{"id":11742,"date":"2026-03-14T10:50:15","date_gmt":"2026-03-14T05:20:15","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=11742"},"modified":"2026-03-14T19:20:24","modified_gmt":"2026-03-14T13:50:24","slug":"jump-game-dp","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/jump-game-dp\/","title":{"rendered":"Jump Game DP"},"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 an integer array nums. You are initially positioned at the array&#8217;s first index, and each element in the array represents your maximum jump length at that position.\n        <\/p>\n\n        <p>\n          Return <code>true<\/code> if you can reach the last index, or <code>false<\/code> otherwise.\n        <\/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> true<\/p>\n                <p>\n                  <code>Explanation:<\/code>\n                  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 = [3,2,1,0,4]<\/p>\n\n                <p><strong>Output:<\/strong> false<\/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] <= 10<sup>5<\/sup><\/code>\n                <\/p>\n                    \n                    <h2>Time Complexity:<\/h2>\n                    <li>\n                      <p><strong>Time Complexity = O(n<sup>2<\/sup>)<\/strong>\n                      <\/li>\n                    <h2>Space Complexity:<\/h2>\n                    <li>\n                      <p><strong>Space Complexity = O(n)<\/strong><\/p>\n                    <\/li>\n\n                <h2>Approach<\/h2>\n                <ul>\n                  <li>Start from <code>index 0<\/code> and try all possible <strong>jumps<\/strong> from that position.<\/li>\n                  <li>Use <strong>DFS recursion <\/strong>to check if we can reach the <code>last index<\/code>.<\/li>\n                  <li>From a position <code>start<\/code>, try jumps from <strong>1 to nums[start]<\/strong>.<\/li>\n                  <li>If any jump leads to the <strong>last index<\/strong> (or a position that can reach it), <code>return true<\/code>.<\/li>\n                  <li>Use a <code>dp array<\/code> (memoization) to store results for already visited <strong>indices to avoid recomputation<\/strong>.<\/li>\n                  <li>If <strong>dp[start]<\/strong> is already computed, <code>return the stored value<\/code>.<\/li>\n                  <li>Store the <code>result<\/code> (true or false) in dp[start] before <strong>returning<\/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   end = 4\n   dp = [-1, -1, -1, -1, -1]\n\nStep 1: Call dfs(0)\n   start = 0\n   nums[0] = 2 \u2192 possible jumps = 1 or 2\n\nStep 2: Try jump of 1\n   Call dfs(1)\n\nStep 3: dfs(1)\n   nums[1] = 3 \u2192 possible jumps = 1, 2, 3\n\nStep 4: Try jump of 1\n   Call dfs(2)\n\nStep 5: dfs(2)\n   nums[2] = 1 \u2192 possible jump = 1\n\nStep 6: Try jump of 1\n   Call dfs(3)\n\nStep 7: dfs(3)\n   nums[3] = 1 \u2192 possible jump = 1\n\nStep 8: Try jump of 1\n   Call dfs(4)\n\nStep 9: dfs(4)\n   start === end\n   \u2192 return true\n\nStep 10: Backtrack\n   dfs(3) receives true\n   dp[3] = true\n\nStep 11: Backtrack\n   dfs(2) receives true\n   dp[2] = true\n\nStep 12: Backtrack\n   dfs(1) receives true\n   dp[1] = true\n\nStep 13: Backtrack\n   dfs(0) receives true\n   dp[0] = true\n\nFinal dp array:\n   [true, true, true, true, -1]\n  <\/pre> \n  \n  <p><strong>Output:<\/strong> <code>true<\/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 canJump = function(nums) {\n    let end = nums.length - 1;\n    let dp = new Array(nums.length).fill(-1);\n\n    let dfs = (start) => {\n        if(start === end) return true;\n\n        if(dp[start] != -1) return dp[start];\n\n        let ans = false;\n\n        for(let i = 1; i <= nums[start] &#038;&#038; !ans; i++){\n            if(start + i <= end){\n                ans = ans || dfs(start + i);\n            }\n        }\n\n        dp[start] = ans;\n        return ans;\n    }\n\n    return dfs(0);\n};\n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n        <pre><code class=\"language-python\">\nclass Solution:\n    def canJump(self, nums):\n        end = len(nums) - 1\n        dp = [-1] * len(nums)\n\n        def dfs(start):\n            if start == end:\n                return True\n\n            if dp[start] != -1:\n                