{"id":7711,"date":"2025-07-09T17:18:31","date_gmt":"2025-07-09T11:48:31","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=7711"},"modified":"2025-07-09T17:19:59","modified_gmt":"2025-07-09T11:49:59","slug":"remove-outermost-parentheses-without-stack","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/remove-outermost-parentheses-without-stack\/","title":{"rendered":"Remove Outermost Parentheses &#8211; without Stack"},"content":{"rendered":"\n<!-- 1021: 2nd approach-->\n<!-- PrismJS for Syntax Highlighting -->\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: #f8c291;\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    \/* 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    .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    .wp_blog_explanation code {\n        background: #fef9f4;\n        padding: 3px 6px;\n        border-radius: 4px;\n        font-family: \"Courier New\", monospace;\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    .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    .wp_blog_code-tab-button:hover {\n        background: var(--secondary);\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    .wp_blog_code-tab-content.active {\n        display: block;\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<\/style>\n\n<div class=\"wp_blog_container wp_blog_theme\">\n<h1 class=\"wp_blog_main-heading\"><\/h1>\n\n<div class=\"wp_blog_explanation\">\n    <h2>Problem Statement:<\/h2>\n    <p>\n       A valid parentheses string is either empty <code>\"\"<\/code>, <code>\"(\" + A + \")\"<\/code>, or <code>A + B<\/code>, where <code>A<\/code> and <code>B<\/code> are valid parentheses strings, and <code>+<\/code> represents string concatenation.\n    <\/p>\n\n    <ul>\n        <li>For example, <code>\"\"<\/code>, <code>\"()\"<\/code>, <code>\"(())()\"<\/code>, and <code>\"(()(()))\"<\/code> are all valid parentheses strings.<\/li>\n    <\/ul>\n\n    <p>\n        A valid parentheses string <code>s<\/code> is primitive if it is nonempty, and there does not exist a way to split it into <code>s = A + B<\/code>, with <code>A<\/code> and <code>B<\/code> nonempty valid parentheses strings.\n    <\/p>\n<br\/>\n    <p>\n        Given a valid parentheses string s, consider its primitive decomposition: <code>s = P1 + P2 + ... + Pk<\/code>, where <code>Pi<\/code> are primitive valid parentheses strings.\n    <\/p>\n<br\/>\n    <p>\n        Return <code>s<\/code> after removing the outermost parentheses of every primitive string in the primitive decomposition of <code>s<\/code>.\n    <\/p>\n\n    <h2>Examples:<\/h2>\n    <p><strong>Example 1:<\/strong><\/p>\n    <p><strong>Input:<\/strong><\/p>\n        <p>s = &#8220;(()())(())&#8221;<\/p>\n    <p><strong>Output:<\/strong><code>\"()()()\"<\/code><\/p>\n    <p><strong>Explanation<\/strong><\/p>\n    <p>The input string is &#8220;(()())(())&#8221;, with primitive decomposition &#8220;(()())&#8221; + &#8220;(())&#8221;.\n    After removing outer parentheses of each part, this is &#8220;()()&#8221; + &#8220;()&#8221; = &#8220;()()()&#8221;.<\/p>\n\n    <p><strong>Example 2:<\/strong><\/p>\n    <p><strong>Input:<\/strong><\/p>\n        <p>s = &#8220;(()())(())(()(()))&#8221;<\/p>\n    <p><strong>Output:<\/strong><code>\"()()()()(())\"<\/code><\/p>\n    <p><strong>Explanation<\/strong><\/p>\n    <p>\n        The input string is &#8220;(()())(())(()(()))&#8221;, with primitive decomposition &#8220;(()())&#8221; + &#8220;(())&#8221; + &#8220;(()(()))&#8221;.\n        After removing outer parentheses of each part, this is &#8220;()()&#8221; + &#8220;()&#8221; + &#8220;()(())&#8221; = &#8220;()()()()(())&#8221;.\n    <\/p>\n\n    <p><strong>Example 2:<\/strong><\/p>\n    <p><strong>Input:<\/strong><\/p>\n        <p>s = &#8220;()()&#8221;<\/p>\n    <p><strong>Output:<\/strong><code>\"\"<\/code><\/p>\n    <p><strong>Explanation<\/strong><\/p>\n    <p>\n        The input string is &#8220;()()&#8221;, with primitive decomposition &#8220;()&#8221; + &#8220;()&#8221;.\n        After removing outer parentheses of each part, this is &#8220;&#8221; + &#8220;&#8221; = &#8220;&#8221;.\n    <\/p>\n\n\n    <h2>Constraints:<\/h2>\n    <ul>\n        <li><code>1 <= s.length <= 10<sup>5<\/sup><\/code><\/li>\n        <li><code>s[i]<\/code> is either <code>'('<\/code> or <code>')'<\/code>.<\/li>\n        <li><code>s<\/code>is a valid parentheses string.