feat: update solutions to lc problems: No.2732+ (#3163)

Author: yanglbme

solution/2700-2799/2732.Find a Good Subset of the Matrix/README.md

@@ -94,7 +94,7 @@ tags:
 -   如果 $k = 4$，每一列的和最大为 $2$，此时一定是 $k = 2$ 不满足条件，也就是说，任意选取两行，都存在至少一个列的和为 $2$。我们在 $4$ 行中任意选取 $2$ 行，一共有 $C_4^2 = 6$ 种选法，那么存在至少 $6$ 个 $2$ 的列。由于列数 $n \le 5$，所以一定存在至少一列的和大于 $2$，所以 $k = 4$ 也不满足条件。
 -   对于 $k \gt 4$ 且 $k$ 为偶数的情况，我们可以得出同样的结论，即 $k$ 一定不满足条件。
 
-综上所述，我们只需要考虑 $k = 1$ 和 $k = 2$ 的情况即可。即判断是否有一行全为 $0$，或者是否存在两行按位或之后的结果为 $0$。
+综上所述，我们只需要考虑 $k = 1$ 和 $k = 2$ 的情况即可。即判断是否有一行全为 $0$，或者是否存在两行按位与之后的结果为 $0$。
 
 时间复杂度 $O(m \times n + 4^n)$，空间复杂度 $O(2^n)$。其中 $m$ 和 $n$ 分别是矩阵的行数和列数。
 

solution/2700-2799/2732.Find a Good Subset of the Matrix/README_EN.md

@@ -92,7 +92,7 @@ We can consider the number of rows $k$ chosen for the answer from smallest to la
 -   If $k = 4$, the maximum sum of each column is $2$. This situation definitely occurs when the condition for $k = 2$ is not met, meaning that for any two selected rows, there exists at least one column with a sum of $2$. When choosing any 2 rows out of 4, there are a total of $C_4^2 = 6$ ways to choose, so there are at least $6$ columns with a sum of $2$. Since the number of columns $n \le 5$, there must be at least one column with a sum greater than $2$, so the condition for $k = 4$ is also not met.
 -   For $k > 4$ and $k$ being even, we can draw the same conclusion, that $k$ definitely does not meet the condition.
 
-In summary, we only need to consider the cases of $k = 1$ and $k = 2$. That is, to check whether there is a row entirely composed of $0$s, or whether there exist two rows whose bitwise OR result is $0$.
+In summary, we only need to consider the cases of $k = 1$ and $k = 2$. That is, to check whether there is a row entirely composed of $0$s, or whether there exist two rows whose bitwise AND result is $0$.
 
 The time complexity is $O(m \times n + 4^n)$, and the space complexity is $O(2^n)$. Here, $m$ and $n$ are the number of rows and columns of the matrix, respectively.
 

solution/2700-2799/2734.Lexicographically Smallest String After Substring Operation/README.md

@@ -74,7 +74,11 @@ tags:
 
 <!-- solution:start -->
 
-### 方法一
+### 方法一：贪心
+
+我们可以从左到右遍历字符串 $s$，找到第一个不是 'a' 的字符所在的位置 $i$，然后找到从 $i$ 开始的第一个 'a' 字符所在的位置 $j$，将 $s[i:j]$ 中的字符都减一，最后返回处理后的字符串即可。
+
+时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 为字符串 $s$ 的长度。
 
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solution/2700-2799/2734.Lexicographically Smallest String After Substring Operation/README_EN.md

@@ -90,7 +90,11 @@ tags:
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Greedy Algorithm
+
+We can traverse the string $s$ from left to right, find the position $i$ of the first character that is not 'a', and then find the position $j$ of the first 'a' character starting from $i$. We decrement each character in $s[i:j]$, and finally return the processed string.
+
+The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the string $s$.
 
