{"id":2345,"date":"2020-07-29T07:34:20","date_gmt":"2020-07-29T07:34:20","guid":{"rendered":"https:\/\/blog.prepbytes.com\/?p=2345"},"modified":"2022-06-17T07:13:04","modified_gmt":"2022-06-17T07:13:04","slug":"play-games-4","status":"publish","type":"post","link":"https:\/\/prepbytes.com\/blog\/play-games-4\/","title":{"rendered":"Play Games 4"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1645180982830-Article_437.png\" alt=\"\" \/><\/p>\n<h3>CONCEPTS USED:<\/h3>\n<blockquote>\n<p>Game theory<\/p>\n<\/blockquote>\n<h3>DIFFICULTY LEVEL:<\/h3>\n<blockquote>\n<p>Medium.<\/p>\n<\/blockquote>\n<h3>PROBLEM STATEMENT(SIMPLIFIED):<\/h3>\n<blockquote>\n<p>Arnab wants to play games with his friend. Now this time Arnab made an array of integers that represent the piles of chocolates. So in each turn, a player can choose only one pile and remove any number of chocolates (greater than or equal to one) from that pile. The player who cannot make a move loses the game. Arnab takes the first move. Both players play optimally.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/mycode.prepbytes.com\/problems\/game-theory\/PLAY4\" title=\"Go to mycode.prepbytes.com\" target=\"_blank\" rel=\"noopener noreferrer\"><u><strong><\/strong><\/u><\/a><\/p>\n<h4>For Example :<\/h4>\n<pre><code>Input\n1\n5 \n1 2 3 4 5 \n\nOutput\nArnab<\/code><\/pre>\n<h3>OBSERVATION:<\/h3>\n<blockquote>\n<p>Take the xor of all the numbers given.<\/p>\n<p>If the xor comes out to be 0,then the friend wins.<\/p>\n<p>If it is not zero,then Arnab wins.<\/p>\n<\/blockquote>\n<h3>SOLUTION:<\/h3>\n<p>\t\t\t\t\t\t<style>\r\n\t\t\t\t\r\n\t\t\t\t\t#tab_container_2346 {\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_2346 .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_2346 .wpsm_nav-tabs {\r\n    border-bottom: 0px solid #ddd;\r\n}\r\n#tab_container_2346 .wpsm_nav-tabs > li.active > a, #tab_container_2346 .wpsm_nav-tabs > li.active > a:hover, #tab_container_2346 .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_2346 .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_2346 .wpsm_nav-tabs > li > a:focus {\r\noutline: 0px !important;\r\n}\r\n\r\n#tab_container_2346 .wpsm_nav-tabs > li > a:before {\r\n\tdisplay:none !important;\r\n}\r\n#tab_container_2346 .wpsm_nav-tabs > li > a:after {\r\n\tdisplay:none !important ;\r\n}\r\n#tab_container_2346 .wpsm_nav-tabs > li{\r\npadding:0px !important ;\r\nmargin:0px;\r\n}\r\n\r\n#tab_container_2346 .wpsm_nav-tabs > li > a:hover , #tab_container_2346 .wpsm_nav-tabs > li > a:focus {\r\n    color: #000000 !important;\r\n    background-color: #e8e8e8 !important;\r\n\tborder: 1px solid #d5d5d5 !important;\r\n\t\r\n}\r\n#tab_container_2346 .wpsm_nav-tabs > li > a .fa{\r\n\r\nmargin-right:5px !important;\r\n\r\nmargin-left:5px !important;\r\n\r\n\r\n}\r\n\r\n\t\t#tab_container_2346 .wpsm_nav-tabs a{\r\n\t\t\tbackground-image: none;\r\n\t\t\tbackground-position: 0 0;\r\n\t\t\tbackground-repeat: repeat-x;\r\n\t\t}\r\n\t\t\t\r\n\r\n\r\n#tab_container_2346 .wpsm_nav-tabs > li {\r\n    float: left;\r\n    margin-bottom: -1px !important;\r\n\tmargin-right:0px !important; \r\n}\r\n\r\n\r\n#tab_container_2346 .tab-content{\r\noverflow:hidden !important;\r\n}\r\n\r\n\r\n@media (min-width: 769px) {\r\n\r\n\t#tab_container_2346 .wpsm_nav-tabs > li{\r\n\t\tfloat:left !important ;\r\n\t\t\t\tmargin-right:-1px !important;\r\n\t\t\t\t\t}\r\n\t#tab_container_2346 .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_2346 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_2346 .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_2346 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_2346 .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_2346 .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_2346\" >\r\n\t \r\n\t\t\t\t\t<ul class=\"wpsm_nav wpsm_nav-tabs\" role=\"tablist\" id=\"myTab_2346\">\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_2346_1\" aria-controls=\"tabs_desc_2346_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\r\n\t\t\t\t\t\t\t<li role=\"presentation\"  onclick=\"do_resize()\">\r\n\t\t\t\t\t\t\t\t<a href=\"#tabs_desc_2346_2\" aria-controls=\"tabs_desc_2346_2\" 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-code\"><\/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\r\n\t\t\t\t\t\t\t<li role=\"presentation\"  onclick=\"do_resize()\">\r\n\t\t\t\t\t\t\t\t<a href=\"#tabs_desc_2346_3\" aria-controls=\"tabs_desc_2346_3\" 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>Java<\/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\r\n\t\t\t\t\t\t\t<li role=\"presentation\"  onclick=\"do_resize()\">\r\n\t\t\t\t\t\t\t\t<a href=\"#tabs_desc_2346_4\" aria-controls=\"tabs_desc_2346_4\" 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>Python<\/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_2346\">\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_2346_1\">\r\n\t\t\t\t\t\t\t\t<!