{"id":9734,"date":"2025-08-28T18:23:55","date_gmt":"2025-08-28T12:53:55","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9734"},"modified":"2025-09-30T12:41:25","modified_gmt":"2025-09-30T07:11:25","slug":"fibnumber_usingrecursion","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/fibnumber_usingrecursion\/","title":{"rendered":"Fibonacci Number using Recursion"},"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; 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\/* 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<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>What is a Fibonacci Number?<\/h2>\n        <p><strong>The Fibonacci sequence<\/strong> is a famous <code>mathematical series<\/code> in which each number is the <strong>sum of two preceding ones<\/strong> It\u2019s defined by the recurrence relation:<\/p>\n        <ul>\n            <li><code>F(0) = 0<\/code><\/li>\n            <li><code>F(1) = 1<\/code><\/li>\n             <li><code>F(n) = F(n-1) + F(n-2)  for n > 1<\/code><\/li>\n        <\/ul>\n\n        <h2>This generates a series like:<\/h2>\n        <p><strong><code>0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...<\/code><\/strong><\/p>\n        <ul>\n            <li><strong>Each number<\/strong> is the <code>sum of the two<\/code> before it.<\/li>\n            <li>This <strong>sequence appears<\/strong> frequently in nature (e.g., flower petals, pine cones, and spiral shells), in <code>algorithms<\/code> <strong>(like dynamic programming)<\/strong>, and <strong>even in computer science problems<\/strong> related to <code>recursion, time complexity, and optimization<\/code>.<\/li>\n        <\/ul>\n\n                <h2>Approach: Recursion<\/h2>\n                <p><srtong>Recursion is a technique<\/srtong> where a function solves a problem by <code>calling itself on smaller sub-problems<\/code>.<\/p>\n                <p>In the context of <strong>Fibonacci:<\/strong><\/p>\n                <ul>\n                    <li>To compute <code>fib(n)<\/code>, we:<\/li>\n                    <li><code>Ask: <\/code><strong>\u201cWhat is fib(n-1)?\u201d<\/strong><\/li>\n                    <li><code>Ask: <\/code><strong>\u201cWhat is fib(n-2)?\u201d<\/strong><\/li>\n                    <li><code>Return: <\/code>the sum of the two <strong>fib(n) = fib(n-1) + fib(n-2)<\/strong><\/li>\n                    <li><strong>This continues until we reach the base cases: <\/strong>\n                    <ul>\n                        <li><code>If n == 0, return 0<\/code><\/li>\n                        <li><code>If n == 1, return 1<\/code><\/li>\n                    <\/ul>\n                    <\/li>\n                <\/ul>\n\n                <h2>Time Complexity: <code>O(2<sup>n<\/sup>)<\/code><\/h2>\n                <li>\n                 This is <strong>because each function call makes 2 recursive calls<\/strong>, leading to a <code>binary tree of calls<\/code>.\n                    <strong>For large n<\/strong>, this becomes very inefficient, as many subproblems are solved repeatedly.\n                <\/li>\n\n                <h2>Space Complexity: <code>O(n)<\/code><\/h2>\n                <li>\n                  Although the <strong>number of calls is exponential<\/strong>, the <code>maximum<\/code> call depth is <code>n<\/code>.\n\n                <\/li>\n                <li>So, <strong>the space used on the call stack<\/strong> is <code>linear<\/code> in the worst case.<\/li>\n\n                <h2>Sample Outputs:<\/h2>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-28-at-6.17.59\u202fPM.png\" alt=\"\">\n    <\/div>\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        <!-- JavaScript -->\n        <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n            <pre><code class=\"language-javascript\">\nvar fib = function(n) {\n    if (n <= 1)\n        return n;\n    return fib(n - 1) + fib(n - 2);\n};\nprintDescending(5);       \n<\/code><\/pre>\n        <\/div>\n\n        <!-- Python -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n            <pre><code class=\"language-python\">\nclass Solution(object):\n    def fib(self, n):\n        \"\"\"\n        :type n: int\n        :rtype: int\n        \"\"\"\n        if n <= 1:\n            return n\n        return self.fib(n - 1) + self.fib(n - 2)\n            <\/code><\/pre>\n        <\/div>\n\n        <!-- Java -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n            <pre><code class=\"language-java\">\nclass Solution {\n    public int fib(int n) {\n        if (n <= 1)\n            return n;\n        return fib(n - 1) + fib(n - 2);\n    }\n}\n            <\/code><\/pre>\n        <\/div>\n\n        <!-- C++ -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n            <pre><code class=\"language-cpp\">\nclass Solution {\npublic:\n    int fib(int n) {\n        if (n <= 1)\n            return n;\n        return fib(n - 1) + fib(n - 2);\n    }\n};\n        <\/code><\/pre>\n        <\/div>\n\n        <!-- C -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n            <pre><code class=\"language-c\">\nint fib(int n) {\n    if (n <= 1)\n        return n;\n    return fib(n - 1) + fib(n - 2);\n}\n                    <\/code><\/pre>\n        <\/div>\n\n        <!-- C# -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n            <pre><code class=\"language-csharp\">\npublic class Solution {\n    public int Fib(int n) {\n        if (n <= 1)\n            return n;\n        return Fib(n - 1) + Fib(n - 2);\n    }\n}         <\/code><\/pre>\n        <\/div>\n    <\/div>\n<\/div>\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 What is a Fibonacci Number? The Fibonacci sequence is a famous mathematical series in which each number is the sum of two preceding ones It\u2019s defined by the recurrence relation: F(0) = 0 F(1) = 1 F(n) = F(n-1) + F(n-2) for n > 1 This generates a series like: 0, 1, 1, 2,<\/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":[210,322,260,176,175,211,811,810,174,172,173],"tags":[],"class_list":["post-9734","post","type-post","status-publish","format-standard","category-algorithms","category-algorithms-and-data-structures","category-c-c-plus-plus","category-csharp","category-cplusplus","category-data-structures","category-data-structures-and-algorithms","category-dsa","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9734","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=9734"}],"version-history":[{"count":3,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9734\/revisions"}],"predecessor-version":[{"id":10176,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9734\/revisions\/10176"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9734"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9734"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9734"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}