feat: add solutions to lcof2 problem: No.101

lcof2 No.101.Partition Equal Subset Sum

lcof2/剑指 Offer II 101. 分割等和子串/README.md

@@ -38,27 +38,164 @@
 
 <p><meta charset="UTF-8" />注意：本题与主站 416&nbsp;题相同：&nbsp;<a href="https://leetcode-cn.com/problems/partition-equal-subset-sum/">https://leetcode-cn.com/problems/partition-equal-subset-sum/</a></p>
 
-
 ## 解法
 
 <!-- 这里可写通用的实现逻辑 -->
 
+题目可以转换为 `0-1` 背包问题，在 m 个数字中选出一些数字（每个数字只能使用一次），这些数字之和恰好等于 `s / 2`（s 表示所有数字之和）。
+
+也可以用 DFS + 记忆化搜索。
+
 <!-- tabs:start -->
 
 ### **Python3**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
 ```python
+class Solution:
+    def canPartition(self, nums: List[int]) -> bool:
+        s = sum(nums)
+        if s % 2 != 0:
+            return False
+
+        m, n = len(nums), (s >> 1) + 1
+        dp = [[False] * n for _ in range(m)]
+        for i in range(m):
+            dp[i][0] = True
+        if nums[0] < n:
+            dp[0][nums[0]] = True
+
+        for i in range(1, m):
+            for j in range(n):
+                dp[i][j] = dp[i - 1][j]
+                if not dp[i][j] and nums[i] <= j:
+                    dp[i][j] = dp[i - 1][j - nums[i]]
+        return dp[-1][-1]
+```
 
+空间优化：
+
+```python
+class Solution:
+    def canPartition(self, nums: List[int]) -> bool:
+        s = sum(nums)
+        if s % 2 != 0:
+            return False
+
+        m, n = len(nums), (s >> 1) + 1
+        dp = [False] * n
+        dp[0] = True
+        if nums[0] < n:
+            dp[nums[0]] = True
+
+        for i in range(1, m):
+            for j in range(n - 1, nums[i] - 1, -1):
+                dp[j] = dp[j] or dp[j - nums[i]]
+        return dp[-1]
+```
+
+DFS + 记忆化搜索：
+
+```python
+class Solution:
+    def canPartition(self, nums: List[int]) -> bool:
+        s = sum(nums)
+        if s % 2 != 0:
+            return False
+        target = s >> 1
+
+        @lru_cache(None)
+        def dfs(i, s):
+            nonlocal target
+            if s > target or i >= len(nums):
+                return False
+            if s == target:
+                return True
+            return dfs(i + 1, s) or dfs(i + 1, s + nums[i])
+
+        return dfs(0, 0)
 ```
 
 ### **Java**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
 ```java
+class Solution {
+    public boolean canPartition(int[] nums) {
+        int s = 0;
+        for (int x : nums) {
+            s += x;
+        }
+        if (s % 2 != 0) {
+            return false;
+        }
+        int m = nums.length, n = (s >> 1) + 1;
+        boolean[] dp = new boolean[n];
+        dp[0] = true;
+        if (nums[0] < n) {
+            dp[nums[0]] = true;
+        }
+        for (int i = 1; i < m; ++i) {
+            for (int j = n - 1; j >= nums[i]; --j) {
+                dp[j] = dp[j] || dp[j - nums[i]];
+            }
+        }
+        return dp[n - 1];
+    }
+}
+```
+
+### **C++**
+
+```cpp
+class Solution {
+public:
+    bool canPartition(vector<int>& nums) {
+        int s = 0;
+        for (int x : nums) s += x;
+        if (s % 2 != 0) return false;
+        int m = nums.size(), n = (s >> 1) + 1;
+        vector<bool> dp(n);
+        dp[0] = true;
+        if (nums[0] < n) dp[nums[0]] = true;
+        for (int i = 1; i < m; ++i)
+        {
+            for (int j = n - 1; j >= nums[i]; --j)
+            {
+                dp[j] = dp[j] || dp[j - nums[i]];
+            }
+        }
+        return dp[n - 1];
+    }
+};
+```
 
+### **Go**
+
+```go
+func canPartition(nums []int) bool {
+	s := 0
+	for _, x := range nums {
+		s += x
+	}
+	if s%2 != 0 {
+		return false
+	}
+	m, n := len(nums), (s>>1)+1
+	dp := make([]bool, n)
+	dp[0] = true
+	if nums[0] < n {
+		dp[nums[0]] = true
+	}
+	for i := 1; i < m; i++ {
+		for j := n - 1; j >= nums[i]; j-- {
+			dp[j] = dp[j] || dp[j-nums[i]]
+		}
+	}
+	return dp[n-1]
+}
 ```
 
