{"id":11762,"date":"2026-03-14T12:13:57","date_gmt":"2026-03-14T06:43:57","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=11762"},"modified":"2026-03-14T19:22:43","modified_gmt":"2026-03-14T13:52:43","slug":"jump-game-ii","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/jump-game-ii\/","title":{"rendered":"Jump Game II"},"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 a 0-indexed array of integers nums of length n. You are initially positioned at index 0.\n        <\/p>\n\n        <p>\n            Each element nums[i] represents the maximum length of a forward jump from index i. In other words, if you are at index i, you can jump to any index (i + j) where:\n        <\/p>\n        <ul>\n            <li><code>0 <= j <= nums[i]<\/code> and <\/li>\n            <li><code>i + j < n<\/code><\/li>\n        <\/ul>\n\n        <p>Return the minimum number of jumps to reach index <code>n - 1<\/code>. The test cases are generated such that you can reach index <code>n - 1<\/code>.<\/p>\n\n                <h2>Examples:<\/h2>\n\n                <h3>Example 1:<\/h3>\n                <p><strong>Input:<\/strong> nums = [2,3,1,1,4]\n                <\/p>\n                <p><strong>Output:<\/strong> 2<\/p>\n                <p>\n                  <code>Explanation:<\/code>\n                  The minimum number of jumps to reach the last index is 2. Jump 1 step from index 0 to 1, then 3 steps to the last index.\n                <\/p>\n\n                <h3>Example 2:<\/h3>\n                <p><strong>Input:<\/strong> nums = [2, 3, 0, 1, 4]<\/p>\n\n                <p><strong>Output:<\/strong> 2<\/p>\n                  <!-- <p>\n                  <code>Explanation:<\/code>\n                 You will always arrive at index 3 no matter what. Its maximum jump length is 0, which makes it impossible to reach the last index.\n                <\/p> -->\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>\n                  1 <= nums.length <= 10<sup>4<\/sup>\n                <\/code><\/p>\n\n                <p>\n                  <code>0 <= nums[i] <= 1000<\/code>\n                <\/p>\n                <p>\n                    It's guaranteed that you can reach <code>nums[n - 1].<\/code>\n                <\/p>\n                    \n                    <h2>Time Complexity:<\/h2>\n                    <li>\n                      <p><strong>Time Complexity = O(n)<\/strong>\n                      <\/li>\n                    <h2>Space Complexity:<\/h2>\n                    <li>\n                      <p><strong>Space Complexity = O(1)<\/strong><\/p>\n                    <\/li>\n\n                <h2>Approach<\/h2>\n                <ul>\n                    <li><code>Traverse<\/code> the array while tracking the <strong>maximum index<\/strong> reachable from the current positions.<\/li>\n                    <li>Use three variables:\n                        <ul>\n                            <li><code>farthest<\/code> \u2192 the farthest index that can be reached from the <strong>current range<\/strong>.<\/li>\n                            <li><code>currEnd <\/code>\u2192 the end of the current <strong>jump range<\/strong>.<\/li>\n                            <li><code>jumps<\/code> \u2192 number of <strong>jumps taken<\/strong>.<\/li>\n                        <\/ul>\n                    <\/li>\n                    <li>For each <code>index i<\/code>, update the farthest reachable position using <strong>farthest = Math.max(farthest, i + nums[i])<\/strong>.<\/li>\n                    <li>\n                        When i reaches <code>currEnd<\/code>, it means the current jump range is exhausted, so:\n                        <ul>\n                            <li>Increase <code>currEnd<\/code>.<\/li>\n                            <li>Update currEnd to farthest to start the <code>next jump range<\/code>.<\/li>\n                        <\/ul>\n                    <\/li>\n\n                    <li>Continue this process until the <strong>second last index<\/strong>, since the <strong>last index<\/strong> does not require <strong>another jump<\/strong>.<\/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>nums = [2, 3, 1, 1, 4]<\/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);\">\nInitialization:\n   currEnd = 0\n   farthest = 0\n   jumps = 0\n\nStep 1: i = 0\n   Update farthest:\n   farthest = max(0, 0 + nums[0])\n   farthest = max(0, 2)\n   farthest = 2\n\n   Check: i == currEnd ?