return dp[start]\n\n            ans = False\n\n            for i in range(1, nums[start] + 1):\n                if not ans and start + i <= end:\n                    ans = ans or dfs(start + i)\n\n            dp[start] = ans\n            return ans\n\n        return dfs(0)\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\n    public boolean dfs(int start, int[] nums, int[] dp) {\n        int end = nums.length - 1;\n\n        if(start == end) return true;\n\n        if(dp[start] != -1) return dp[start] == 1;\n\n        boolean ans = false;\n\n        for(int i = 1; i <= nums[start] &#038;&#038; !ans; i++){\n            if(start + i <= end){\n                ans = ans || dfs(start + i, nums, dp);\n            }\n        }\n\n        dp[start] = ans ? 1 : 0;\n        return ans;\n    }\n\n    public boolean canJump(int[] nums) {\n        int[] dp = new int[nums.length];\n        Arrays.fill(dp, -1);\n\n        return dfs(0, nums, dp);\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;iostream&gt;\nclass Solution {\npublic:\n    bool dfs(int start, vector<int>& nums, vector<int>& dp) {\n        int end = nums.size() - 1;\n\n        if(start == end) return true;\n\n        if(dp[start] != -1) return dp[start];\n\n        bool ans = false;\n\n        for(int i = 1; i <= nums[start] &#038;&#038; !ans; i++) {\n            if(start + i <= end) {\n                ans = ans || dfs(start + i, nums, dp);\n            }\n        }\n\n        dp[start] = ans;\n        return ans;\n    }\n\n    bool canJump(vector<int>& nums) {\n        vector<int> dp(nums.size(), -1);\n        return dfs(0, nums, 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#include &lt;stdbool.h&gt;\n\nbool dfs(int start, int* nums, int size, int* dp) {\n    int end = size - 1;\n\n    if(start == end)\n        return true;\n\n    if(dp[start] != -1)\n        return dp[start];\n\n    bool ans = false;\n\n    for(int i = 1; i <= nums[start] &#038;&#038; !ans; i++) {\n        if(start + i <= end) {\n            ans = ans || dfs(start + i, nums, size, dp);\n        }\n    }\n\n    dp[start] = ans;\n    return ans;\n}\n\nbool canJump(int* nums, int numsSize) {\n    int* dp = (int*)malloc(numsSize * sizeof(int));\n\n    for(int i = 0; i < numsSize; i++)\n        dp[i] = -1;\n\n    bool result = dfs(0, nums, numsSize, dp);\n\n    free(dp);\n    return result;\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\n    public bool Dfs(int start, int[] nums, int[] dp)\n    {\n        int end = nums.Length - 1;\n\n        if(start == end)\n            return true;\n\n        if(dp[start] != -1)\n            return dp[start] == 1;\n\n        bool ans = false;\n\n        for(int i = 1; i <= nums[start] &#038;&#038; !ans; i++)\n        {\n            if(start + i <= end)\n            {\n                ans = ans || Dfs(start + i, nums, dp);\n            }\n        }\n\n        dp[start] = ans ? 1 : 0;\n        return ans;\n    }\n\n    public bool CanJump(int[] nums) {\n        int[] dp = new int[nums.Length];\n        Array.Fill(dp, -1);\n\n        return Dfs(0, nums, dp);\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\n","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Problem Statement: You are given an integer array nums. You are initially positioned at the array&#8217;s first index, and each element in the array represents your maximum jump length at that position. Return true if you can reach the last index, or false otherwise. Examples: Example 1: Input: nums = [2,3,1,1,4] Output: true Explanation:<\/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":[210,322,260,176,175,211,810,174,172,173],"tags":[],"class_list":["post-11742","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-dsa","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11742","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=11742"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11742\/revisions"}],"predecessor-version":[{"id":11757,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11742\/revisions\/11757"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=11742"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=11742"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=11742"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}