{"id":9254,"date":"2025-08-12T17:12:14","date_gmt":"2025-08-12T11:42:14","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9254"},"modified":"2025-10-15T18:34:48","modified_gmt":"2025-10-15T13:04:48","slug":"kth-largest-element-in-a-stream","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/kth-largest-element-in-a-stream\/","title":{"rendered":"Kth Largest Element in a Stream"},"content":{"rendered":"\n<!-- Evaluate Reverse Polish Notation 11-->\n<link\n    href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.min.css\"\n    rel=\"stylesheet\"\n\/>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/prism.min.js\"><\/script>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/plugins\/autoloader\/prism-autoloader.min.js\"><\/script>\n\n<style>\n.wp_blog_theme {\n  --primary: #E58C32;\n  --secondary: #030302;\n  --light-bg: #fef9f4;\n  --text-dark: #2d2d2d;\n  --tab-radius: 12px;\n  --shadow: 0 4px 12px rgba(0, 0, 0, 0.08);\n  --code-bg: #001f3f;\n  --code-text: #d4f1ff;\n}\n\n.wp_blog_container {\n  font-family: 'Segoe UI', sans-serif;\n  background: var(--light-bg);\n  margin: 0;\n  padding: 0;\n  color: var(--text-dark);\n}\n\n\/* Heading *\/\n.wp_blog_main-heading {\n  text-align: center;\n  font-size: 2.4rem;\n  color: var(--primary);\n  margin-top: 2.5rem;\n  font-weight: bold;\n}\n\n\/* Explanation Card *\/\n.wp_blog_explanation,\n.wp_blog_code-tabs-container {\n  max-width: 940px;\n  margin: 2rem auto;\n  padding: 2rem;\n  background: white;\n  border-radius: var(--tab-radius);\n  box-shadow: var(--shadow);\n}\n\n\/* Text and Visuals *\/\n.wp_blog_explanation h2 {\n  font-size: 1.4rem;\n  color: var(--primary);\n  margin-bottom: 0.5rem;\n}\n\n.wp_blog_explanation p,\n.wp_blog_explanation li {\n  font-size: 1.05rem;\n  line-height: 1.7;\n  margin: 0.5rem 0;\n}\n\n.wp_blog_explanation code {\n  background: #fef9f4;   \/* light bg instead of dark blue *\/\n  color: #E58C32;        \/* brand orange *\/\n  padding: 3px 6px;\n  border-radius: 4px;\n  font-family: 'Courier New', monospace;\n  font-weight: 600;      \/* optional, makes it pop *\/\n}\n\n.wp_blog_explanation img {\n  max-width: 100%;\n  border-radius: var(--tab-radius);\n  margin-top: 1rem;\n  box-shadow: 0 2px 12px rgba(0, 0, 0, 0.06);\n}\n\n\/* Tab Buttons *\/\n.wp_blog_code-tabs-header {\n  display: flex;\n  flex-wrap: wrap;\n  gap: 0.5rem;\n  margin-bottom: 1rem;\n}\n\n.wp_blog_code-tab-button {\n  padding: 0.6rem 1.2rem;\n  border: 1px solid var(--primary);\n  background: white;\n  color: var(--primary);\n  border-radius: 50px;\n  font-weight: 600;\n  cursor: pointer;\n  transition: all 0.3s ease;\n}\n\n.wp_blog_code-tab-button:hover {\n  background: var(--secondary);\n}\n\n.wp_blog_code-tab-button.active {\n  background: var(--primary);\n  color: white;\n}\n\n\/* Code Content *\/\n.wp_blog_code-tab-content {\n  display: none;\n  background: var(--code-bg);\n  border-radius: var(--tab-radius);\n}\n\n.wp_blog_code-tab-content.active {\n  display: block;\n}\n\n.wp_blog_code-tab-content pre {\n  margin: 0;\n  padding: 1.5rem;\n  font-size: 1rem;\n  overflow-x: auto;\n  background: var(--code-bg);\n  border-radius: var(--tab-radius);\n  color: var(--code-text);\n}\n\n\/* Dark mode variables *\/\n.wp_blog_theme.dark-mode {\n  --light-bg: #121212;\n  --text-dark: #f5f5f5;\n  --shadow: 0 4px 12px rgba(255, 255, 255, 0.08);\n  --code-bg: #1e1e1e;\n  --code-text: #c5f0ff;\n}\n\n.wp_blog_theme.dark-mode .wp_blog_explanation {\n  background: #1e1e1e;\n}\n\n\/* Dark mode code highlight *\/\n.wp_blog_theme.dark-mode .wp_blog_explanation code {\n  background: #333;\n  color: #ffd27f;\n}\n\n.wp_blog_theme {\n  position: relative; \/* makes it the reference for absolute children *\/\n}\n\n.wp_blog_toggle-btn {\n  position: absolute;\n  top: 1rem;\n  right: 1rem;\n  z-index: 9999;\n  padding: 0.5rem 0.8rem;\n  border-radius: 10%;\n  background: var(--primary);\n  color: white;\n  font-weight: bold;\n  cursor: pointer;\n  border: none;\n  box-shadow: var(--shadow);\n  transition: background 0.3s, transform 0.2s;\n}\n\n.wp_blog_toggle-btn:hover {\n  background: #cc772e;\n}\n\n.wp_blog_theme.dark-mode .wp_blog_code-tabs-container {\n  background: #1e1e1e;\n}\n<\/style>\n\n\n<div class=\"wp_blog_container wp_blog_theme\">\n      <button id=\"blogNotesThemeToggle\" class=\"wp_blog_toggle-btn\">\ud83c\udf19<\/button>\n<h1 class=\"wp_blog_main-heading\"><\/h1>\n\n<div class=\"wp_blog_explanation\">\n    <h2>Problem Statement:<\/h2>\n    <p>\n        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.