CF1027C Minimum Value Rectangle
之前做的時候沒想出來...現在來數學推導一波。
題意:從n個木棒中選出4個拼成一個矩形,使得 (周長)2/面積 最小。
解:設矩形寬a長b。我們要最小化下面這個式子:
去掉常數,不妨設b = a + len,則化為下式:
取倒數,也就是最大化下式:
顯然對於每個確定的a,len越小越好。所以直接取相鄰的即可。
好像還有一種推導方法......
原式可直接化為a/b + b/a,這就是個耐克函數雙鉤函數,讓a/b趨近1也就是a=b,所以a和b越接近越好。
CF1027C Minimum Value Rectangle
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