{"id":27851,"date":"2022-12-27T02:34:37","date_gmt":"2022-12-26T21:04:37","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-chasing-game-in-c-closed\/"},"modified":"2022-12-27T02:34:37","modified_gmt":"2022-12-26T21:04:37","slug":"solved-chasing-game-in-c-closed","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-chasing-game-in-c-closed\/","title":{"rendered":"[Solved] Chasing game in C [closed]"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-20994383\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"20994383\" data-parentid=\"20980038\" data-score=\"0\" data-position-on-page=\"1\" data-highest-scored=\"1\" data-question-has-accepted-highest-score=\"1\" itemprop=\"acceptedAnswer\" itemscope itemtype=\"https:\/\/schema.org\/Answer\">\n<div class=\"post-layout\">\n<div class=\"votecell post-layout--left\"><\/div>\n<div class=\"answercell post-layout--right\">\n<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>It is an interesting problem. Let&#8217;s go over the rules again. Players<\/p>\n<ol>\n<li>Chicken: takes shortest path to field (there could be multiple shortest paths) and away from eagle (maximise the distance between itself and eagle among shortest paths).<\/li>\n<li>Eagle: takes shortest path to chicken<\/li>\n<\/ol>\n<p>To solve the problem we have to assume it is played in turns: first chicken then eagle and so on.<br \/>\nGame is over when :<\/p>\n<ol>\n<li>Eagle is on chicken.<\/li>\n<li>Chicken is on field.<\/li>\n<\/ol>\n<p>Here is the trick for the distance: <\/p>\n<p><strong>Update<\/strong><\/p>\n<p>The distance you want is called <a rel=\"nofollow noopener\" target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Chebyshev_distance\">Chebyshev distance<\/a>. You can easily calculate it:<\/p>\n<p><code>distance = max of(difference of corresponding coordinates between the two points)<\/code><\/p>\n<p>For (1,1) and (2,3) distance = max(|1-2|,|2-3|) = 2<\/p>\n<p>For (2,3) and (4,7) distance = 4<\/p>\n<p>For (4,5,6) and (1,1,1) distance = 5<\/p>\n<p>You can ignore the older answer if you want.<\/p>\n<hr>\n<p><strong>Old<\/strong><\/p>\n<p><code>distance = Manhattan distance - length of longest 45 deg diagonal<\/code><\/p>\n<p>Manhattan distance is easy to understand. See its <a rel=\"nofollow noopener\" target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/Manhattan_distance\">wiki<\/a>. Take some examples :<\/p>\n<pre><code>    ---\/F\n    --\/-|\n    -\/--|\n    C---X\n\n    manhattan distance = 7\n    length of max diagonal = 3\n    distance = 7-3 = 4\n<\/code><\/pre>\n<p>Another one<\/p>\n<pre><code>    ---\/-F\n    --\/--|\n    -\/---|\n    C----X\n\n    distance = 8-3 = 5\n<\/code><\/pre>\n<p><strong>Caveat<\/strong>: Remember there can be many shortest possible paths. For eg.<\/p>\n<pre><code>    ---F\n    --\/F\n    -\/-F\n    C--F\n    -\\-F\n    --\\F\n    ---F\n<\/code><\/pre>\n<p>Lots of places to go in 3 moves. Pick one which is farthest from eagle using distance calculator.<br \/>\nAlso if distance between eagle and chicken is less than chicken and field at any time then eagle wins else chicken. Just simulate the moves and you will know.<\/p>\n<\/p><\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\">2<\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved Chasing game in C [closed] <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] It is an interesting problem. Let&#8217;s go over the rules again. Players Chicken: takes shortest path to field (there could be multiple shortest paths) and away from eagle (maximise the distance between itself and eagle among shortest paths). Eagle: takes shortest path to chicken To solve the problem we have to assume it is &#8230; <a title=\"[Solved] Chasing game in C [closed]\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-chasing-game-in-c-closed\/\" aria-label=\"More on [Solved] Chasing game in C [closed]\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[3763,5495,324],"class_list":["post-27851","post","type-post","status-publish","format-standard","hentry","category-solved","tag-backtracking","tag-branch-and-bound","tag-c"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>[Solved] Chasing game in C [closed] - JassWeb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jassweb.com\/solved\/solved-chasing-game-in-c-closed\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] Chasing game in C [closed] - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] It is an interesting problem. 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