\n    <\/p>\n\n    <p>\n        You are tasked to implement a class which, for a given integer k, maintains a stream of test scores and continuously returns the kth highest test score after a new score has been submitted. More specifically, we are looking for the kth highest score in the sorted list of all scores.\n    <\/p>\n\n    <p>Implement the KthLargest class:\n        <ul>\n            <li><code>KthLargest(int k, int[] nums)<\/code> Initializes the object with the integer k and the stream of test scores <code>nums<\/code>.<\/li>\n            <li><code>int add(int val)<\/code> Adds a new test score <code>val<\/code> to the stream and returns the element representing the <code>k<sup>th<\/sup><\/code> largest element in the pool of test scores so far.<\/li>\n        <\/ul>\n    <\/p>\n    <p><strong>Example 1:<\/strong><\/p>\n    <p><strong>Input:<\/strong><\/p>\n        <p>[&#8220;KthLargest&#8221;, &#8220;add&#8221;, &#8220;add&#8221;, &#8220;add&#8221;, &#8220;add&#8221;, &#8220;add&#8221;]\n            [[3, [4, 5, 8, 2]], [3], [5], [10], [9], [4]]<\/p>\n    <p><strong>Output:<\/strong><code>[null, 4, 5, 5, 8, 8]<\/code><\/p>\n    <p><strong>Explanation:<\/strong>\n    <code>\n    <pre>\n        KthLargest kthLargest = new KthLargest(3, [4, 5, 8, 2]);\n        kthLargest.add(3); \/\/ return 4\n        kthLargest.add(5); \/\/ return 5\n        kthLargest.add(10); \/\/ return 5\n        kthLargest.add(9); \/\/ return 8\n        kthLargest.add(4); \/\/ return 8\n    <\/pre>\n    <\/code>\n    <\/p>\n\n    <p><strong>Example 2:<\/strong><\/p>\n    <p><strong>Input:<\/strong><\/p>\n        <p>[&#8220;KthLargest&#8221;, &#8220;add&#8221;, &#8220;add&#8221;, &#8220;add&#8221;, &#8220;add&#8221;]\n            [[4, [7, 7, 7, 7, 8, 3]], [2], [10], [9], [9]]<\/p>\n\n    <p><strong>Output:<\/strong><code>[null, 7, 7, 7, 8]<\/code><\/p>\n    <p><strong>Explanation:<\/strong>\n    <code>\n    <pre>\n        KthLargest kthLargest = new KthLargest(4, [7, 7, 7, 7, 8, 3]);\n        kthLargest.add(2); \/\/ return 7\n        kthLargest.add(10); \/\/ return 7\n        kthLargest.add(9); \/\/ return 7\n        kthLargest.add(9); \/\/ return 8\n    <\/pre>\n    <\/code>\n    <\/p>\n\n    <h2>Constraints:<\/h2>\n    <ul>\n        <li><code>0 <= nums.length <= 10<sup>4<\/sup><\/code><\/li>\n        <li><code>1 <= k <= nums.length + 1<\/code><\/li>\n        <li><code>-10<sup>4<\/sup> <= nums[i] <= 10<sup>4<\/sup><\/code><\/li>\n        <li><code>-10<sup>4<\/sup> <= val <= 10<sup>4<\/sup><\/code><\/li>\n        <li>At most <code>10<sup>4<\/sup> calls will be made to <code>add<\/code><\/code>.<\/li>\n    <\/ul>\n\n    <h2>Approach:<\/h2>\n    <ul>\n        <li>Insert elements into the heap one by one.<\/li>\n        <li>If the heap size exceeds <code>k<\/code>, remove the smallest element (top of the min-heap).<\/li>\n        <li>The smallest element in the heap <code>(heap.front())<\/code> is always the <strong>kth largest<\/strong> in the stream.