From 162724ec530e7f0e4a4d9b6b127406a07d4c61f3 Mon Sep 17 00:00:00 2001
From: mt2324 <63892273+mt2324@users.noreply.github.com>
Date: Fri, 11 Sep 2026 14:28:21 +0900
Subject: [PATCH] Create 703. Kth Largest Element in a Stream.md

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+## Description
+[703. Kth Largest Element in a Stream](https://leetcode.com/problems/kth-largest-element-in-a-stream/)
+
+You are part of a university admissions office and need to keep track of the `kth` highest test score from applicants in real-time. This helps to determine cut-off marks for interviews and admissions dynamically as new applicants submit their scores.
+
+You are tasked to implement a class which, for a given integer `k`, maintains a stream of test scores and continuously returns the `k`th highest test score **after** a new score has been submitted. More specifically, we are looking for the `k`th highest score in the sorted list of all scores.
+
+Implement the `KthLargest` class:
+
+- `KthLargest(int k, int[] nums)` Initializes the object with the integer `k` and the stream of test scores `nums`.
+- `int add(int val)` Adds a new test score `val` to the stream and returns the element representing the `kth` largest element in the pool of test scores so far.
+
+**Example 1:**
+
+**Input:**  
+["KthLargest", "add", "add", "add", "add", "add"]  
+[[3, [4, 5, 8, 2]], [3], [5], [10], [9], [4]]
+
+**Output:** [null, 4, 5, 5, 8, 8]
+
+**Explanation:**
+
+KthLargest kthLargest = new KthLargest(3, [4, 5, 8, 2]);  
+kthLargest.add(3); // return 4  
+kthLargest.add(5); // return 5  
+kthLargest.add(10); // return 5  
+kthLargest.add(9); // return 8  
+kthLargest.add(4); // return 8
+
+**Example 2:**
+
+**Input:**  
+["KthLargest", "add", "add", "add", "add"]  
+[[4, [7, 7, 7, 7, 8, 3]], [2], [10], [9], [9]]
+
+**Output:** [null, 7, 7, 7, 8]
+
+**Explanation:**
+
+KthLargest kthLargest = new KthLargest(4, [7, 7, 7, 7, 8, 3]);  
+kthLargest.add(2); // return 7  
+kthLargest.add(10); // return 7  
+kthLargest.add(9); // return 7  
+kthLargest.add(9); // return 8
+
+**Constraints:**
+
+- `0 <= nums.length <= 104`
+- `1 <= k <= nums.length + 1`
+- `-104 <= nums[i] <= 104`
+- `-104 <= val <= 104`
+- At most `104` calls will be made to `add`.
+
+
+## STEP1
+max heapにするのかと思ったけど、kの大きさのmin heapを用意しておけば先頭が必然的にk番目に大きい。
+```python
+class KthLargest:
+
+    def __init__(self, k: int, nums: List[int]):
+        self.k = k
+        self.heap = nums
+        heapq.heapify(self.heap)
+        while len(self.heap) > k:
+            heapq.heappop(self.heap)
+
+    def add(self, val: int) -> int:
+        heapq.heappush(self.heap, val)
+        if len(self.heap) > self.k:
+            heapq.heappop(self.heap)
+        return self.heap[0] 
+
+
+# Your KthLargest object will be instantiated and called as such:
+# obj = KthLargest(k, nums)
+# param_1 = obj.add(val)
+```
+## STEP 2
+ちょっと変数名が雑すぎるので改善。与えられたnumsは破壊しない方がいい。addの返り値が個人的には直感的でないので、commentを足しておく。
+
+```python
+class KthLargest:
+
+    def __init__(self, k: int, nums: List[int]):
+        self.k = k
+        self.top_k_scores = nums.copy()
+        heapq.heapify(self.top_k_scores)
+        while len(self.top_k_scores) > k:
+            heapq.heappop(self.top_k_scores)
+
+	### Adds a new score to the heap which keeps top k elements and returns the new Kth Largest Element.
+    def add(self, val: int) -> int:
+        heapq.heappush(self.top_k_scores, val)
+        if len(self.top_k_scores) > self.k:
+            heapq.heappop(self.top_k_scores)
+        return self.top_k_scores[0] 
+
+
+# Your KthLargest object will be instantiated and called as such:
+# obj = KthLargest(k, nums)
+# param_1 = obj.add(val)
+```
+https://docs.python.org/3.14/tutorial/datastructures.html
+リストのcopyメソッドはshallow copyで
+
+https://docs.python.org/3.14/library/copy.html
+copyモジュールにshallow copyのcopy()とdeepcopy()があることを確認。新しくreplace()という関数がリリースされており、dataclassとかnamedtupleで使える。shallow copyしつつ、一部を書き換える操作をしている。
+
+dataclassってなんだっけと脱線
+https://docs.python.org/3/library/dataclasses.html
+
+## STEP 3
+
+```python
+import heapq
+class KthLargest:
+
+    def __init__(self, k: int, nums: List[int]):
+        self.k = k
+        self.top_k_scores = nums.copy()
+        heapq.heapify(self.top_k_scores)
+        while len(self.top_k_scores) > self.k:
+            heapq.heappop(self.top_k_scores)
+
+	# Adds a new score to KthLargest and returns the new Kth Largest Element.
+    def add(self, val: int) -> int:
+        heapq.heappush(self.top_k_scores, val)
+        if len(self.top_k_scores) > self.k:
+            heapq.heappop(self.top_k_scores)
+        return self.top_k_scores[0]
+```
+
+## Min Heapの実装
+heap の実装って内部的にどうやってるのかなーと思ったけど内部的にはcで配列のポインタの位置でheapを動かしてた。
+https://github.com/python/cpython/blob/3.14/Lib/heapq.py
+
+heapの実装は別ファイル。