{"id":6274,"date":"2023-12-23T23:09:19","date_gmt":"2023-12-23T15:09:19","guid":{"rendered":"https:\/\/zyrastory.com\/?p=6274"},"modified":"2024-01-21T18:37:20","modified_gmt":"2024-01-21T10:37:20","slug":"codeforces-282b-painting-eggs-solution-and-explanation-en","status":"publish","type":"post","link":"https:\/\/zyrastory.com\/en\/coding-en\/codeforces-en\/codeforces-282b-painting-eggs-solution-and-explanation-en\/","title":{"rendered":"Codeforces 282B Painting Eggs Solution &#038; Explanation"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_66_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title \" >\u5167\u5bb9\u76ee\u9304<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/codeforces-en\/codeforces-282b-painting-eggs-solution-and-explanation-en\/#problem-description\" title=\"Problem Description\">Problem Description<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/codeforces-en\/codeforces-282b-painting-eggs-solution-and-explanation-en\/#solution\" title=\"Solution\">Solution<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/codeforces-en\/codeforces-282b-painting-eggs-solution-and-explanation-en\/#c-solution\" title=\"C# Solution\">C# Solution<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/codeforces-en\/codeforces-282b-painting-eggs-solution-and-explanation-en\/#java-solution\" title=\"Java Solution\">Java Solution<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/codeforces-en\/codeforces-282b-painting-eggs-solution-and-explanation-en\/#conclusion\" title=\"Conclusion\">Conclusion<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>Difficulty : 1500<\/p>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"problem-description\"><\/span><strong>Problem Description<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The Bitlandians are quite weird people. They have very peculiar customs.<\/p>\n\n\n\n<p>As is customary, Uncle J. wants to have&nbsp;<em>n<\/em>&nbsp;eggs painted for Bitruz (an ancient Bitland festival). He has asked G. and A. to do the work.<\/p>\n\n\n\n<p>The kids are excited because just as is customary, they&#8217;re going to be paid for the job!<\/p>\n\n\n\n<p>Overall uncle J. has got&nbsp;<em>n<\/em>&nbsp;eggs. G. named his price for painting each egg. Similarly, A. named his price for painting each egg. It turns out that for each egg the sum of the money both A. and G. want for the painting equals&nbsp;1000.<\/p>\n\n\n\n<p>Uncle J. wants to distribute the eggs between the children so as to give each egg to exactly one child. Also, Uncle J. wants the total money paid to A. to be different from the total money paid to G. by no more than&nbsp;500.<\/p>\n\n\n\n<p>Help Uncle J. Find the required distribution of eggs or otherwise say that distributing the eggs in the required manner is impossible.<\/p>\n\n\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>Input<\/strong><\/p>\n\n\n\n<p>The first line contains integer&nbsp;<em>n<\/em>&nbsp;(1\u2009\u2264\u2009<em>n<\/em>\u2009\u2264\u200910<sup>6<\/sup>)&nbsp;\u2014 the number of eggs.<\/p>\n\n\n\n<p>Next&nbsp;<em>n<\/em>&nbsp;lines contain two integers&nbsp;<em>a<\/em><sub><em>i<\/em><\/sub>&nbsp;and&nbsp;<em>g<\/em><sub><em>i<\/em><\/sub>&nbsp;each&nbsp;(0\u2009\u2264\u2009<em>a<\/em><sub><em>i<\/em><\/sub>,\u2009<em>g<\/em><sub><em>i<\/em><\/sub>\u2009\u2264\u20091000;&nbsp;<em>a<\/em><sub><em>i<\/em><\/sub>\u2009+\u2009<em>g<\/em><sub><em>i<\/em><\/sub>\u2009=\u20091000):&nbsp;<em>a<\/em><sub><em>i<\/em><\/sub>&nbsp;is the price said by A. for the&nbsp;<em>i<\/em>-th egg and&nbsp;<em>g<\/em><sub><em>i<\/em><\/sub>&nbsp;is the price said by G. for the&nbsp;<em>i<\/em>-th egg.<\/p>\n\n\n\n<p><strong>Output<\/strong><\/p>\n\n\n\n<p>If it is impossible to assign the painting, print &#8220;-1&#8221; (without quotes).