{"id":11777,"date":"2026-03-14T19:16:56","date_gmt":"2026-03-14T13:46:56","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=11777"},"modified":"2026-03-14T19:24:13","modified_gmt":"2026-03-14T13:54:13","slug":"super-egg-drop","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/super-egg-drop\/","title":{"rendered":"Super Egg Drop"},"content":{"rendered":"\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<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    <div class=\"wp_blog_explanation\">\n        <h2>Problem Statement:<\/h2>\n        <p>\n            You are given k identical eggs and you have access to a building with n floors labeled from <code>1<\/code> to <code>n<\/code>.\n        <\/p>\n        <p>\n            You know that there exists a floor f where 0 <= f <= n such that any egg dropped at a floor higher than f will break, and any egg dropped at or below floor f will not break.\n        <\/p>\n\n        <p>\n            Each move, you may take an unbroken egg and drop it from any floor x (where 1 <= x <= n). If the egg breaks, you can no longer use it. However, if the egg does not break, you may reuse it in future moves.\n        <\/p>\n\n        <p>\n            Return the minimum number of moves that you need to determine with certainty what the value of f is.\n        <\/p>\n\n                <h2>Examples:<\/h2>\n\n                <h3>Example 1:<\/h3>\n                <p><strong>Input:<\/strong> k = 1, n = 2\n                <\/p>\n                <p><strong>Output:<\/strong> 2<\/p>\n                <p>\n                  <code>Explanation:<\/code>\n                  Drop the egg from floor 1. If it breaks, we know that f = 0.\n                    Otherwise, drop the egg from floor 2. If it breaks, we know that f = 1.\n                    If it does not break, then we know f = 2.\n                    Hence, we need at minimum 2 moves to determine with certainty what the value of f is.\n                <\/p>\n\n\n                <h3>Example 2:<\/h3>\n                <p><strong>Input:<\/strong>  k = 2, n = 6<\/p>\n\n                <p><strong>Output:<\/strong> 3<\/p>\n\n                <h3>Example 3:<\/h3>\n                <p><strong>Input:<\/strong>  k = 3, n = 14<\/p>\n\n                <p><strong>Output:<\/strong> 4<\/p>\n        \n\n                <!-- <h5>Example 3:<\/h5>\n                <p><strong>Input:<\/strong>\n                <\/p>\n                <p>\n                    nums1 = [0], m = 0\n                    nums2 = [1], n = 1\n                <\/p>    \n                <p><strong>Output:<\/strong>[1]<\/p>\n                  <p>\n                  <code>Explanation:<\/code>\n                 The arrays we are merging are [] and [1].\n                    The result of the merge is [1].\n                    Note that because m = 0, there are no elements in nums1. \n                    The 0 is only there to ensure the merge result can fit in nums1.\n                <\/p> -->\n\n                <h2>Constraints<\/h2>\n                <p><code>1 <= k <= 100<\/code><\/p>\n                <p><code>\n                  1 <= n <= 10<sup>4<\/sup>\n                <\/code><\/p>\n\n                    <h2>Time Complexity:<\/h2>\n                    <li>\n                      <p><strong>Time Complexity = O(k x moves)<\/strong>\n                      <\/li>\n                    <h2>Space Complexity:<\/h2>\n                    <li>\n                      <p><strong>Space Complexity = O(k)<\/strong><\/p>\n                    <\/li>\n\n                <h2>Approach<\/h2>\n                <ul>\n                    <li>\n                        Instead of directly finding the <code>minimum moves<\/code> for <strong>k eggs<\/strong> and <strong>n floors<\/strong>, we reverse the thinking. We calculate how many floors can be tested with a given number of moves and eggs.\n                    <\/li>\n\n                    <li>\n                        Let <code>dp[i]<\/code> represent the maximum number of floors that can be checked using <code>i<\/code> eggs and the current number of moves.\n                    <\/li>\n\n                    <li>Initialize a DP array of size <strong>k + 1<\/strong> with all <strong>values 0<\/strong>.<\/li>\n\n                    <li>Increase the <code>number of moves<\/code> step by step until we can check at <code>least n floors<\/code> with <code>k eggs<\/code>.<\/li>\n\n                    <li>For every <strong>move<\/strong>, update the DP values from <strong>right<\/strong> to <strong>left<\/strong> using the relation:\n                        <ul>\n                            <li><strong><code>If an egg is dropped<\/code><\/strong>:\n                                <ul>\n                                    <li><strong>Egg breaks<\/strong> \u2192 we check floors below with <code>i-1 eggs<\/code>.<\/li>\n                                    <li><strong>Egg survives<\/strong> \u2192 we check floors above with <code>i eggs<\/code>.<\/li>\n                                <\/ul>\n                            <\/li>\n                            <li>So the recurrence becomes: <code>dp[i] = 1 + dp[i] + dp[i-1]<\/code>\n                            where: <code>1<\/code> = current floor, <code>dp[i]<\/code>= floors we can check if egg survives and <code>dp[i-1]<\/code> = floors we can check if egg breaks.