<\/li>\n    <\/ul>\n\n    <h2>Time Complexity:<\/h2>\n    <li><p><strong>Time Complexity = O(log k)<\/strong><\/p><\/li> \n    <h2>Space Complexity:<\/h2>\n    <li><p><strong>Space Complexity = O(K)<\/strong><\/p><\/li>\n\n<h2>Dry Run<\/h2>\n<div style=\"background: var(--light-bg); border-left: 4px solid var(--primary); padding: 1rem; border-radius: var(--tab-radius); margin: 1rem 0; color: var(--text-dark);\"> \n\n  <p><strong>Input:<\/strong> <code>nums = [3, 2, 1, 5, 6, 4], k = 2<\/code><\/p> \n  \n  <p><strong>State Transitions:<\/strong><\/p>\n  \n  <pre style=\"white-space: pre-wrap; background: var(--code-bg); padding: 1rem; border-radius: 8px; overflow-x: auto; color: var(--code-text);\">\n\nInitialize: pq = MinPriorityQueue()\n\ni = 0 \u2192 nums[0] = 3\n\u2192 pq.enqueue(3) \u2192 pq = [3]\n\ni = 1 \u2192 nums[1] = 2\n\u2192 pq.enqueue(2) \u2192 pq = [2, 3]  (min-heap: 2 is root)\n\ni = 2 \u2192 nums[2] = 1\n\u2192 pq.enqueue(1) \u2192 pq = [1, 3, 2]\n\u2192 pq.size() = 3 > k (2) \u2192 pq.dequeue() removes smallest (1)\n\u2192 pq = [2, 3]\n\ni = 3 \u2192 nums[3] = 5\n\u2192 pq.enqueue(5) \u2192 pq = [2, 3, 5]\n\u2192 pq.size() = 3 > k \u2192 pq.dequeue() removes smallest (2)\n\u2192 pq = [3, 5]\n\ni = 4 \u2192 nums[4] = 6\n\u2192 pq.enqueue(6) \u2192 pq = [3, 5, 6]\n\u2192 pq.size() = 3 > k \u2192 pq.dequeue() removes smallest (3)\n\u2192 pq = [5, 6]\n\ni = 5 \u2192 nums[5] = 4\n\u2192 pq.enqueue(4) \u2192 pq = [4, 6, 5]\n\u2192 pq.size() = 3 > k \u2192 pq.dequeue() removes smallest (4)\n\u2192 pq = [5, 6]\n  <\/pre> \n  \n  <p><strong>Final Output:<\/strong> <code>5<\/code><\/p> \n  <p><strong>Explanation:<\/strong> pq.front() returns the smallest in the heap \u2192 the 2nd largest element overall.<\/p> \n<\/div>\n\n<\/div>\n\n\n<div class=\"wp_blog_code-tabs-container\">\n    <div class=\"wp_blog_code-tabs-header\">\n        <button class=\"wp_blog_code-tab-button active\" data-lang=\"js\">JavaScript<\/button>\n        <button class=\"wp_blog_code-tab-button\" data-lang=\"py\">Python<\/button>\n        <button class=\"wp_blog_code-tab-button\" data-lang=\"java\">Java<\/button>\n        <button class=\"wp_blog_code-tab-button\" data-lang=\"cpp\">C++<\/button>\n        <button class=\"wp_blog_code-tab-button\" data-lang=\"c\">C<\/button>\n        <button class=\"wp_blog_code-tab-button\" data-lang=\"cs\">C#<\/button>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n<pre><code class=\"language-javascript\">\nvar KthLargest = function(k, nums) {\n    this.heap = new MinPriorityQueue();\n    this.k = k;\n    for(let i=0; i<nums.length; i++){\n        this.add(nums[i]);\n    }\n};\nKthLargest.prototype.add = function(val) {\n    this.heap.enqueue(val);\n    if(this.heap.size() > this.k){\n        this.heap.dequeue();\n    }\n    return this.heap.front();\n};\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n<pre><code class=\"language-python\">\nimport heapq\nclass KthLargest:\n    def __init__(self, k: int, nums: list[int]):\n        self.min_heap = []\n        self.k = k\n        for num in nums:\n            self.add(num)\n    def add(self, val: int) -> int:\n        heapq.heappush(self.min_heap, val)\n        if len(self.min_heap) > self.k:\n            heapq.heappop(self.min_heap)\n        return self.min_heap[0]\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n<pre><code class=\"language-java\">\nimport java.util.PriorityQueue;\n\nclass KthLargest {\n    private PriorityQueue<Integer> minHeap;\n    private int k;\n\n    public KthLargest(int k, int[] nums) {\n        this.k = k;\n        minHeap = new PriorityQueue<>();\n\n        for (int num : nums) {\n            add(num);\n        }\n    }\n    public int add(int val) {\n        minHeap.offer(val);\n        if (minHeap.size() > k) {\n            minHeap.poll();\n        }\n        return minHeap.peek();\n    }\n}\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n<pre><code class=\"language-cpp\">\n#include &lt;vector&gt;\n#include &lt;queue&gt;\nclass KthLargest {\nprivate:\n    std::priority_queue<int, std::vector<int>, std::greater<int>> minHeap;\n    int k;\npublic:\n    KthLargest(int k, std::vector<int>& nums) {\n        this->k = k;\n        for (int num : nums) {\n            add(num);\n        }\n    }\n    int add(int val) {\n        minHeap.push(val);\n        if (minHeap.size() > k) {\n            