solutions: 2530 - Maximal Score After Applying K Operations (Medium)

Author: wingkwong

solutions/2500-2599/2530-maximal-score-after-applying-k-operations-medium.md

@@ -1,8 +1,9 @@
 ---
-description: 'Author: @wingkwong | https://leetcode.com/problems/maximal-score-after-applying-k-operations/'
+description: "Author: @wingkwong | https://leetcode.com/problems/maximal-score-after-applying-k-operations/"
+tags: [Array, Greedy, Heap (Priority Queue)]
 ---
 
-# 2530 - Maximal Score After Applying K Operations (Medium) 
+# 2530 - Maximal Score After Applying K Operations (Medium)
 
 ## Problem Link
 
@@ -18,7 +19,7 @@ In one **operation**:
 2. increase your **score** by `nums[i]`, and
 3. replace `nums[i]` with `ceil(nums[i] / 3)`.
 
-Return *the maximum possible **score** you can attain after applying **exactly*** `k` *operations*.
+Return \*the maximum possible **score** you can attain after applying **exactly\*** `k` _operations_.
 
 The ceiling function `ceil(val)` is the least integer greater than or equal to `val`.
 
@@ -49,6 +50,12 @@ The final score is 10 + 4 + 3 = 17.
 
 ## Approach 1: Priority Queue
 
+When you see a question asking you to find something maximum / minimum after `K` operations. It's a hint that this could be solved by priority queue.
+
+In this question, it is easy to see that we should apply the operation on the largest number each time (i.e. greedy approach). If we just write a brute force solution, after each operation, we need to iterate `nums` again to find out the largest number which costs $O(n)$ where $n$ is the number of elements in `nums` and this happens $K$ times, which is not efficient.
+
+To optimise the solution, we can apply priority queue / heap (in python) so that we could find the largest number efficiently, which takes $O(1)$ for finding the max number.
+
 <Tabs>
 <TabItem value="cpp" label="C++">
 <SolutionAuthor name="@wingkwong"/>
@@ -63,11 +70,11 @@ public:
         // perform k rounds
         while (k--) {
             // get the max one
-            int t = pq.top(); 
+            int t = pq.top();
             // pop it out
             pq.pop();
             // add to answer
-            ans += t; 
+            ans += t;
             // add the ceil value
             // ceil(x / y) = (x + y - 1) / y
             // ceil(t / 3) = (t + 3 - 1) / 3 = (t + 2) / 3
@@ -79,4 +86,32 @@ public:
 ```
 
 </TabItem>
-</Tabs>
+
+<TabItem value="py" label="Python">
+<SolutionAuthor name="@wingkwong"/>
+
+```py
+class Solution:
+    def maxKelements(self, nums: List[int], k: int) -> int:
+        res = 0
+        # we want to take the max one in each round
+        # create a max heap by pushing negative values
+        mx_heap = [-num for num in nums]
+        heapq.heapify(mx_heap)
+        # perform k rounds
+        while k > 0:
+            k -= 1
+            # get the max one (negative because of max-heap simulation)
+            t = -heapq.heappop(mx_heap)
+            # add to answer
+            res += t
+            # push the ceil value of t / 3 back into the heap
+            # ceil(x / y) = (x + y - 1) / y
+            # ceil(t / 3) = (t + 3 - 1) / 3 = (t + 2) / 3
+            heapq.heappush(mx_heap, -((t + 2) // 3))
+        return res
+```
+
+</TabItem>
+
+</Tabs>