feat: update solutions to lc problems: No.2526,2528 (doocs#3722)

* No.2526.Find Consecutive Integers from a Data Stream
* No.2528.Maximize the Minimum Powered City

Author: yanglbme

solution/2500-2599/2526.Find Consecutive Integers from a Data Stream/README.md

@@ -43,7 +43,7 @@ tags:
 [null, false, false, true, false]
 
 <strong>解释：</strong>
-DataStream dataStream = new DataStream(4, 3); // value = 4, k = 3 
+DataStream dataStream = new DataStream(4, 3); // value = 4, k = 3
 dataStream.consec(4); // 数据流中只有 1 个整数，所以返回 False 。
 dataStream.consec(4); // 数据流中只有 2 个整数
                       // 由于 2 小于 k ，返回 False 。
@@ -70,9 +70,9 @@ dataStream.consec(3); // 最后 k 个整数分别是 [4,4,3] 。
 
 ### 方法一：计数
 
-维护一个计数器 $cnt$，记录当前连续整数为 `value` 的个数。
+我们可以维护一个计数器 $\textit{cnt}$，记录当前连续整数为 $\textit{value}$ 的个数。
 
-当 `num` 与 `value` 相等时，$cnt$ 自增 1，否则 $cnt$ 重置为 0。然后判断 $cnt$ 是否大于等于 `k` 即可。
+调用 `consec` 方法时，如果 $\textit{num}$ 与 $\textit{value}$ 相等，我们将 $\textit{cnt}$ 自增 1，否则将 $\textit{cnt}$ 重置为 0。然后判断 $\textit{cnt}$ 是否大于等于 $\textit{k}$ 即可。
 
 时间复杂度 $O(1)$，空间复杂度 $O(1)$。
 

solution/2500-2599/2526.Find Consecutive Integers from a Data Stream/README_EN.md

@@ -42,11 +42,11 @@ tags:
 [null, false, false, true, false]
 
 <strong>Explanation</strong>
-DataStream dataStream = new DataStream(4, 3); //value = 4, k = 3 
-dataStream.consec(4); // Only 1 integer is parsed, so returns False. 
+DataStream dataStream = new DataStream(4, 3); //value = 4, k = 3
+dataStream.consec(4); // Only 1 integer is parsed, so returns False.
 dataStream.consec(4); // Only 2 integers are parsed.
-                      // Since 2 is less than k, returns False. 
-dataStream.consec(4); // The 3 integers parsed are all equal to value, so returns True. 
+                      // Since 2 is less than k, returns False.
+dataStream.consec(4); // The 3 integers parsed are all equal to value, so returns True.
 dataStream.consec(3); // The last k integers parsed in the stream are [4,4,3].
                       // Since 3 is not equal to value, it returns False.
 </pre>
@@ -66,7 +66,13 @@ dataStream.consec(3); // The last k integers parsed in the stream are [4,4,3].
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Counting
+
+We can maintain a counter $\textit{cnt}$ to record the current number of consecutive integers equal to $\textit{value}$.
+
+When calling the `consec` method, if $\textit{num}$ is equal to $\textit{value}$, we increment $\textit{cnt}$ by 1; otherwise, we reset $\textit{cnt}$ to 0. Then we check whether $\textit{cnt}$ is greater than or equal to $\textit{k}$.
+
+The time complexity is $O(1)$, and the space complexity is $O(1)$.
 
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solution/2500-2599/2528.Maximize the Minimum Powered City/README.md

@@ -95,7 +95,7 @@ tags:
 
 函数 $check(x, k)$ 的实现逻辑是：
 
-遍历每座城市，如果当前城市 $i$ 的供电站数目小于 $x$，此时我们可以贪心地在尽可能右边的位置上建造供电站，位置 $j = min(i + r, n - 1)$，这样可以使得供电站覆盖尽可能多的城市。过程中我们可以借助差分数组，给一段连续的位置加上某个值。如果需要额外建造的供电站数量超过 $k$，那么 $x$ 不满足条件，返回 `false`。否则遍历结束后，返回 `true`。
+遍历每座城市，如果当前城市 $i$ 的供电站数目小于 $x$，此时我们可以贪心地在尽可能右边的位置上建造供电站，位置 $j = \min(i + r, n - 1)$，这样可以使得供电站覆盖尽可能多的城市。过程中我们可以借助差分数组，给一段连续的位置加上某个值。如果需要额外建造的供电站数量超过 $k$，那么 $x$ 不满足条件，返回 `false`。否则遍历结束后，返回 `true`。
 
 时间复杂度 $O(n \times \log M)$，空间复杂度 $O(n)$。其中 $n$ 为城市数量，而 $M$ 我们固定取 $2^{40}$。
 

solution/2500-2599/2528.Maximize the Minimum Powered City/README_EN.md

@@ -45,8 +45,8 @@ tags:
 <pre>
 <strong>Input:</strong> stations = [1,2,4,5,0], r = 1, k = 2
 <strong>Output:</strong> 5
-<strong>Explanation:</strong> 
-One of the optimal ways is to install both the power stations at city 1. 
+<strong>Explanation:</strong>
+One of the optimal ways is to install both the power stations at city 1.
 So stations will become [1,4,4,5,0].
 - City 0 is provided by 1 + 4 = 5 power stations.
 - City 1 is provided by 1 + 4 + 4 = 9 power stations.
@@ -62,7 +62,7 @@ Since it is not possible to obtain a larger power, we return 5.
 <pre>
 <strong>Input:</strong> stations = [4,4,4,4], r = 0, k = 3
 <strong>Output:</strong> 4
-<strong>Explanation:</strong> 
+<strong>Explanation:</strong>
 It can be proved that we cannot make the minimum power of a city greater than 4.
 </pre>
 
@@ -83,7 +83,19 @@ It can be proved that we cannot make the minimum power of a city greater than 4.
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Binary Search + Difference Array + Greedy
+
+According to the problem description, the minimum number of power stations increases as the value of $k$ increases. Therefore, we can use binary search to find the largest minimum number of power stations, ensuring that the additional power stations needed do not exceed $k$.
+
+First, we use a difference array and prefix sum to calculate the initial number of power stations in each city, recording it in the array $s$, where $s[i]$ represents the number of power stations in the $i$-th city.
+
+Next, we define the left boundary of the binary search as $0$ and the right boundary as $2^{40}$. Then, we implement a function $check(x, k)$ to determine whether the minimum number of power stations in the cities can be $x$, ensuring that the additional power stations needed do not exceed $k$.
+
+The implementation logic of the function $check(x, k)$ is as follows:
+
+Traverse each city. If the number of power stations in the current city $i$ is less than $x$, we can greedily build a power station at the rightmost possible position, $j = \min(i + r, n - 1)$, to cover as many cities as possible. During this process, we can use the difference array to add a certain value to a continuous segment. If the number of additional power stations needed exceeds $k$, then $x$ does not meet the condition, and we return `false`. Otherwise, after the traversal, return `true`.
+
+The time complexity is $O(n \times \log M)$, and the space complexity is $O(n)$. Here, $n$ is the number of cities, and $M$ is fixed at $2^{40}$.
 
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