\n   0 == 0 \u2192 true\n\n   Take a jump\n   jumps = 1\n   currEnd = farthest = 2\n\nStep 2: i = 1\n   Update farthest:\n   farthest = max(2, 1 + nums[1])\n   farthest = max(2, 4)\n   farthest = 4\n\n   Check: i == currEnd ?\n   1 == 2 \u2192 false\n   No jump taken\n\nStep 3: i = 2\n   Update farthest:\n   farthest = max(4, 2 + nums[2])\n   farthest = max(4, 3)\n   farthest = 4\n\n   Check: i == currEnd ?\n   2 == 2 \u2192 true\n\n   Take a jump\n   jumps = 2\n   currEnd = farthest = 4\n\nLoop stops at i = nums.length - 2 (i = 3 was not needed to extend range further)\nCurrent range already reaches the last index.\n  <\/pre> \n  \n  <p><strong>Output:<\/strong> <code>2<\/code><\/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\">\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 jump = function(nums) {\n    let currEnd = farthest = jumps = 0;\n    for(let i=0; i < nums.length - 1; i++) {\n        farthest = Math.max(farthest, i + nums[i]);\n        if(i == currEnd) {\n            currEnd = farthest;\n            jumps++;\n        }\n    }\n    return jumps;\n};\n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n        <pre><code class=\"language-python\">\ndef jump(nums):\n    currEnd = 0\n    farthest = 0\n    jumps = 0\n\n    for i in range(len(nums) - 1):\n        farthest = max(farthest, i + nums[i])\n\n        if i == currEnd:\n            currEnd = farthest\n            jumps += 1\n\n    return jumps\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 jump(int[] nums) {\n        int currEnd = 0;\n        int farthest = 0;\n        int jumps = 0;\n\n        for(int i = 0; i < nums.length - 1; i++) {\n            farthest = Math.max(farthest, i + nums[i]);\n\n            if(i == currEnd) {\n                currEnd = farthest;\n                jumps++;\n            }\n        }\n\n        return jumps;\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;\n#include &lt;algorithm&gt;\n\nusing namespace std;\n\nclass Solution {\npublic:\n    int jump(vector<int>& nums) {\n        int currEnd = 0;\n        int farthest = 0;\n        int jumps = 0;\n\n        for(int i = 0; i < nums.size() - 1; i++) {\n            farthest = max(farthest, i + nums[i]);\n\n            if(i == currEnd) {\n                currEnd = farthest;\n                jumps++;\n            }\n        }\n\n        return jumps;\n    }\n};\n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n        <pre><code class=\"language-c\">\nint jump(int* nums, int numsSize) {\n    int currEnd = 0;\n    int farthest = 0;\n    int jumps = 0;\n\n    for(int i = 0; i < numsSize - 1; i++) {\n        if(farthest < i + nums[i])\n            farthest = i + nums[i];\n\n        if(i == currEnd) {\n            currEnd = farthest;\n            jumps++;\n        }\n    }\n\n    return jumps;\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 Jump(int[] nums) {\n        int currEnd = 0;\n        int farthest = 0;\n        int jumps = 0;\n\n        for(int i = 0; i < nums.Length - 1; i++) {\n            farthest = Math.Max(farthest, i + nums[i]);\n\n            if(i == currEnd) {\n                currEnd = farthest;\n                jumps++;\n            }\n        }\n\n        return jumps;\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 a 0-indexed array of integers nums of length n. You are initially positioned at index 0. Each element nums[i] represents the maximum length of a forward jump from index i. In other words, if you are at index i, you can jump to any index (i + j) where:<\/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-11762","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\/11762","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=11762"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11762\/revisions"}],"predecessor-version":[{"id":11763,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11762\/revisions\/11763"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=11762"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=11762"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=11762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}