-- wp:enlighter\/codeblock {\"language\":\"c\"} -->\r\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"c\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\r\n#include &lt;stdio.h&gt;\r\n\r\nvoid solve()\r\n{\r\n  long long int n;\r\n        long long int x;\r\n        scanf(&quot;%lld&quot;,&amp;n);\r\n        scanf(&quot;%lld&quot;,&amp;x);\r\n        long long int result=x;\r\n        for(long long int j=1;j&lt;n;j++)\r\n        {\r\n            scanf(&quot;%lld&quot;,&amp;x);\r\n            result=result^x;\r\n        }\r\n        if(result==0)\r\n          printf(&quot;Friend&#92;n&quot;);\r\n        else\r\n          printf(&quot;Arnab&#92;n&quot;);\r\n}\r\nint main()\r\n{  \r\n  int t;\r\n  scanf(&quot;%d&quot;,&amp;t);\r\n  while(t--)\r\n  {\r\n    solve();\r\n  }\r\n\treturn 0;\r\n}\r\n\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\r\n\r\n\t\t\t\t\t\t <\/div>\r\n\t\t\t\t\t\t\t\t\t\t\t\t <div role=\"tabpanel\" class=\"tab-pane \" id=\"tabs_desc_2346_2\">\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 &lt;bits\/stdc++.h&gt;\r\nusing namespace std;\r\nvoid solve()\r\n{\r\n  long long int n;\r\n        long long int x;\r\n        cin&gt;&gt;n;\r\n        cin&gt;&gt;x;\r\n        long long int result=x;\r\n        for(long long int j=1;j&lt;n;j++)\r\n        {\r\n            cin&gt;&gt;x;\r\n            result=result^x;\r\n        }\r\n        if(result==0)\r\n          cout&lt;&lt;&quot;Friend&quot;&lt;&lt;endl;\r\n        else\r\n          cout&lt;&lt;&quot;Arnab&quot;&lt;&lt;endl;\r\n}\r\nint main()\r\n{  \r\n  int t;\r\n  cin&gt;&gt;t;\r\n  while(t--)\r\n  {\r\n    solve();\r\n  }\r\n\r\nreturn 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\t\t\t\t\t <div role=\"tabpanel\" class=\"tab-pane \" id=\"tabs_desc_2346_3\">\r\n\t\t\t\t\t\t\t\t<!-- wp:enlighter\/codeblock {\"language\":\"java\"} -->\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\nimport java.util.*;\r\nclass PlayGames3 \r\n{\r\n    static Scanner sc=new Scanner(System.in);\r\n    static void solve()\r\n    {\r\n        long n=sc.nextLong();\r\n        long x=sc.nextLong();\r\n        long result=x;\r\n\r\n        for(int j=1;j&lt;n;j++)\r\n        {\r\n            x=sc.nextLong();\r\n            result=result^x;\r\n        }\r\n        if(result==0)\r\n        {\r\n            System.out.println(&quot;Friend&quot;);\r\n        }\r\n        else \r\n        {\r\n            System.out.println(&quot;Arnab&quot;);\r\n        }\r\n\r\n    }   \r\n    public static void main(String[] args) \r\n    {\r\n        int t=sc.nextInt();\r\n        while(t!=0)\r\n        {\r\n            solve();\r\n            t--;\r\n        }\r\n    }    \r\n}\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\t\t\t\t\t <div role=\"tabpanel\" class=\"tab-pane \" id=\"tabs_desc_2346_4\">\r\n\t\t\t\t\t\t\t\t<!-- wp:enlighter\/codeblock {\"language\":\"python\"} -->\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\ndef solve():\r\n\tn = int(input())\r\n\ta = list(map(int,input().split()))\r\n\tresult = a[0]\r\n\t\r\n\tfor j in range(1, n):\r\n\t\r\n\t\tresult = result ^ a[j]\r\n\t\r\n\tif(result == 0):\r\n\t\tprint(&quot;Friend&quot;)\r\n\telse:\r\n\t\tprint(&quot;Arnab&quot;)\r\n\r\nfor _ in range(int(input())):\r\n\t\r\n\tsolve()\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_2346 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_2346 a\"),jQuery(\"#tab-content_2346\"));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<br \/>\n[forminator_quiz id=&quot;2347&quot;]<\/p>\n<p>So, in this blog, we have tried to explain the concept of Game Theory. If you want to solve more questions on Game Theory, which are curated by our expert mentors at PrepBytes, you can follow this link <a href=\"https:\/\/mycode.prepbytes.com\/interview-coding\/practice\">Game Theory<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>CONCEPTS USED: Game theory DIFFICULTY LEVEL: Medium. PROBLEM STATEMENT(SIMPLIFIED): Arnab wants to play games with his friend. Now this time Arnab made an array of integers that represent the piles of chocolates. So in each turn, a player can choose only one pile and remove any number of chocolates (greater than or equal to one) [&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":[129],"tags":[],"class_list":["post-2345","post","type-post","status-publish","format-standard","hentry","category-game-theory"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Play Games 4 | Game Theory | Prepbytes<\/title>\n<meta name=\"description\" content=\"Take the Xor of All the Numbers Given. If the Xor Comes Out to Be 0, then the Friend Wins. If it Is Not Zero,then Arnab Wins.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/prepbytes.com\/blog\/play-games-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Play Games 4 | Game Theory | Prepbytes\" \/>\n<meta property=\"og:description\" content=\"Take the Xor of All the Numbers Given. If the Xor Comes Out to Be 0, then the Friend Wins. 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