 ### **...**

lcof2/剑指 Offer II 101. 分割等和子串/Solution.cpp

@@ -0,0 +1,20 @@
+class Solution {
+public:
+    bool canPartition(vector<int>& nums) {
+        int s = 0;
+        for (int x : nums) s += x;
+        if (s % 2 != 0) return false;
+        int m = nums.size(), n = (s >> 1) + 1;
+        vector<bool> dp(n);
+        dp[0] = true;
+        if (nums[0] < n) dp[nums[0]] = true;
+        for (int i = 1; i < m; ++i)
+        {
+            for (int j = n - 1; j >= nums[i]; --j)
+            {
+                dp[j] = dp[j] || dp[j - nums[i]];
+            }
+        }
+        return dp[n - 1];
+    }
+};

lcof2/剑指 Offer II 101. 分割等和子串/Solution.go

@@ -0,0 +1,21 @@
+func canPartition(nums []int) bool {
+	s := 0
+	for _, x := range nums {
+		s += x
+	}
+	if s%2 != 0 {
+		return false
+	}
+	m, n := len(nums), (s>>1)+1
+	dp := make([]bool, n)
+	dp[0] = true
+	if nums[0] < n {
+		dp[nums[0]] = true
+	}
+	for i := 1; i < m; i++ {
+		for j := n - 1; j >= nums[i]; j-- {
+			dp[j] = dp[j] || dp[j-nums[i]]
+		}
+	}
+	return dp[n-1]
+}

lcof2/剑指 Offer II 101. 分割等和子串/Solution.java

@@ -0,0 +1,23 @@
+class Solution {
+    public boolean canPartition(int[] nums) {
+        int s = 0;
+        for (int x : nums) {
+            s += x;
+        }
+        if (s % 2 != 0) {
+            return false;
+        }
+        int m = nums.length, n = (s >> 1) + 1;
+        boolean[] dp = new boolean[n];
+        dp[0] = true;
+        if (nums[0] < n) {
+            dp[nums[0]] = true;
+        }
+        for (int i = 1; i < m; ++i) {
+            for (int j = n - 1; j >= nums[i]; --j) {
+                dp[j] = dp[j] || dp[j - nums[i]];
+            }
+        }
+        return dp[n - 1];
+    }
+}

lcof2/剑指 Offer II 101. 分割等和子串/Solution.py

@@ -0,0 +1,16 @@
+class Solution:
+    def canPartition(self, nums: List[int]) -> bool:
+        s = sum(nums)
+        if s % 2 != 0:
+            return False
+
+        m, n = len(nums), (s >> 1) + 1
+        dp = [False] * n
+        dp[0] = True
+        if nums[0] < n:
+            dp[nums[0]] = True
+
+        for i in range(1, m):
+            for j in range(n - 1, nums[i] - 1, -1):
+                dp[j] = dp[j] or dp[j - nums[i]]
+        return dp[-1]

solution/0400-0499/0416.Partition Equal Subset Sum/README.md

@@ -40,6 +40,8 @@
 
 题目可以转换为 `0-1` 背包问题，在 m 个数字中选出一些数字（每个数字只能使用一次），这些数字之和恰好等于 `s / 2`（s 表示所有数字之和）。
 
+也可以用 DFS + 记忆化搜索。
+
 <!-- tabs:start -->
 
 ### **Python3**
@@ -89,6 +91,28 @@ class Solution:
         return dp[-1]
 ```
 
+DFS + 记忆化搜索：
+
+```python
+class Solution:
+    def canPartition(self, nums: List[int]) -> bool:
+        s = sum(nums)
+        if s % 2 != 0:
+            return False
+        target = s >> 1
+
+        @lru_cache(None)
+        def dfs(i, s):
+            nonlocal target
+            if s > target or i >= len(nums):
+                return False
+            if s == target:
+                return True
+            return dfs(i + 1, s) or dfs(i + 1, s + nums[i])
+
+        return dfs(0, 0)
+```
+
 ### **Java**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->

solution/0400-0499/0416.Partition Equal Subset Sum/README_EN.md

@@ -78,6 +78,26 @@ class Solution:
         return dp[-1]
 ```
 
+```python
+class Solution:
+    def canPartition(self, nums: List[int]) -> bool:
+        s = sum(nums)
+        if s % 2 != 0:
+            return False
+        target = s >> 1
+
+        @lru_cache(None)
+        def dfs(i, s):
+            nonlocal target
+            if s > target or i >= len(nums):
+                return False
+            if s == target:
+                return True
+            return dfs(i + 1, s) or dfs(i + 1, s + nums[i])
+
+        return dfs(0, 0)
+```
+
 ### **Java**
 
 ```java