<\/li>\n    <\/ul>\n\n    <h2>Second Approach: Without Stack<\/h2>\n    <ul>\n        <li>Initialize: a counter <code>level<\/code> to <code>-1<\/code> and an empty string <code>ans<\/code>.\n        <\/li>\n        <li><strong>Traverse<\/strong> each character of the string <code>s<\/code>.<\/li>\n\n        <li>If the character is <code>'('<\/code>\n            <ul>\n                <li>Increment <code>level<\/code>.<\/li>\n                <li>If <code>level<\/code> is not <code>0<\/code>, append <code>'('<\/code> to <code>ans<\/code>.<\/li>\n            <\/ul>\n        <\/li>\n\n        <li>If the character is <code>')'<\/code>\n            <ul>\n                <li>If <code>level<\/code> is not <code>0<\/code>, append <code>')'<\/code> to ans.<\/li>\n                <li>Then decrement <code>level<\/code>.<\/li>\n            <\/ul>\n        <\/li>\n\n        <li><strong>Return<\/strong> the final <code> ans<\/code> string.<\/li>\n\n    <\/ul>\n\n    <h2>Visualisation:<\/h2>\n    <img decoding=\"async\"\n        src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/07\/Screenshot-2025-07-09-at-12.30.01\u202fPM.png\"\n        alt=\"stack\"\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> \n                <\/p>\n                <\/li>\n\n<h2>Dry Run<\/h2> \n<div style=\"background: #f9f9f9; border-left: 4px solid var(--primary); padding: 1rem; border-radius: var(--tab-radius); margin: 1rem 0;\"> \n  <p><strong>Input:<\/strong><\/p> \n  <pre style=\"white-space: pre-wrap; background: #fff5ea; padding: 1rem; border-radius: 8px; overflow-x: auto;\"> \ns = \"(()())(())(()(()))\" \n  <\/pre> \n\n  <p><strong>State Transitions:<\/strong><\/p> \n  <pre style=\"white-space: pre-wrap; background: #fff5ea; padding: 1rem; border-radius: 8px; overflow-x: auto;\"> \nInitialize: level = -1, ans = \"\"\n\ni = 0 \u2192 s[0] = \"(\"\n\u2192 ++level \u2192 level = 0\n\u2192 level is 0 \u2192 Do NOT add to ans\n\ni = 1 \u2192 s[1] = \"(\"\n\u2192 ++level \u2192 level = 1\n\u2192 level is non-zero \u2192 ans += \"(\" \u2192 ans = \"(\"\n\ni = 2 \u2192 s[2] = \")\"\n\u2192 level is non-zero \u2192 ans += \")\" \u2192 ans = \"()\"\n\u2192 --level \u2192 level = 0\n\ni = 3 \u2192 s[3] = \")\"\n\u2192 level is 0 \u2192 Do NOT add to ans\n\u2192 --level \u2192 level = -1\n\ni = 4 \u2192 s[4] = \"(\"\n\u2192 ++level \u2192 level = 0\n\u2192 level is 0 \u2192 Do NOT add to ans\n\ni = 5 \u2192 s[5] = \"(\"\n\u2192 ++level \u2192 level = 1\n\u2192 level is non-zero \u2192 ans += \"(\" \u2192 ans = \"()(\"\n\ni = 6 \u2192 s[6] = \")\"\n\u2192 level is non-zero \u2192 ans += \")\" \u2192 ans = \"()()\"\n\u2192 --level \u2192 level = 0\n\ni = 7 \u2192 s[7] = \")\"\n\u2192 level is 0 \u2192 Do NOT add to ans\n\u2192 --level \u2192 level = -1\n\ni = 8 \u2192 s[8] = \"(\"\n\u2192 ++level \u2192 level = 0\n\u2192 level is 0 \u2192 Do NOT add to ans\n\ni = 9 \u2192 s[9] = \"(\"\n\u2192 ++level \u2192 level = 1\n\u2192 level is non-zero \u2192 ans += \"(\" \u2192 ans = \"()()(\"\n\ni = 10 \u2192 s[10] = \")\"\n\u2192 level is non-zero \u2192 ans += \")\" \u2192 ans = \"()()()\"\n\u2192 --level \u2192 level = 0\n\ni = 11 \u2192 s[11] = \"(\"\n\u2192 ++level \u2192 level = 1\n\u2192 level is non-zero \u2192 ans += \"(\" \u2192 ans = \"()()()(\"\n\ni = 12 \u2192 s[12] = \"(\"\n\u2192 ++level \u2192 level = 2\n\u2192 level is non-zero \u2192 ans += \"(\" \u2192 ans = \"()()()((\"\n\ni = 13 \u2192 s[13] = \")\"\n\u2192 level is non-zero \u2192 ans += \")\" \u2192 ans = \"()()()(()\"\n\u2192 --level \u2192 level = 1\n\ni = 14 \u2192 s[14] = \")\"\n\u2192 level is non-zero \u2192 ans += \")\" \u2192 ans = \"()()()(())\"\n\u2192 --level \u2192 level = 0\n\ni = 15 \u2192 s[15] = \")\"\n\u2192 level is 0 \u2192 Do NOT add to ans\n\u2192 --level \u2192 level = -1\n  <\/pre>\n\n  <p><strong>Final Output:<\/strong> <code>()()()(())<\/code><\/p> \n  <p><strong>Final State:<\/strong> <code>level = -1<\/code>, <code>ans = \"()()()(())\"<\/code><\/p> \n<\/div>\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\">\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 removeOuterParentheses = function(s) {\n    let level = -1;\n    let ans = \"\";\n    for (let i = 0; i < s.length; i++) {\n        if (s[i] === \"(\") {\n            ++level;\n            ans += (level ? s[i] : \"\");\n        } else {\n            ans += (level ? s[i] : \"\");\n            --level;\n        }\n    }\n    return ans;\n};\n<\/code><\/pre>\n\n<\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n        <pre><code class=\"language-python\">\ndef removeOuterParentheses(s: str) -> str:\n    level = -1\n    ans = \"\"\n    for i in range(len(s)):\n        if s[i] == \"(\":\n            level += 1\n            ans += s[i] if level else \"\"\n        else:\n            ans += s[i] if level else \"\"\n            level -= 1\n    return ans\n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n        <pre><code class=\"language-java\">\npublic class Solution {\n    public String removeOuterParentheses(String s) {\n        int level = -1;\n        StringBuilder ans = new StringBuilder();\n        for(int i = 0; i < s.length(); i++) {\n            if(s.charAt(i) == '(') {\n                ++level;\n                if(level != 0) ans.append(s.charAt(i));\n            } else {\n                if(level != 0) ans.append(s.charAt(i));\n                --level;\n            }\n        }\n        return ans.toString();\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;string&gt;\nusing namespace std;\nstring removeOuterParentheses(string s) {\n    int level = -1;\n    string ans = \"\";\n    for(int i = 0; i < s.length(); i++) {\n        if(s[i] == '(') {\n            ++level;\n            ans += (level ? s[i] : '\\0');\n        } else {\n            ans += (level ? s[i] : '\\0');\n            --level;\n        }\n    }\n    ans.erase(remove(ans.begin(), ans.end(), '\\0'), ans.end());\n    return ans;\n}\n<\/code><\/pre>\n    <\/div>\n\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;string.h&gt;\nchar* removeOuterParentheses(char* s) {\n    int level = -1;\n    int len = strlen(s);\n    char* ans = (char*)malloc(len + 1);\n    int index = 0;\n    for(int i = 0; i < len; i++) {\n        if(s[i] == '(') {\n            ++level;\n            if(level) ans[index++] = s[i];\n        } else {\n            if(level) ans[index++] = s[i];\n            --level;\n        }\n    }\n    ans[index] = '\\0';\n    return ans;\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 string RemoveOuterParentheses(string s) {\n        int level = -1;\n        string ans = \"\";\n        for(int i = 0; i < s.Length; i++) {\n            if(s[i] == '(') {\n                ++level;\n                ans += (level != 0) ? s[i].ToString() : \"\";\n            } else {\n                ans += (level != 0) ? s[i].ToString() : \"\";\n                --level;\n            }\n        }\n        return ans;\n    }\n}\n  <\/code><\/pre>\n    <\/div>\n<\/div>\n<\/div>\n<script>\n    document.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                buttons.forEach((btn) => btn.classList.remove(\"active\"));\n                contents.forEach((content) =>\n                    content.classList.remove(\"active\")\n                );\n                button.classList.add(\"active\");\n                document\n                    .querySelector(\n                        `.wp_blog_code-tab-content[data-lang=\"${lang}\"]`\n                    )\n                    .classList.add(\"active\");\n            });\n        });\n    });\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Problem Statement: A valid parentheses string is either empty &#8220;&#8221;, &#8220;(&#8221; + A + &#8220;)&#8221;, or A + B, where A and B are valid parentheses strings, and + represents string concatenation. For example, &#8220;&#8221;, &#8220;()&#8221;, &#8220;(())()&#8221;, and &#8220;(()(()))&#8221; are all valid parentheses strings. A valid parentheses string s is primitive if it is nonempty,<\/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":[322,260,176,175,211,811,810,174,172,173],"tags":[],"class_list":{"0":"post-7711","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-csharp","9":"category-cplusplus","10":"category-data-structures","11":"category-data-structures-and-algorithms","12":"category-dsa","13":"category-java","14":"category-javascript","15":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/7711","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=7711"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/7711\/revisions"}],"predecessor-version":[{"id":10213,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/7711\/revisions\/10213"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=7711"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=7711"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=7711"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}