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solution/2700-2799/2736.Maximum Sum Queries/README.md

@@ -210,53 +210,6 @@ class Solution {
 }
 ```
 
-#### Java
-
-```java
-class Solution {
-    public int[] maximumSumQueries(int[] nums1, int[] nums2, int[][] q) {
-        int n = nums1.length, m = q.length;
-        int[][] a = new int[n][2];
-        for (int i = 0; i < n; i++) {
-            a[i][0] = nums1[i];
-            a[i][1] = nums2[i];
-        }
-        int[][] b = new int[m][3];
-        for (int i = 0; i < m; i++) {
-            b[i][0] = q[i][0];
-            b[i][1] = q[i][1];
-            b[i][2] = i;
-        }
-        Arrays.sort(a, (o1, o2) -> o1[0] - o2[0]);
-        Arrays.sort(b, (o1, o2) -> o1[0] - o2[0]);
-        TreeMap<Integer, Integer> map = new TreeMap<>();
-        int[] res = new int[m];
-        int max = -1;
-        for (int i = m - 1, j = n - 1; i >= 0; i--) {
-            int x = b[i][0], y = b[i][1], idx = b[i][2];
-            while (j >= 0 && a[j][0] >= x) {
-                if (max < a[j][1]) {
-                    max = a[j][1];
-                    Integer key = map.floorKey(a[j][1]);
-                    while (key != null && map.get(key) <= a[j][0] + a[j][1]) {
-                        map.remove(key);
-                        key = map.floorKey(key);
-                    }
-                    map.put(max, a[j][0] + a[j][1]);
-                }
-                j--;
-            }
-            Integer key = map.ceilingKey(y);
-            if (key == null)
-                res[idx] = -1;
-            else
-                res[idx] = map.get(key);
-        }
-        return res;
-    }
-}
-```
-
 #### C++
 
 ```cpp

solution/2700-2799/2736.Maximum Sum Queries/README_EN.md

@@ -214,53 +214,6 @@ class Solution {
 }
 ```
 
-#### Java
-
-```java
-class Solution {
-    public int[] maximumSumQueries(int[] nums1, int[] nums2, int[][] q) {
-        int n = nums1.length, m = q.length;
-        int[][] a = new int[n][2];
-        for (int i = 0; i < n; i++) {
-            a[i][0] = nums1[i];
-            a[i][1] = nums2[i];
-        }
-        int[][] b = new int[m][3];
-        for (int i = 0; i < m; i++) {
-            b[i][0] = q[i][0];
-            b[i][1] = q[i][1];
-            b[i][2] = i;
-        }
-        Arrays.sort(a, (o1, o2) -> o1[0] - o2[0]);
-        Arrays.sort(b, (o1, o2) -> o1[0] - o2[0]);
-        TreeMap<Integer, Integer> map = new TreeMap<>();
-        int[] res = new int[m];
-        int max = -1;
-        for (int i = m - 1, j = n - 1; i >= 0; i--) {
-            int x = b[i][0], y = b[i][1], idx = b[i][2];
-            while (j >= 0 && a[j][0] >= x) {
-                if (max < a[j][1]) {
-                    max = a[j][1];
-                    Integer key = map.floorKey(a[j][1]);
-                    while (key != null && map.get(key) <= a[j][0] + a[j][1]) {
-                        map.remove(key);
-                        key = map.floorKey(key);
-                    }
-                    map.put(max, a[j][0] + a[j][1]);
-                }
-                j--;
-            }
-            Integer key = map.ceilingKey(y);
-            if (key == null)
-                res[idx] = -1;
-            else
-                res[idx] = map.get(key);
-        }
-        return res;
-    }
-}
-```
-
 #### C++
 
 ```cpp

solution/2700-2799/2736.Maximum Sum Queries/Solution2.java

@@ -78,7 +78,7 @@ tags:
 
 对于每个查询 $q = (r, i)$，其窗口左边界为 $l = r - x$，我们需要统计在窗口 $[l, r]$ 内有多少个服务器收到了请求。我们用双指针 $j$ 和 $k$ 分别维护窗口的左右边界，初始时 $j = k = 0$。每一次，如果 $k$ 指向的日志的时间小于等于 $r$，我们就将其加入到窗口中，然后将 $k$ 向右移动一位。如果 $j$ 指向的日志的时间小于 $l$，我们就将其从窗口中移除，然后将 $j$ 向右移动一位。在移动的过程中，我们需要统计窗口中有多少个不同的服务器，这可以使用哈希表来实现。移动结束后，当前时间区间中没有收到请求的服务器数目就是 $n$ 减去哈希表中不同的服务器数目。
 
