{"id":5811,"date":"2021-10-25T10:12:35","date_gmt":"2021-10-25T10:12:35","guid":{"rendered":"https:\/\/www.prepbytes.com\/blog\/?p=5811"},"modified":"2022-03-10T16:50:45","modified_gmt":"2022-03-10T16:50:45","slug":"find-pairs-with-given-sum-in-a-doubly-linked-list","status":"publish","type":"post","link":"https:\/\/prepbytes.com\/blog\/find-pairs-with-given-sum-in-a-doubly-linked-list\/","title":{"rendered":"Find Pairs With Given Sum In A Doubly Linked List"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1645012142585-Article_201.png\" alt=\"\" \/><\/p>\n<h3>Problem Statement<\/h3>\n<p>In this problem, we will be given a sorted doubly linked list and a target integer. We need to find and print the pairs whose sum is equal to the given target.<\/p>\n<\/p>\n<p><strong>Note:<\/strong> The integer value inside each node is unique.<\/p>\n<h3>Problem Statement understanding:<\/h3>\n<p>The problem statement is quite straightforward; we need to print pairs whose sum is equal to the given target.<\/p>\n<p>Let&#8217;s try to understand the problem with the help of an example:<br \/>\nIf the list given to us is:<br \/>\n<img decoding=\"async\" src=\"https:\/\/prepbytes.com\/blog\/wp-content\/uploads\/2021\/10\/p_1-1.jpg\" alt=\"\" \/><\/p>\n<p>and the target = 14<\/p>\n<ul>\n<li>We can easily see that the pairs (2,12) and (4,10) both sum up to the given target of 14.<\/li>\n<li>So, we need to just print both these pairs as output.<\/li>\n<\/ul>\n<p>At this point, we have understood the problem statement. Now we will try to formulate an approach for this problem.<\/p>\n<h5>Brute Force Approach<\/h5>\n<p>A straightforward approach to solve this problem is to use nested for loops. Using the outer for loop, pick each node one by one, and then using the inner for loop traverse in the forward direction from the current node to find a second node in the linked list such that the sum of nodes is equal to target.<\/p>\n<p>The time complexity of this approach is O(N<sup>2<\/sup>).  N is the number of nodes in the linked list.<\/p>\n<p>Although this above approach will work fine, but for longer linked lists having <strong>length &gt;= 10<sup>4<\/sup><\/strong>, it will give a time limit exceed error. So, now we will try to see some other approaches having less time complexity.<\/p>\n<p>Before jumping onto the optimized approach, try to think about how you can optimize the current approach such that it can find pairs for longer linked lists.<\/p>\n<ul>\n<li>If stuck, no problem, we will thoroughly see the better approach in the next section.<\/li>\n<\/ul>\n<p>Let\u2019s move to the approach section.<\/p>\n<h3>Approach<\/h3>\n<ul>\n<li>We will follow two pointer approach in which one pointer will point to the smallest node initially i.e., the first node, and the second one will point to the largest node i.e., the last node.<\/li>\n<li>Now, we will iterate till both the pointers do not meet each other.<\/li>\n<li>In every iteration, we will calculate the sum of nodes pointed by both the pointers.<\/li>\n<li>If the sum is equal to the target, that means we have found the pair, and we have to print it and move the first pointer and the second pointer one node forward and backward, respectively.<\/li>\n<li>If the sum is smaller than the target, then it means that we need to increase it to make it equal to the target. Since the list is sorted, so moving the first pointer forward will increase the sum.