feat: add solutions to lc problems: No.1422,1424,1425 (doocs#3427)

* No.1424.Diagonal Traverse II
* No.1425.Constrained Subsequence Sum

Author: yanglbme

solution/1400-1499/1422.Maximum Score After Splitting a String/README.md

@@ -28,13 +28,13 @@ tags:
 <p><strong>示例 1：</strong></p>
 
 <pre><strong>输入：</strong>s = &quot;011101&quot;
-<strong>输出：</strong>5 
+<strong>输出：</strong>5
 <strong>解释：</strong>
 将字符串 s 划分为两个非空子字符串的可行方案有：
-左子字符串 = &quot;0&quot; 且 右子字符串 = &quot;11101&quot;，得分 = 1 + 4 = 5 
-左子字符串 = &quot;01&quot; 且 右子字符串 = &quot;1101&quot;，得分 = 1 + 3 = 4 
-左子字符串 = &quot;011&quot; 且 右子字符串 = &quot;101&quot;，得分 = 1 + 2 = 3 
-左子字符串 = &quot;0111&quot; 且 右子字符串 = &quot;01&quot;，得分 = 1 + 1 = 2 
+左子字符串 = &quot;0&quot; 且 右子字符串 = &quot;11101&quot;，得分 = 1 + 4 = 5
+左子字符串 = &quot;01&quot; 且 右子字符串 = &quot;1101&quot;，得分 = 1 + 3 = 4
+左子字符串 = &quot;011&quot; 且 右子字符串 = &quot;101&quot;，得分 = 1 + 2 = 3
+左子字符串 = &quot;0111&quot; 且 右子字符串 = &quot;01&quot;，得分 = 1 + 1 = 2
 左子字符串 = &quot;01110&quot; 且 右子字符串 = &quot;1&quot;，得分 = 2 + 1 = 3
 </pre>
 
@@ -66,7 +66,13 @@ tags:
 
 <!-- solution:start -->
 
-### 方法一
+### 方法一：计数
+
+我们用两个变量 $l$ 和 $r$ 分别记录左子字符串中 $0$ 的数量和右子字符串中 $1$ 的数量。初始时 $l = 0$，而 $r$ 则等于字符串 $s$ 中 $1$ 的数量。
+
+遍历字符串 $s$ 的前 $n - 1$ 个字符，对于每一个位置 $i$，如果 $s[i] = 0$，则 $l$ 自增 $1$，否则 $r$ 自减 $1$。然后我们更新答案为 $l + r$ 的最大值。
+
+时间复杂度 $O(n)$，其中 $n$ 为字符串 $s$ 的长度。空间复杂度 $O(1)$。
 
 <!-- tabs:start -->
 
@@ -75,28 +81,32 @@ tags:
 ```python
 class Solution:
     def maxScore(self, s: str) -> int:
-        return max(s[:i].count('0') + s[i:].count('1') for i in range(1, len(s)))
+        l, r = 0, s.count("1")
+        ans = 0
+        for x in s[:-1]:
+            l += int(x) ^ 1
+            r -= int(x)
+            ans = max(ans, l + r)
+        return ans
 ```
 
 #### Java
 
 ```java
 class Solution {
     public int maxScore(String s) {
-        int ans = 0;
-        for (int i = 1; i < s.length(); ++i) {
-            int t = 0;
-            for (int j = 0; j < i; ++j) {
-                if (s.charAt(j) == '0') {
-                    ++t;
-                }
-            }
-            for (int j = i; j < s.length(); ++j) {
-                if (s.charAt(j) == '1') {
-                    ++t;
-                }
+        int l = 0, r = 0;
+        int n = s.length();
+        for (int i = 0; i < n; ++i) {
+            if (s.charAt(i) == '1') {
+                ++r;
             }
-            ans = Math.max(ans, t);
+        }
+        int ans = 0;
+        for (int i = 0; i < n - 1; ++i) {
+            l += (s.charAt(i) - '0') ^ 1;
+            r -= s.charAt(i) - '0';
+            ans = Math.max(ans, l + r);
         }
         return ans;
     }
@@ -109,16 +119,12 @@ class Solution {
 class Solution {
 public:
     int maxScore(string s) {
+        int l = 0, r = count(s.begin(), s.end(), '1');
         int ans = 0;
-        for (int i = 1, n = s.size(); i < n; ++i) {
-            int t = 0;
-            for (int j = 0; j < i; ++j) {
-                t += s[j] == '0';
-            }
-            for (int j = i; j < n; ++j) {
-                t += s[j] == '1';
-            }
-            ans = max(ans, t);
+        for (int i = 0; i < s.size() - 1; ++i) {
+            l += (s[i] - '0') ^ 1;
+            r -= s[i] - '0';
+            ans = max(ans, l + r);
         }
         return ans;
     }
@@ -128,51 +134,38 @@ public:
 #### Go
 