-时间复杂度 $O(l \times \log l + m \times \log m + n)$，空间复杂度 $O(l + m)$。其中 $l$ 和 $n$ 分别是数组 $logs$ 的长度和服务器的数量，而 $m$ 是数组 $queries$ 的长度。
+时间复杂度 $O(l \times \log l + m \times \log m + n)$，空间复杂度 $O(l + m)$。其中 $l$ 和 $n$ 分别是数组 $\text{logs}$ 的长度和服务器的数量，而 $m$ 是数组 $\text{queries}$ 的长度。
 
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solution/2700-2799/2747.Count Zero Request Servers/README.md

@@ -72,7 +72,13 @@ For queries[1]: Only server with id 3 gets no request in the duration [2,4].
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Offline Queries + Sorting + Two Pointers
+
+We can sort all the queries by time from smallest to largest, and then process each query in chronological order.
+
+For each query $q = (r, i)$, its window left boundary is $l = r - x$, and we need to count how many servers received requests within the window $[l, r]$. We use two pointers $j$ and $k$ to maintain the left and right boundaries of the window, initially $j = k = 0$. Each time, if the log time pointed by $k$ is less than or equal to $r$, we add it to the window, and then move $k$ to the right by one. If the log time pointed by $j$ is less than $l$, we remove it from the window, and then move $j$ to the right by one. During the movement, we need to count how many different servers are in the window, which can be implemented using a hash table. After the movement, the number of servers that did not receive requests in the current time interval is $n$ minus the number of different servers in the hash table.
+
+The time complexity is $O(l \times \log l + m \times \log m + n)$, and the space complexity is $O(l + m)$. Here, $l$ and $n$ are the lengths of the arrays $\text{logs}$ and the number of servers, respectively, while $m$ is the length of the array $\text{queries}$.
 
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solution/2700-2799/2747.Count Zero Request Servers/README_EN.md

@@ -66,9 +66,9 @@ tags:
 
 ### 方法一：枚举
 
-如果我们操作了 $k$ 次，那么问题实际上就变成了：判断 $num1 - k \times num2$ 能否拆分成 $k$ 个 $2^i$ 之和。
+如果我们操作了 $k$ 次，那么问题实际上就变成了：判断 $\text{num1} - k \times \text{num2}$ 能否拆分成 $k$ 个 $2^i$ 之和。
 
-我们不妨假设 $x = num1 - k \times num2$，接下来分类讨论：
+我们不妨假设 $x = \text{num1} - k \times \text{num2}$，接下来分类讨论：
 
 -   如果 $x \lt 0$，那么 $x$ 无法拆分成 $k$ 个 $2^i$ 之和，因为 $2^i \gt 0$，显然无解；
 -   如果 $x$ 的二进制表示中 $1$ 的个数大于 $k$，此时也是无解；

solution/2700-2799/2749.Minimum Operations to Make the Integer Zero/README.md

@@ -62,7 +62,19 @@ It can be proven, that 3 is the minimum number of operations that we need to per
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Enumeration
+
+If we operate $k$ times, then the problem essentially becomes: determining whether $\text{num1} - k \times \text{num2}$ can be split into the sum of $k$ $2^i$s.
+
+Let's assume $x = \text{num1} - k \times \text{num2}$. Next, we discuss in categories:
+
+-   If $x < 0$, then $x$ cannot be split into the sum of $k$ $2^i$s, because $2^i > 0$, which obviously has no solution;
+-   If the number of $1$s in the binary representation of $x$ is greater than $k$, there is also no solution in this case;
+-   Otherwise, for the current $k$, there must exist a splitting scheme.
+
+Therefore, we start enumerating $k$ from $1$. Once we find a $k$ that meets the condition, we can directly return the answer.
+
+The time complexity is $O(\log x)$, and the space complexity is $O(1)$.
 
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solution/2700-2799/2749.Minimum Operations to Make the Integer Zero/README_EN.md

@@ -62,7 +62,11 @@ tags:
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Multiplication Principle
+
+Based on the problem description, we can draw a dividing line between two $1$s. Assuming the indices of the two $1$s are $j$ and $i$ respectively, then the number of different dividing lines that can be drawn is $i - j$. We find all the pairs of $j$ and $i$ that meet the condition, and then multiply all the $i - j$ together. If no dividing line can be found between two $1$s, it means there are no $1$s in the array, and the answer is $0$.
+
+The time complexity is $O(n)$, where $n$ is the length of the array. The space complexity is $O(1)$.
 
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