\n                            <\/li>\n                        <\/ul>\n                    <\/li>\n                    <li>Continue increasing moves until <code>dp[k] >= n<\/code>.<\/li>\n                    <li>The number of moves taken is the <strong>minimum number of attempts<\/strong> required in the worst case.<\/li>\n                <\/ul>\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  <p><strong>Input:<\/strong> <code>k = 2, n = 6<\/code><\/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);\">\nMeaning:\ndp[i] = maximum floors we can test with i eggs and current number of moves\n\nInitialization:\n   dp = [0, 0, 0]   (index 0..k)\n   moves = 0\n\nStep 1: moves = 1\n\nUpdate dp from right to left\n\ni = 2\ndp[2] = 1 + dp[2] + dp[1]\n      = 1 + 0 + 0\n      = 1\n\ni = 1\ndp[1] = 1 + dp[1] + dp[0]\n      = 1 + 0 + 0\n      = 1\n\ndp = [0, 1, 1]\n\nInterpretation:\nWith 1 move:\n   1 egg \u2192 test 1 floor\n   2 eggs \u2192 test 1 floor\n\nCondition check:\ndp[2] = 1 < 6 \u2192 continue\n\nStep 2: moves = 2\n\ni = 2\ndp[2] = 1 + dp[2] + dp[1]\n      = 1 + 1 + 1\n      = 3\n\ni = 1\ndp[1] = 1 + dp[1] + dp[0]\n      = 1 + 1 + 0\n      = 2\n\ndp = [0, 2, 3]\n\nInterpretation:\nWith 2 moves:\n   1 egg \u2192 test 2 floors\n   2 eggs \u2192 test 3 floors\n\nCondition check:\ndp[2] = 3 < 6 \u2192 continue\n\nStep 3: moves = 3\n\ni = 2\ndp[2] = 1 + dp[2] + dp[1]\n      = 1 + 3 + 2\n      = 6\n\ni = 1\ndp[1] = 1 + dp[1] + dp[0]\n      = 1 + 2 + 0\n      = 3\n\ndp = [0, 3, 6]\n\nInterpretation:\nWith 3 moves:\n   1 egg \u2192 test 3 floors\n   2 eggs \u2192 test 6 floors\n\nCondition check:\ndp[2] = 6 \u2265 6 \u2192 stop\n  <\/pre> \n  \n  <p><strong>Output:<\/strong> <code>3<\/code><\/p> \n<\/div>\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\">\n            JavaScript\n        <\/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 superEggDrop = function(k, n) {\n    let dp = new Array(k + 1).fill(0);\n    let moves = 0;\n\n    while(dp[k] < n){\n        moves++;\n        for(let i = k; i >= 1; i--) {\n            dp[i] = 1 + dp[i] + dp[i-1];\n        }\n    }\n    return moves;\n};\n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n        <pre><code class=\"language-python\">\ndef superEggDrop(k, n):\n    dp = [0] * (k + 1)\n    moves = 0\n\n    while dp[k] < n:\n        moves += 1\n        for i in range(k, 0, -1):\n            dp[i] = 1 + dp[i] + dp[i-1]\n\n    return moves\n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n        <pre><code class=\"language-java\">\nclass Solution {\n    public int superEggDrop(int k, int n) {\n        int[] dp = new int[k + 1];\n        int moves = 0;\n\n        while(dp[k] < n){\n            moves++;\n            for(int i = k; i >= 1; i--){\n                dp[i] = 1 + dp[i] + dp[i-1];\n            }\n        }\n\n        return moves;\n    }\n}\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n        <pre><code class=\"language-cpp\">\n#include &lt;vector&gt;\nusing namespace std;\n\nclass Solution {\npublic:\n    int superEggDrop(int k, int n) {\n        vector<int> dp(k + 1, 0);\n        int moves = 0;\n\n        while(dp[k] < n){\n            moves++;\n            for(int i = k; i >= 1; i--){\n                dp[i] = 1 + dp[i] + dp[i-1];\n            }\n        }\n\n        return moves;\n    }\n};\n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n        <pre><code class=\"language-c\">\n#include &lt;stdio.h&gt;\n\nint superEggDrop(int k, int n) {\n    int dp[k + 1];\n    \n    for(int i = 0; i <= k; i++)\n        dp[i] = 0;\n\n    int moves = 0;\n\n    while(dp[k] < n){\n        moves++;\n\n        for(int i = k; i >= 1; i--){\n            dp[i] = 1 + dp[i] + dp[i-1];\n        }\n    }\n\n    return moves;\n}\n   <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n        <pre><code class=\"language-csharp\">\npublic class Solution {\n    public int SuperEggDrop(int k, int n) {\n        int[] dp = new int[k + 1];\n        int moves = 0;\n\n        while(dp[k] < n){\n            moves++;\n\n            for(int i = k; i >= 1; i--){\n                dp[i] = 1 + dp[i] + dp[i - 1];\n            }\n        }\n\n        return moves;\n    }\n}\n  <\/code><\/pre>\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\n","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Problem Statement: You are given k identical eggs and you have access to a building with n floors labeled from 1 to n. You know that there exists a floor f where 0<\/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":[322,260,211,811,810,174,172,173],"tags":[],"class_list":{"0":"post-11777","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-algorithms-and-data-structures","7":"category-c-c-plus-plus","8":"category-data-structures","9":"category-data-structures-and-algorithms","10":"category-dsa","11":"category-java","12":"category-javascript","13":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11777","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=11777"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11777\/revisions"}],"predecessor-version":[{"id":11778,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11777\/revisions\/11778"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=11777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=11777"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=11777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}