From 2137778d44d256795bd0ca6c9b880b2c3be180d1 Mon Sep 17 00:00:00 2001
From: damon <245211612@qq.com>
Date: Thu, 26 May 2022 00:29:02 +0800
Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A0=EF=BC=880015.=E4=B8=89?=
 =?UTF-8?q?=E6=95=B0=E4=B9=8B=E5=92=8C.md=EF=BC=89=EF=BC=9A=E5=A2=9E?=
 =?UTF-8?q?=E5=8A=A0javascript=E7=89=88=E6=9C=ACnsum=E7=9A=84=E9=80=9A?=
 =?UTF-8?q?=E7=94=A8=E8=A7=A3=E6=B3=95?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 problems/0015.三数之和.md | 70 +++++++++++++++++++++++++++++++++++
 1 file changed, 70 insertions(+)

diff --git a/problems/0015.三数之和.md b/problems/0015.三数之和.md
index cc184c87..12d83d8f 100644
--- a/problems/0015.三数之和.md
+++ b/problems/0015.三数之和.md
@@ -345,6 +345,76 @@ var threeSum = function(nums) {
     return res
 };
 ```
+
+解法二：nSum通用解法。递归
+
+```js
+/**
+ *  nsum通用解法，支持2sum，3sum，4sum...等等
+ *  时间复杂度分析：
+ *  1. n = 2时，时间复杂度O(NlogN)，排序所消耗的时间。、
+ *  2. n > 2时，时间复杂度为O(N^n-1)，即N的n-1次方，至少是2次方，此时可省略排序所消耗的时间。举例：3sum为O(n^2)，4sum为O(n^3)
+ * @param {number[]} nums
+ * @return {number[][]}
+ */
+var threeSum = function (nums) {
+    // nsum通用解法核心方法
+    function nSumTarget(nums, n, start, target) {
+        // 前提：nums要先排序好
+        let res = [];
+        if (n === 2) {
+            res = towSumTarget(nums, start, target);
+        } else {
+            for (let i = start; i < nums.length; i++) {
+                // 递归求(n - 1)sum
+                let subRes = nSumTarget(
+                    nums,
+                    n - 1,
+                    i + 1,
+                    target - nums[i]
+                );
+                for (let j = 0; j < subRes.length; j++) {
+                    res.push([nums[i], ...subRes[j]]);
+                }
+                // 跳过相同元素
+                while (nums[i] === nums[i + 1]) i++;
+            }
+        }
+        return res;
+    }
+
+    function towSumTarget(nums, start, target) {
+        // 前提：nums要先排序好
+        let res = [];
+        let len = nums.length;
+        let left = start;
+        let right = len - 1;
+        while (left < right) {
+            let sum = nums[left] + nums[right];
+            if (sum < target) {
+                while (nums[left] === nums[left + 1]) left++;
+                left++;
+            } else if (sum > target) {
+                while (nums[right] === nums[right - 1]) right--;
+                right--;
+            } else {
+                // 相等
+                res.push([nums[left], nums[right]]);
+                // 跳过相同元素
+                while (nums[left] === nums[left + 1]) left++;
+                while (nums[right] === nums[right - 1]) right--;
+                left++;
+                right--;
+            }
+        }
+        return res;
+    }
+    nums.sort((a, b) => a - b);
+    // n = 3，此时求3sum之和
+    return nSumTarget(nums, 3, 0, 0);
+};
+```
+
 TypeScript:
 
 ```typescript