{"id":10116,"date":"2025-09-26T14:28:20","date_gmt":"2025-09-26T08:58:20","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10116"},"modified":"2025-09-26T14:52:46","modified_gmt":"2025-09-26T09:22:46","slug":"climbing-stairs","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/climbing-stairs\/","title":{"rendered":"Climbing Stairs"},"content":{"rendered":"\n<!-- PrismJS for Syntax Highlighting -->\n<link href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.min.css\" rel=\"stylesheet\">\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\n  <div class=\"wp_blog_explanation\">\n    <h2>Problem Statement:<\/h2>\n    <p>\n        You are climbing a staircase. It takes <code>n<\/code> steps to reach the top.\n    <\/p>\n    <p>Each time you can either climb <code>1<\/code> or <code>2<\/code> steps. In how many distinct ways can you climb to the top?<\/p>\n    \n    <h3>Example 1:<\/h2>\n    <p><strong>Input:<\/strong> n = 2<\/p>\n    <p><strong>Output:<\/strong> 2<\/p>\n    <p><strong>Explanation:<\/strong>  There are two ways to climb to the top.<\/p>\n    <ul>\n        <li>1 step + 1 step<\/li>\n        <li>2 steps<\/li>\n    <\/ul>\n\n        <h3>Example 2:<\/h2>\n    <p><strong>Input:<\/strong> n = 3<\/p>\n    <p><strong>Output:<\/strong> 3<\/p>\n    <p><strong>Explanation:<\/strong> There are three ways to climb to the top.\n        <ul>\n            <li>1 step + 1 step + 1 step<\/li>\n            <li>1 step + 2 steps<\/li>\n            <li>2 steps + 1 step<\/li>\n        <\/ul>\n\n<\/p>\n\n    <h3>Constraints<\/h3>\n    <ul>\n       <li><code>1 <= n <= 45<\/code><\/li>\n    <\/ul>\n    \n<h2>Approach:<\/h2>\n   <ul>\n    <li><strong>Identify the recurrence relation:<\/strong>\n      <ul>\n        <li>To reach <code>step n<\/code>, there are only <strong>two possibilities<\/strong>:\n          <ul>\n            <li>You came from <code>step n-1<\/code> (taking 1 step).<\/li>\n            <li>You came from <code>step n-2<\/code> (taking 2 steps).<\/li>\n          <\/ul>\n        <\/li>\n        <li>So, the <strong>total ways<\/strong> to reach <code>step n<\/code> is:<\/li>\n        <p><code>dp[n] = dp[n-1] + dp[n-2]<\/code><\/p>\n      <\/ul>\n    <\/li>\n\n    <li><strong>Base cases:<\/strong>\n      <ul>\n        <li><code>dp[1] = 1<\/code> \u2192 Only 1 way to climb <strong>1 step<\/strong>.<\/li>\n        <li><code>dp[2] = 2 <\/code> \u2192 Either take <strong>two 1-steps or one 2-step<\/strong>.<\/li>\n      <\/ul>\n    <\/li>\n\n    <li><strong>DP array construction:<\/strong>\n      <ul>\n        <li>We create an array dp where <code>dp[i]<\/code> represents the number of ways to reach <strong>step i<\/strong>.<\/li>\n        <li>Start from <code>i = 3<\/code> and use the <code>recurrence relation to fill the array<\/code>.<\/li>\n      <\/ul>\n    <\/li>\n\n    <li><code>Return dp[n]<\/code>, which contains the number of ways to reach the <code>nth step.<\/code><\/li>\n  \n  <\/ul>\n\n    <h2>Time & Space Complexity:<\/h2>\n    <p><strong>Time Complexity:<\/strong> <code>O(n)<\/code><\/p>\n    <p><strong>Space Complexity:<\/strong> <code>O(n)<\/code><\/p>\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>n = 5<\/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);\">\n\nStep 0: Start Function: climbStairs(5)\nn = 5\ndp = [0, 1, 2]   \/\/ base cases\n\nIteration (i = 3):\n- dp[3] = dp[2] + dp[1] = 2 + 1 = 3\n- dp = [0, 1, 2, 3]\n\nIteration (i = 4):\n- dp[4] = dp[3] + dp[2] = 3 + 2 = 5\n- dp = [0, 1, 2, 3, 5]\n\nIteration (i = 5):\n- dp[5] = dp[4] + dp[3] = 5 + 3 = 8\n- dp = [0, 1, 2, 3, 5, 8]\n\nLoop ends (i > n)\n\nStep 3: End\nReturn dp[5] = 8\n  <\/pre> \n  \n  <p><strong>Output:<\/strong> <code>8<\/code><\/p> \n<\/div>\n\n        <h2>Visualisation:<\/h2>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/09\/4.png\" alt=\"\">\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 climbStairs = function(n) {\n    let dp = [0, 1, 2];\n    for (let i = 3; i <= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n};\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\ndef climbStairs(n):\n    dp = [0, 1, 2]\n    for i in range(3, n + 1):\n        dp.append(dp[i - 1] + dp[i - 2])\n    return dp[n]\n\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 climbStairs(int n) {\n        int[] dp = new int[n + 1];\n        dp[0] = 0;\n        dp[1] = 1;\n        dp[2] = 2;\n\n        for (int i = 3; i <= n; i++) {\n            dp[i] = dp[i - 1] + dp[i - 2];\n        }\n        return dp[n];\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;\nusing namespace std;\n\nint climbStairs(int n) {\n    vector<int> dp(n + 1, 0);\n    dp[0] = 0;\n    dp[1] = 1;\n    dp[2] = 2;\n\n    for (int i = 3; i <= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[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#include &lt;stdlib.h&gt;\n\nint climbStairs(int n) {\n    int* dp = (int*)malloc((n + 1) * sizeof(int));\n    dp[0] = 0;\n    dp[1] = 1;\n    dp[2] = 2;\n\n    for (int i = 3; i <= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    int result = dp[n];\n    free(dp);\n    return result;\n}\n <\/code><\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n      <pre><code class=\"language-csharp\">\npublic class Solution {\n    public int ClimbStairs(int n) {\n        int[] dp = new int[n + 1];\n        dp[0] = 0;\n        dp[1] = 1;\n        dp[2] = 2;\n\n        for (int i = 3; i <= n; i++) {\n            dp[i] = dp[i - 1] + dp[i - 2];\n        }\n        return dp[n];\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 climbing a staircase. It takes n steps to reach the top. Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top? Example 1: Input: n = 2 Output: 2 Explanation: There are two ways to climb to the top.<\/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":[210,322,176,175,211,810,174,172,173],"tags":[],"class_list":{"0":"post-10116","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-algorithms","7":"category-algorithms-and-data-structures","8":"category-csharp","9":"category-cplusplus","10":"category-data-structures","11":"category-dsa","12":"category-java","13":"category-javascript","14":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10116","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=10116"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10116\/revisions"}],"predecessor-version":[{"id":10126,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10116\/revisions\/10126"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}