<\/li>\n<li>If the sum is larger than the target, then it means that we need to decrease it to make it equal to the target. Since the list is sorted, so moving the second pointer backward will decrease the sum.<\/li>\n<\/ul>\n<h3>Algorithm<\/h3>\n<p>1) Initialize two pointers <strong>left<\/strong> and <strong>right<\/strong> with the first and last node of the list.<br \/>\n2) Run a while loop till both <strong>left<\/strong> and <strong>right<\/strong> are not equal or adjacent to each other.<br \/>\n3) Calculate the sum of the nodes pointed by the <strong>left<\/strong> and the <strong>right<\/strong> pointers.<\/p>\n<ul>\n<li>If the sum equals the <strong>target<\/strong>, print both the numbers and move <strong>left<\/strong> and <strong>right<\/strong> by one node forward and backward, respectively.<\/li>\n<li>Else if the sum is less than the <strong>target<\/strong>, move <strong>left<\/strong> forward by one node.<\/li>\n<li>Else, move <strong>right<\/strong> backward by one node.<\/li>\n<\/ul>\n<h3>Dry Run<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes.com\/blog\/wp-content\/uploads\/2021\/10\/p_2-1.jpg\" alt=\"\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/prepbytes.com\/blog\/wp-content\/uploads\/2021\/10\/p_3.jpg\" alt=\"\" \/><\/p>\n<h3>Code Implementation<\/h3>\n\t\t\t\t\t\t<style>\r\n\t\t\t\t\r\n\t\t\t\t\t#tab_container_5812 {\r\n\toverflow:hidden;\r\n\tdisplay:block;\r\n\twidth:100%;\r\n\tborder:0px solid #ddd;\r\n\tmargin-bottom:30px;\r\n\t}\r\n\r\n#tab_container_5812 .tab-content{\r\n\tpadding:20px;\r\n\tborder: 1px solid #e6e6e6 !important;\r\n\tmargin-top: 0px;\r\n\tbackground-color:#ffffff !important;\r\n\tcolor: #000000 !important;\r\n\tfont-size:16px !important;\r\n\tfont-family: Open Sans !important;\r\n\t\r\n\t\tborder: 1px solid #e6e6e6 !important;\r\n\t}\r\n#tab_container_5812 .wpsm_nav-tabs {\r\n    border-bottom: 0px solid #ddd;\r\n}\r\n#tab_container_5812 .wpsm_nav-tabs > li.active > a, #tab_container_5812 .wpsm_nav-tabs > li.active > a:hover, #tab_container_5812 .wpsm_nav-tabs > li.active > a:focus {\r\n\tcolor: #000000 !important;\r\n\tcursor: default;\r\n\tbackground-color: #ffffff !important;\r\n\tborder: 1px solid #e6e6e6 !important;\r\n}\r\n\r\n#tab_container_5812 .wpsm_nav-tabs > li > a {\r\n    margin-right: 0px !important; \r\n    line-height: 1.42857143 !important;\r\n    border: 1px solid #d5d5d5 !important;\r\n    border-radius: 0px 0px 0 0 !important; \r\n\tbackground-color: #e8e8e8 !important;\r\n\tcolor: #000000 !important;\r\n\tpadding: 15px 18px 15px 18px !important;\r\n\ttext-decoration: none !important;\r\n\tfont-size: 14px !important;\r\n\ttext-align:center !important;\r\n\tfont-family: Open Sans !important;\r\n}\r\n#tab_container_5812 .wpsm_nav-tabs > li > a:focus {\r\noutline: 0px !important;\r\n}\r\n\r\n#tab_container_5812 .wpsm_nav-tabs > li > a:before {\r\n\tdisplay:none !important;\r\n}\r\n#tab_container_5812 .wpsm_nav-tabs > li > a:after {\r\n\tdisplay:none !important ;\r\n}\r\n#tab_container_5812 .wpsm_nav-tabs > li{\r\npadding:0px 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!important;\r\n\t\t\t\t\t}\r\n\t#tab_container_5812 .wpsm_nav-tabs{\r\n\t\tfloat:none !important;\r\n\t\tmargin:0px !important;\r\n\t}\r\n\r\n\t#tab_container_5812 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_5812 .wpsm_nav{\r\n\t\t\t}\r\n\r\n}\r\n\r\n\r\n\r\n@media (max-width: 768px) {\r\n\t#tab_container_5812 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_5812 .wpsm_nav{\r\n\t\t\t}\r\n}\r\n\r\n\r\n\t.wpsm_nav-tabs li:before{\r\n\t\tdisplay:none !important;\r\n\t}\r\n\r\n\t@media (max-width: 768px) {\r\n\t\t\t\t\r\n\t\t\t\t.wpsm_nav-tabs{\r\n\t\t\tmargin-left:0px !important;\r\n\t\t\tmargin-right:0px !important; \r\n\t\t\t\r\n\t\t}\r\n\t\t\t\t#tab_container_5812 .wpsm_nav-tabs > li{\r\n\t\t\tfloat:none !important;\r\n\t\t}\r\n\t\t\t\r\n\t}\t\t\t\t<\/style>\r\n\t\t\t\t<div id=\"tab_container_5812\" >\r\n\t \r\n\t\t\t\t\t<ul class=\"wpsm_nav wpsm_nav-tabs\" role=\"tablist\" id=\"myTab_5812\">\r\n\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t<li role=\"presentation\"  class=\"active\"  onclick=\"do_resize()\">\r\n\t\t\t\t\t\t\t\t<a href=\"#tabs_desc_5812_1\" aria-controls=\"tabs_desc_5812_1\" role=\"tab\" data-toggle=\"tab\">\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<i class=\"fa fa-laptop\"><\/i> \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t<span>C++<\/span>\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t<\/a>\r\n\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t\t\t\t\t\t <\/ul>\r\n\r\n\t\t\t\t\t  <!-- Tab panes -->\r\n\t\t\t\t\t  <div class=\"tab-content\" id=\"tab-content_5812\">\r\n\t\t\t\t\t\t\t\t\t\t\t\t <div role=\"tabpanel\" class=\"tab-pane  in active \" id=\"tabs_desc_5812_1\">\r\n\t\t\t\t\t\t\t\t<!-- wp:enlighter\/codeblock {\"language\":\"cpp\"} -->\r\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\r\n#include <bits\/stdc++.h>\r\nusing namespace std;\r\n\r\nclass Node\r\n{\r\n    public:\r\n    int data;\r\n    Node* next;\r\n    Node* prev;\r\n};\r\n\r\nvoid add_at_begin(Node** head, int x){\r\n    \/\/create node of doubly linked list\r\n    Node* new_node = new Node();\r\n \r\n    \/\/assign the data entered by user\r\n    new_node->data = x;\r\n \r\n    \/\/ node is inserted in beginning so, prev will always \r\n    \/\/ be NULL\r\n    new_node->prev = NULL;\r\n \r\n    \/\/the node created is inserted at beginning so we need to\r\n    \/\/connect it with previous head\r\n    new_node->next = (*head);\r\n     \r\n    \/\/ change the head to the current node\u2019s address\r\n    if ((*head) != NULL)\r\n        (*head)->prev = new_node;\r\n \r\n    (*head) = new_node;\r\n}\r\n\r\nvoid print_list(Node* node){\r\n    while (node != NULL)\r\n    {\r\n        cout << node->data << \",\";\r\n        node = node->next;\r\n    }\r\n}\r\n\r\nvoid pairSum(Node *head, int x){\r\n    \/\/initialize two pointers\r\n    Node *left = head;\r\n    Node *right = head;\r\n    \/\/move right pointer to last node\r\n    while (right->next != NULL)\r\n        right = right->next;\r\n \r\n    \/\/ break the loop when two pointers meet\r\n    \/\/ each other or cross each other\r\n    while (left != right && right->next != left)\r\n    {\r\n        int sum = (left->data + right->data);\r\n        \/\/ sum is equal to target so, pair found\r\n        if (sum == x)\r\n        {\r\n            cout << \"(\" << left->data<< \", \"\r\n                << right->data << \")\" << endl;\r\n \r\n            \/\/ move left forward by one node\r\n            left = left->next;\r\n \r\n            \/\/ move right backward by one node\r\n            right = right->prev;\r\n        }\r\n        else\r\n        {\r\n            if (sum < x)\r\n                