 ```go
-func maxScore(s string) int {
-	ans := 0
-	for i, n := 1, len(s); i < n; i++ {
-		t := 0
-		for j := 0; j < i; j++ {
-			if s[j] == '0' {
-				t++
-			}
-		}
-		for j := i; j < n; j++ {
-			if s[j] == '1' {
-				t++
-			}
+func maxScore(s string) (ans int) {
+	l, r := 0, strings.Count(s, "1")
+	for _, c := range s[:len(s)-1] {
+		if c == '0' {
+			l++
+		} else {
+			r--
 		}
-		ans = max(ans, t)
+		ans = max(ans, l+r)
 	}
-	return ans
+	return
 }
 ```
 
 #### TypeScript
 
 ```ts
 function maxScore(s: string): number {
-    const n = s.length;
-    let res = 0;
-    let score = 0;
-    if (s[0] === '0') {
-        score++;
+    let [l, r] = [0, 0];
+    for (const c of s) {
+        r += c === '1' ? 1 : 0;
     }
-    for (let i = 1; i < n; i++) {
-        if (s[i] === '1') {
-            score++;
-        }
-    }
-    res = Math.max(res, score);
-    for (let i = 1; i < n - 1; i++) {
+    let ans = 0;
+    for (let i = 0; i < s.length - 1; ++i) {
         if (s[i] === '0') {
-            score++;
-        } else if (s[i] === '1') {
-            score--;
+            ++l;
+        } else {
+            --r;
         }
-        res = Math.max(res, score);
+        ans = Math.max(ans, l + r);
     }
-    return res;
+    return ans;
 }
 ```
 
@@ -181,121 +174,17 @@ function maxScore(s: string): number {
 ```rust
 impl Solution {
     pub fn max_score(s: String) -> i32 {
-        let n = s.len();
-        let mut res = 0;
-        let mut score = 0;
-        let bs = s.as_bytes();
-        if bs[0] == b'0' {
-            score += 1;
-        }
-        for i in 1..n {
-            if bs[i] == b'1' {
-                score += 1;
-            }
-        }
-        res = res.max(score);
-        for i in 1..n - 1 {
-            if bs[i] == b'0' {
-                score += 1;
-            } else if bs[i] == b'1' {
-                score -= 1;
-            }
-            res = res.max(score);
-        }
-        res
-    }
-}
-```
-
-<!-- tabs:end -->
-
-<!-- solution:end -->
-
-<!-- solution:start -->
-
-### 方法二
-
-<!-- tabs:start -->
-
-#### Python3
-
-```python
-class Solution:
-    def maxScore(self, s: str) -> int:
-        ans = t = (s[0] == '0') + s[1:].count('1')
-        for i in range(1, len(s) - 1):
-            t += 1 if s[i] == '0' else -1
-            ans = max(ans, t)
-        return ans
-```
-
-#### Java
-
-```java
-class Solution {
-    public int maxScore(String s) {
-        int t = 0;
-        if (s.charAt(0) == '0') {
-            t++;
-        }
-        for (int i = 1; i < s.length(); ++i) {
-            if (s.charAt(i) == '1') {
-                t++;
-            }
-        }
-        int ans = t;
-        for (int i = 1; i < s.length() - 1; ++i) {
-            t += s.charAt(i) == '0' ? 1 : -1;
-            ans = Math.max(ans, t);
-        }
-        return ans;
-    }
-}
-```
-
-#### C++
-
-```cpp
-class Solution {
-public:
-    int maxScore(string s) {
-        int t = 0;
-        if (s[0] == '0') ++t;
-        for (int i = 1; i < s.size(); ++i) t += s[i] == '1';
-        int ans = t;
-        for (int i = 1; i < s.size() - 1; ++i) {
-            t += s[i] == '0' ? 1 : -1;
-            ans = max(ans, t);
+        let mut l = 0;
+        let mut r = s.bytes().filter(|&b| b == b'1').count() as i32;
+        let mut ans = 0;
+        let cs = s.as_bytes();
+        for i in 0..s.len() - 1 {
+            l += ((cs[i] - b'0') ^ 1) as i32;
+            r -= (cs[i] - b'0') as i32;
+            ans = ans.max(l + r);
         }
-        return ans;
+        ans
     }
-};
-```
-
-#### Go
-
-```go
-func maxScore(s string) int {
-	t := 0
-	if s[0] == '0' {
-		t++
-	}
-	n := len(s)
-	for i := 1; i < n; i++ {
-		if s[i] == '1' {
-			t++
-		}
-	}
-	ans := t
-	for i := 1; i < n-1; i++ {
-		if s[i] == '0' {
-			t++
-		} else {
-			t--
-		}
-		ans = max(ans, t)
-	}
-	return ans
 }
 ```