<\/p>\n\n\n\n<p>Otherwise print a string, consisting of&nbsp;<em>n<\/em>&nbsp;letters &#8220;G&#8221; and &#8220;A&#8221;. The&nbsp;<em>i<\/em>-th letter of this string should represent the child who will get the&nbsp;<em>i<\/em>-th egg in the required distribution. Letter &#8220;A&#8221; represents A. and letter &#8220;G&#8221; represents G. If we denote the money Uncle J. must pay A. for the painting as&nbsp;<em>S<\/em><sub><em>a<\/em><\/sub>, and the money Uncle J. must pay G. for the painting as&nbsp;<em>S<\/em><sub><em>g<\/em><\/sub>, then this inequality must hold:&nbsp;|<em>S<\/em><sub><em>a<\/em><\/sub>\u2009\u2009-\u2009\u2009<em>S<\/em><sub><em>g<\/em><\/sub>|\u2009\u2009\u2264\u2009\u2009500.<\/p>\n\n\n\n<p>If there are several solutions, you are allowed to print any of them.<\/p>\n\n\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>Examples<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-border-color has-palette-color-4-border-color has-fixed-layout\"><tbody><tr><td>Input<\/td><td>2<br>1 999<br>999 1<\/td><\/tr><tr><td>Output<\/td><td>AG<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-border-color has-palette-color-4-border-color has-fixed-layout\"><tbody><tr><td>Input<\/td><td>3<br>400 600<br>400 600<br>400 600<\/td><\/tr><tr><td>Output<\/td><td>AGA<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div style=\"height:35px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"solution\"><\/span><strong>Solution<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"c-solution\"><\/span><strong>C# Solution<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>In my solution,<\/p>\n\n\n\n<ul>\n<li>Start looping through each egg.<\/li>\n\n\n\n<li>For each egg, read the prices named by G. and A. from the input.<\/li>\n\n\n\n<li>Calculate two possible total prices, tmp1 and tmp2:\n<ul>\n<li>tmp1 = sum + a, representing the total price if the egg is given to A.<\/li>\n\n\n\n<li>tmp2 = sum &#8211; g, representing the total price if the egg is given to G.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Choose the one with a smaller absolute value between tmp1 and tmp2 to minimize the difference in total prices between A. and G., i.e., |sum|.<\/li>\n\n\n\n<li>Update sum with the chosen total price, and mark the selected child (A. or G.) as the recipient of the egg.<\/li>\n\n\n\n<li>Repeat this process until all eggs are assigned.<\/li>\n\n\n\n<li>Finally, check if the absolute value of sum exceeds 500. If yes, it means Uncle J.&#8217;s conditions cannot be satisfied, so output &#8220;-1&#8221;. Otherwise, output the final distribution of eggs.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>First try &#8211; <mark style=\"background-color:rgba(0, 0, 0, 0);color:#cf2e2e\" class=\"has-inline-color\">Time limit exceeded&nbsp;<\/mark><\/strong><\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism undefined-numbers lang-csharp\" data-lang=\"C#\"><code>int n = int.Parse(Console.ReadLine());  \/\/number of eggs \n\nint sum = 0;\nstring res = &quot;&quot;;\n\nfor(int i=0; i&lt;n;i++){\n    string[] arr = Console.ReadLine().Split(&#39; &#39;); \/\/split by space\n    int a = int.Parse(arr[0]);\n    int g = int.Parse(arr[1]);\n    \n    int tmp1 = sum+a;\n    int tmp2 = sum-g;\n    \n    if(Math.Abs(tmp1)&lt;Math.Abs(tmp2)){\n        res+=&quot;A&quot;;\n        sum = tmp1;\n    }\n    else{\n        res+=&quot;G&quot;;\n        sum = tmp2;\n    }\n}\n\nif(Math.Abs(sum)&gt;500){\n    Console.WriteLine(&quot;-1&quot;);\n}\nelse\n{\n    Console.WriteLine(res);\n}<\/code><\/pre><\/div>\n\n\n\n<p>The overall logic is correct, but the issue of running for an extended period has arisen.<\/p>\n\n\n\n<p>So, we&#8217;ll make some improvements in our next solution.<\/p>\n\n\n\n<ul>\n<li>Firstly, given that the sum of \u2009<em>a<\/em><sub><em>i<\/em><\/sub><em> <\/em>and <em>g<\/em><sub><em>i<\/em><\/sub> always equals 1000, we can replace the line <strong><em>int g = int.Parse(arr[1]);<\/em><\/strong> with <strong><em>int g = 1000 &#8211; a;<\/em><\/strong>.<\/li>\n\n\n\n<li>Secondly, in a loop where string concatenation (+=) is used extensively, it incurs a significant time cost due to copying at each iteration. To address this, we can optimize the process by using a char array instead.