left = left->next;\r\n            else\r\n                right = right->prev;\r\n        }\r\n    }\r\n}\r\n\r\n\r\nint main()\r\n{\r\n    Node* head = NULL;\r\n \r\n    add_at_begin(&head, 12);\r\n    add_at_begin(&head, 10);\r\n    add_at_begin(&head, 4);\r\n    add_at_begin(&head, 3);\r\n    add_at_begin(&head, 2);\r\n\r\n    cout<<\"The pairs with sum equal to target are: \"<<endl;\r\n    pairSum(head, 14);\r\n    \r\n \r\n    return 0;\r\n}\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\r\n\t\t\t\t\t\t <\/div>\r\n\t\t\t\t\t\t\t\r\n\t\t\t\t\t <\/div>\r\n\t\t\t\t\t \r\n\t\t\t\t <\/div>\r\n <script>\r\n\t\tjQuery(function () {\r\n\t\t\tjQuery('#myTab_5812 a:first').tab('show')\r\n\t\t});\r\n\t\t\r\n\t\t\t\tjQuery(function(){\r\n\t\t\tvar b=\"fadeIn\";\r\n\t\t\tvar c;\r\n\t\t\tvar a;\r\n\t\t\td(jQuery(\"#myTab_5812 a\"),jQuery(\"#tab-content_5812\"));function d(e,f,g){\r\n\t\t\t\te.click(function(i){\r\n\t\t\t\t\ti.preventDefault();\r\n\t\t\t\t\tjQuery(this).tab(\"show\");\r\n\t\t\t\t\tvar h=jQuery(this).data(\"easein\");\r\n\t\t\t\t\tif(c){c.removeClass(a);}\r\n\t\t\t\t\tif(h){f.find(\"div.active\").addClass(\"animated \"+h);a=h;}\r\n\t\t\t\t\telse{if(g){f.find(\"div.active\").addClass(\"animated \"+g);a=g;}else{f.find(\"div.active\").addClass(\"animated \"+b);a=b;}}c=f.find(\"div.active\");\r\n\t\t\t\t});\r\n\t\t\t}\r\n\t\t});\r\n\t\t\r\n\r\n\t\tfunction do_resize(){\r\n\r\n\t\t\tvar width=jQuery( '.tab-content .tab-pane iframe' ).width();\r\n\t\t\tvar height=jQuery( '.tab-content .tab-pane iframe' ).height();\r\n\r\n\t\t\tvar toggleSize = true;\r\n\t\t\tjQuery('iframe').animate({\r\n\t\t\t    width: toggleSize ? width : 640,\r\n\t\t\t    height: toggleSize ? height : 360\r\n\t\t\t  }, 250);\r\n\r\n\t\t\t  toggleSize = !toggleSize;\r\n\t\t}\r\n\r\n\r\n\t<\/script>\r\n\t\t\t\t\r\n\t\t\t\n<h4>Output<\/h4>\n<p>The pairs with sum equal to target are:<br \/>\n(2, 12)<br \/>\n(4, 10)<\/p>\n<p><strong>Time Complexity:<\/strong> O(n), n is the total number of nodes in the list.<br \/>\n[forminator_quiz id=&#8221;5813&#8243;]<\/p>\n<p>So, in this blog, we have tried to explain how we can find a pair with a given sum in a doubly-linked list in the most optimal way. If you want to solve more questions on Linked List, which are curated by our expert mentors at PrepBytes, you can follow this link <a href=\"https:\/\/mycode.prepbytes.com\/interview-coding\/practice\/linked-list\">Linked List<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problem Statement In this problem, we will be given a sorted doubly linked list and a target integer. We need to find and print the pairs whose sum is equal to the given target. Note: The integer value inside each node is unique. Problem Statement understanding: The problem statement is quite straightforward; we need to [&hellip;]<\/p>\n","protected":false},"author":52,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[125],"tags":[],"class_list":["post-5811","post","type-post","status-publish","format-standard","hentry","category-linked-list"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Find Pairs With Given Sum In A Doubly Linked List | Linked list articles | PrepBytes Blog<\/title>\n<meta name=\"description\" content=\"Learn how to find pairs with a given sum in a doubly-linked list.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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