }
 ```
 
+## [39. 组合总和](https://leetcode.cn/problems/combination-sum/)
+
 ## [216. 组合总和 III](https://leetcode.cn/problems/combination-sum-iii/)
-
-
diff --git a/src/s0039_combination_sum.cpp b/src/s0039_combination_sum.cpp
index f05a703..a951bc7 100644
--- a/src/s0039_combination_sum.cpp
+++ b/src/s0039_combination_sum.cpp
@@ -1,27 +1,31 @@
 #include "s0039_combination_sum.hpp"
 
-void S0039::dfs(vector<int>& candidates, int target, vector<vector<int>>& ans,
-                vector<int>& combine, int idx) {
-  if (idx == candidates.size()) {
+void combinationSumDFS(vector<int> &candidates, int target, int startIndex,
+                       vector<int> &path, int sum,
+                       vector<vector<int>> &result) {
+  // 结束条件：总和等于 target 。不存在总和大于 target 的情况，因为已经被剪枝了
+  if (sum == target) {
+    result.push_back(path);
     return;
   }
-  if (target == 0) {
-    ans.emplace_back(combine);
-    return;
-  }
-  // 直接跳过
-  dfs(candidates, target, ans, combine, idx + 1);
-  // 选择当前数
-  if (target - candidates[idx] >= 0) {
-    combine.emplace_back(candidates[idx]);
-    dfs(candidates, target - candidates[idx], ans, combine, idx);
-    combine.pop_back();
+
+  // 开始迭代
+  int size = candidates.size();
+  for (int i = startIndex; i < size; ++i) {
+    // 剪枝，当现在节点的 sum 已经超过了 target，就没必要继续迭代了
+    if (sum + candidates[i] > target) break;
+    path.push_back(candidates[i]);
+    combinationSumDFS(candidates, target, i, path, sum + candidates[i], result);
+    path.pop_back();
   }
 }
 
-vector<vector<int>> S0039::combinationSum(vector<int>& candidates, int target) {
-  vector<vector<int>> ans;
-  vector<int> combine;
-  dfs(candidates, target, ans, combine, 0);
-  return ans;
+vector<vector<int>> S0039::combinationSum(vector<int> &candidates, int target) {
+  // 对 candidates 进行升序排序，这是为了进行剪枝
+  sort(candidates.begin(), candidates.end());
+  // 初始化
+  vector<int> path{};
+  vector<vector<int>> result{};
+  combinationSumDFS(candidates, target, 0, path, 0, result);
+  return result;
 }