minHeap.pop();\n        }\n        return minHeap.top();\n    }\n};\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n<pre><code class=\"language-c\">\n#include &lt;stdio.h&gt;\n#include &lt;stdlib.h&gt;\n\ntypedef struct {\n    int *arr;\n    int size;\n    int k;\n} KthLargest;\n\nint compare(const void *a, const void *b) {\n    return (*(int*)a - *(int*)b); \/\/ ascending\n}\nKthLargest* kthLargestCreate(int k, int* nums, int numsSize) {\n    KthLargest* obj = (KthLargest*)malloc(sizeof(KthLargest));\n    obj->arr = (int*)malloc(sizeof(int) * (numsSize + 1));\n    obj->size = 0;\n    obj->k = k;\n    for (int i = 0; i < numsSize; i++) {\n        int val = nums[i];\n        obj->arr[obj->size++] = val;\n        qsort(obj->arr, obj->size, sizeof(int), compare);\n        if (obj->size > k) {\n            for (int j = 0; j < obj->size - 1; j++)\n                obj->arr[j] = obj->arr[j + 1];\n            obj->size--;\n        }\n    }\n    return obj;\n}\nint kthLargestAdd(KthLargest* obj, int val) {\n    obj->arr[obj->size++] = val;\n    qsort(obj->arr, obj->size, sizeof(int), compare);\n    if (obj->size > obj->k) {\n        for (int j = 0; j < obj->size - 1; j++)\n            obj->arr[j] = obj->arr[j + 1];\n        obj->size--;\n    }\n    return obj->arr[0];\n}\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n<pre><code class=\"language-csharp\">\nusing System;\nusing System.Collections.Generic;\n\npublic class KthLargest {\n    private PriorityQueue<int, int> minHeap;\n    private int k;\n\n    public KthLargest(int k, int[] nums) {\n        this.k = k;\n        minHeap = new PriorityQueue<int, int>();\n\n        foreach (int num in nums) {\n            Add(num);\n        }\n    }\n    public int Add(int val) {\n        minHeap.Enqueue(val, val);\n        if (minHeap.Count > k) {\n            minHeap.Dequeue();\n        }\n        return minHeap.Peek();\n    }\n}\n<\/code><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n<script>\ndocument.addEventListener(\"DOMContentLoaded\", () => {\n  const buttons = document.querySelectorAll(\".wp_blog_code-tab-button\");\n  const contents = document.querySelectorAll(\".wp_blog_code-tab-content\");\n\n  buttons.forEach((button) => {\n    button.addEventListener(\"click\", () => {\n      const lang = button.getAttribute(\"data-lang\");\n\n      buttons.forEach((btn) => btn.classList.remove(\"active\"));\n      contents.forEach((content) => content.classList.remove(\"active\"));\n\n      button.classList.add(\"active\");\n      document\n        .querySelector(`.wp_blog_code-tab-content[data-lang=\"${lang}\"]`)\n        .classList.add(\"active\");\n    });\n  });\n\n  const themeToggle = document.getElementById(\"blogNotesThemeToggle\");\n  const themeContainer = document.querySelector(\".wp_blog_theme\");\n\n  themeToggle.addEventListener(\"click\", () => {\n    themeContainer.classList.toggle(\"dark-mode\");\n    themeToggle.textContent =\n      themeContainer.classList.contains(\"dark-mode\") ? \"\u2600\ufe0f\" : \"\ud83c\udf19\";\n  });\n});\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Problem Statement: 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<\/p>\n","protected":false},"author":108,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[210,322,176,175,211,174,172,173],"tags":[],"class_list":["post-9254","post","type-post","status-publish","format-standard","category-algorithms","category-algorithms-and-data-structures","category-csharp","category-cplusplus","category-data-structures","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9254","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/users\/108"}],"replies":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/comments?post=9254"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9254\/revisions"}],"predecessor-version":[{"id":10353,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9254\/revisions\/10353"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}