+ problem 410

fruit-in · fruit-in · commit 73b52198f008 · 2023-08-06T08:43:01.000+08:00
diff --git a/Problemset/0410-Split Array Largest Sum/README.md b/Problemset/0410-Split Array Largest Sum/README.md
@@ -0,0 +1,53 @@
+# 410. Split Array Largest Sum
+Given an integer array `nums` and an integer `k`, split `nums` into `k` non-empty subarrays such that the largest sum of any subarray is **minimized**.
+
+Return *the minimized largest sum of the split*.
+
+A **subarray** is a contiguous part of the array.
+
+#### Example 1:
+<pre>
+<strong>Input:</strong> nums = [7,2,5,10,8], k = 2
+<strong>Output:</strong> 18
+<strong>Explanation:</strong> There are four ways to split nums into two subarrays.
+The best way is to split it into [7,2,5] and [10,8], where the largest sum among the two subarrays is only 18.
+</pre>
+
+#### Example 2:
+<pre>
+<strong>Input:</strong> nums = [1,2,3,4,5], k = 2
+<strong>Output:</strong> 9
+<strong>Explanation:</strong> There are four ways to split nums into two subarrays.
+The best way is to split it into [1,2,3] and [4,5], where the largest sum among the two subarrays is only 9.
+</pre>
+
+#### Constraints:
+* `1 <= nums.length <= 1000`
+* <code>0 <= nums[i] <= 10<sup>6</sup></code>
+* `1 <= k <= min(50, nums.length)`
+
+## Solutions (Rust)
+
+### 1. Solution
+```Rust
+impl Solution {
+    pub fn split_array(nums: Vec<i32>, k: i32) -> i32 {
+        let mut dp = vec![vec![0; k as usize + 1]; nums.len() + 1];
+
+        for i in 1..=nums.len() {
+            dp[i][1] = dp[i - 1][1] + nums[i - 1];
+        }
+
+        for i in 2..=nums.len() {
+            for j in 2..=i.min(k as usize) {
+                dp[i][j] = i32::MAX;
+                for x in j - 1..i {
+                    dp[i][j] = dp[i][j].min(dp[x][j - 1].max(dp[i][1] - dp[x][1]));
+                }
+            }
+        }
+
+        dp[nums.len()][k as usize]
+    }
+}
+```
diff --git a/Problemset/0410-Split Array Largest Sum/README_CN.md b/Problemset/0410-Split Array Largest Sum/README_CN.md
@@ -0,0 +1,57 @@
+# 410. 分割数组的最大值
+给定一个非负整数数组 `nums` 和一个整数 `m` ，你需要将这个数组分成 `m` 个非空的连续子数组。
+
+设计一个算法使得这 `m` 个子数组各自和的最大值最小。
+
+#### 示例 1:
+<pre>
+<strong>输入:</strong> nums = [7,2,5,10,8], k = 2
+<strong>输出:</strong> 18
+<strong>解释:</strong>
+一共有四种方法将 nums 分割为 2 个子数组。
+其中最好的方式是将其分为 [7,2,5] 和 [10,8] 。
+因为此时这两个子数组各自的和的最大值为18，在所有情况中最小。
+</pre>
+
+#### 示例 2:
+<pre>
+<strong>输入:</strong> nums = [1,2,3,4,5], k = 2
+<strong>输出:</strong> 9
+</pre>
+
+#### 示例 2:
+<pre>
+<strong>输入:</strong> nums = [1,4,4], m = 3
+<strong>输出:</strong> 4
+</pre>
+
+#### 提示:
+* `1 <= nums.length <= 1000`
+* <code>0 <= nums[i] <= 10<sup>6</sup></code>
+* `1 <= k <= min(50, nums.length)`
+
+## 题解 (Rust)
+
+### 1. 题解
+```Rust
+impl Solution {
+    pub fn split_array(nums: Vec<i32>, k: i32) -> i32 {
+        let mut dp = vec![vec![0; k as usize + 1]; nums.len() + 1];
+
+        for i in 1..=nums.len() {
+            dp[i][1] = dp[i - 1][1] + nums[i - 1];
+        }
+
+        for i in 2..=nums.len() {
+            for j in 2..=i.min(k as usize) {
+                dp[i][j] = i32::MAX;
+                for x in j - 1..i {
+                    dp[i][j] = dp[i][j].min(dp[x][j - 1].max(dp[i][1] - dp[x][1]));
+                }
+            }
+        }
+
+        dp[nums.len()][k as usize]
+    }
+}
+```
diff --git a/Problemset/0410-Split Array Largest Sum/Solution.rs b/Problemset/0410-Split Array Largest Sum/Solution.rs
@@ -0,0 +1,20 @@
+impl Solution {
+    pub fn split_array(nums: Vec<i32>, k: i32) -> i32 {
+        let mut dp = vec![vec![0; k as usize + 1]; nums.len() + 1];
+
+        for i in 1..=nums.len() {
+            dp[i][1] = dp[i - 1][1] + nums[i - 1];
+        }
+
+        for i in 2..=nums.len() {