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>Solution1<\/strong><\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism undefined-numbers lang-csharp\" data-lang=\"C#\"><code>int n = int.Parse(Console.ReadLine());  \/\/number of eggs \n\nint sum = 0;\nstring res = &quot;&quot;;\nchar[] resArr = new char[n];\n\nfor(int i=0; i&lt;n;i++){\n    string[] arr = Console.ReadLine().Split(&#39; &#39;); \/\/split by space\n    int a = int.Parse(arr[0]);\n    \/\/int g = int.Parse(arr[1]);\n    int g = 1000 - a;\n    \n    int tmp1 = sum+a;\n    int tmp2 = sum-g;\n    \n    if(Math.Abs(tmp1)&lt;Math.Abs(tmp2)){\n        \/\/res+=&quot;A&quot;;\n        resArr[i] = &#39;A&#39;;\n        sum = tmp1;\n    }\n    else{\n        \/\/res+=&quot;G&quot;;\n        resArr[i] = &#39;G&#39;;\n        sum = tmp2;\n    }\n}\n\nif(sum&gt;500 || sum&lt;-500){\n    Console.WriteLine(&quot;-1&quot;);\n}\nelse\n{\n    \/\/Console.WriteLine(res);\n    Console.WriteLine(new string(resArr));\n}<\/code><\/pre><\/div>\n\n\n\n<p>And then the solution passed the time constraints! Congratulations!<\/p>\n\n\n\n<div style=\"height:45px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"java-solution\"><\/span><strong>Java Solution<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p><strong>Solution1<\/strong><\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism undefined-numbers lang-java\" data-lang=\"Java\"><code>import java.util.Scanner;\n\npublic class Main {\n    public static void main(String[] args) {\n        Scanner scanner = new Scanner(System.in);\n        int n = scanner.nextInt();\n        scanner.nextLine();\n        \n        int sum = 0;\n        String res = &quot;&quot;;\n        char[] resArr = new char[n];\n        \n        for(int i=0; i&lt;n;i++){\n            String[]arr = scanner.nextLine().split(&quot; &quot;); \/\/ split by space\n            int a = Integer.parseInt(arr[0]);\n            int g = 1000 - a;\n            \n            int tmp1 = sum+a;\n            int tmp2 = sum-g;\n            \n            if(Math.abs(tmp1)&lt;Math.abs(tmp2)){\n                resArr[i] = &#39;A&#39;;\n                sum = tmp1;\n            }\n            else{\n                resArr[i] = &#39;G&#39;;\n                sum = tmp2;\n            }\n        }\n        \n        if(sum&gt;500 || sum&lt;-500){\n            System.out.println(&quot;-1&quot;);\n        }\n        else\n        {\n            System.out.println(new String(resArr));\n        }\n\n    }\n}<\/code><\/pre><\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"tw-target-text\"><span class=\"ez-toc-section\" id=\"conclusion\"><\/span><strong>Conclusion<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>This is the second problem from codeforces contest &#8211; <a href=\"https:\/\/codeforces.com\/contest\/282\" target=\"_blank\" rel=\"noreferrer noopener\">Dashboard &#8211; Codeforces Round 173 (Div. 2) &#8211; Codeforces<\/a><\/p>\n\n\n\n<p>You can find the solution for the first problem here &#8211; <a href=\"https:\/\/zyrastory.com\/en\/coding-en\/codeforces-en\/codeforces-282a-bit-solution-and-explanation-en\/\" target=\"_blank\" rel=\"noreferrer noopener\">Codeforces 282A Bit++ Solution &amp; Explanation<\/a><\/p>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size\">\ud83e\udde1<strong>If my solution helps, that is my honor!<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">\ud83e\udde1<strong>You can support me by sharing my posts, thanks you~~<\/strong><\/p>\n\n\n\n<p><strong>\u2705If you got any problem about the explanation or you need other programming language solution, please feel free to let me know !!<\/strong><\/p>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>The problem link :<\/strong> <a href=\"https:\/\/codeforces.com\/problemset\/problem\/282\/B\" target=\"_blank\" rel=\"noreferrer noopener\">Problem &#8211; 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