+            for j in 2..=i.min(k as usize) {
+                dp[i][j] = i32::MAX;
+                for x in j - 1..i {
+                    dp[i][j] = dp[i][j].min(dp[x][j - 1].max(dp[i][1] - dp[x][1]));
+                }
+            }
+        }
+
+        dp[nums.len()][k as usize]
+    }
+}
diff --git a/README.md b/README.md
@@ -221,6 +221,7 @@
 [404][404l]  |[Sum of Left Leaves][404]                                                             |![py]
 [405][405l]  |[Convert a Number to Hexadecimal][405]                                                |![py]
 [409][409l]  |[Longest Palindrome][409]                                                             |![rs]
+[410][410l]  |[Split Array Largest Sum][410]                                                        |![rs]
 [412][412l]  |[Fizz Buzz][412]                                                                      |![py]
 [413][413l]  |[Arithmetic Slices][413]                                                              |![rb]&nbsp;&nbsp;![rs]
 [414][414l]  |[Third Maximum Number][414]                                                           |![rs]
@@ -1375,6 +1376,7 @@
 [404]:Problemset/0404-Sum%20of%20Left%20Leaves/README.md#404-sum-of-left-leaves
 [405]:Problemset/0405-Convert%20a%20Number%20to%20Hexadecimal/README.md#405-convert-a-number-to-hexadecimal
 [409]:Problemset/0409-Longest%20Palindrome/README.md#409-longest-palindrome
+[410]:Problemset/0410-Split%20Array%20Largest%20Sum/README.md#410-split-array-largest-sum
 [412]:Problemset/0412-Fizz%20Buzz/README.md#412-fizz-buzz
 [413]:Problemset/0413-Arithmetic%20Slices/README.md#413-arithmetic-slices
 [414]:Problemset/0414-Third%20Maximum%20Number/README.md#414-third-maximum-number
@@ -2530,6 +2532,7 @@
 [404l]:https://leetcode.com/problems/sum-of-left-leaves/
 [405l]:https://leetcode.com/problems/convert-a-number-to-hexadecimal/
 [409l]:https://leetcode.com/problems/longest-palindrome/
+[410l]:https://leetcode.com/problems/split-array-largest-sum/
 [412l]:https://leetcode.com/problems/fizz-buzz/
 [413l]:https://leetcode.com/problems/arithmetic-slices/
 [414l]:https://leetcode.com/problems/third-maximum-number/
diff --git a/README_CN.md b/README_CN.md
@@ -221,6 +221,7 @@
 [404][404l]  |[左叶子之和][404]                                         |![py]
 [405][405l]  |[数字转换为十六进制数][405]                               |![py]
 [409][409l]  |[最长回文串][409]                                         |![rs]
+[410][410l]  |[分割数组的最大值][410]                                   |![rs]
 [412][412l]  |[Fizz Buzz][412]                                          |![py]
 [413][413l]  |[等差数列划分][413]                                       |![rb]&nbsp;&nbsp;![rs]
 [414][414l]  |[第三大的数][414]                                         |![rs]
@@ -1375,6 +1376,7 @@
 [404]:Problemset/0404-Sum%20of%20Left%20Leaves/README_CN.md#404-左叶子之和
 [405]:Problemset/0405-Convert%20a%20Number%20to%20Hexadecimal/README_CN.md#405-数字转换为十六进制数
 [409]:Problemset/0409-Longest%20Palindrome/README_CN.md#409-最长回文串
+[410]:Problemset/0410-Split%20Array%20Largest%20Sum/README_CN.md#410-分割数组的最大值
 [412]:Problemset/0412-Fizz%20Buzz/README_CN.md#412-fizz-buzz
 [413]:Problemset/0413-Arithmetic%20Slices/README_CN.md#413-等差数列划分
 [414]:Problemset/0414-Third%20Maximum%20Number/README_CN.md#414-第三大的数
@@ -2530,6 +2532,7 @@
 [404l]:https://leetcode.cn/problems/sum-of-left-leaves/
 [405l]:https://leetcode.cn/problems/convert-a-number-to-hexadecimal/
 [409l]:https://leetcode.cn/problems/longest-palindrome/
+[410l]:https://leetcode.cn/problems/split-array-largest-sum/
 [412l]:https://leetcode.cn/problems/fizz-buzz/
 [413l]:https://leetcode.cn/problems/arithmetic-slices/
 [414l]:https://leetcode.cn/problems/third-maximum-number/
