{"id":9894,"date":"2011-09-30T17:01:00","date_gmt":"2011-09-30T17:01:00","guid":{"rendered":"http:\/\/melotopia.net\/b\/?p=9894"},"modified":"2011-09-30T17:01:00","modified_gmt":"2011-09-30T17:01:00","slug":"%ec%a6%9d%ea%b0%80%ea%b0%90%ec%86%8c-%ec%88%ab%ec%9e%90","status":"publish","type":"post","link":"http:\/\/melotopia.net\/b\/?p=9894","title":{"rendered":"\uc99d\uac00\/\uac10\uc18c \uc22b\uc790"},"content":{"rendered":"
\n 10\uc9c4\uc218\ub85c \ud558\uc790.
\n
\n \uc5b4\ub290 \uc218\ub97c 10\uc9c4 \uae30\uc218\ubc95\uc73c\ub85c \uc368 \ub193\uace0 \uc67c\ucabd\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c \uc77d\uc73c\uba74\uc11c, \uc5b4\ub290 \uc790\ub9bf\uc218\uc758 \uc22b\uc790\ub77c\ub3c4 \uadf8 \uc67c\ucabd\uc5d0 \uc788\ub294 \uc22b\uc790\ub97c \ucd08\uacfc\ud558\uc9c0 \uc54a\uc73c\uba74 \uadf8 \uc218\ub294 \uac10\uc18c\ud558\ub294 \uc218\uc774\ub2e4. \ubc18\ub300\ub85c, \ud56d\uc0c1 \uac19\uac70\ub098 \ud06c\ub2e4\uba74 \uadf8 \uc218\ub294 \uc99d\uac00\ud558\ub294 \uc218\uc774\ub2e4.
\n
\n \uc99d\uac00\ud558\uc9c0\ub3c4 \uc54a\uace0 \uac10\uc18c\ud558\uc9c0\ub3c4 \uc54a\ub294 \uc218\ub294 bouncy number\ub77c\uace0 \ud55c\ub2e4.<\/p>\n

10^6\uc774\ud558\uc758 \uc218 \uc911\uc5d0\ub294 12951\uac1c\uc758 bouncy number\uac00 \uc788\uace0, 10^10\uc774\ud558\uc758 \uc218 \uc911\uc5d0\ub294 277032\uac1c\uac00 \uc788\ub2e4\uace0 \ud55c\ub2e4.
\n
\n \uad6c\uace8(10^100)\uc774\ud558\uc758 \uc218 \uc911\uc5d0\ub294 \uba87\uac1c\uc758 bouncy number\uac00 \uc788\ub294\uac00?<\/p>\n


\n \ucd9c\ucc98 http:\/\/projecteuler.net\/problem=113
\n <\/a><\/p>\n

\ud480\uc5b4\ubcf4\uc790.<\/p>\n

1.
\n
\n \uc6b0\uc120, \uc5b4\ub5a4 \uc591\uc758 \uc815\uc218 N\ubcf4\ub2e4 \uc791\uc740 bouncy number\uc758 \uc218\ub97c B(N)\ub77c \ud558\uace0, increasing number\uc758 \uc218\ub97c I(N), decreasing number\uc758 \uc218\ub97c D(N)\ub77c\uace0 \ud558\uc790. \uc784\uc758\uc758 \uc591\uc758 \uc815\uc218 N\uc5d0 \ub300\ud558\uc5ec, N=B(N)+D(N)+I(N)\uac00 \uc131\ub9bd\ud55c\ub2e4. N, B, D, I\uc758 \uc815\uc758\uc5d0 \uc758\ud574 \ub2f9\uc5f0\ud558\ub2e4.<\/p>\n

2.
\n
\n \uc608\ub97c \ub4e4\uc5b4, n\uc790\ub9ac\uc218\uc758 increasing number\uc758 \uc218\ub97c I[n]\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7fc n\uc790\ub9ac\uc218\uc778 \uc591\uc758 \uc815\uc218 N\uc5d0 \ub300\ud558\uc5ec, N\uc774\ud558\uc758 increasing number\uc758 \uc218 I(N)\uc740 I(N)=I[0]+I[1]+I[2]+…+I[n] \uc774\ub2e4.
\n
\n \uc774 \uc0ac\uc2e4\uc740 I\uac00 \uc544\ub2c8\ub77c D\uc5d0 \ub300\ud574\uc11c\ub3c4 \uc131\ub9bd\ud55c\ub2e4.
\n
\n \uc989, D(N) = D[0]+D[1]+…+D[n] \uc774\ub2e4.<\/p>\n

3.
\n
\n \uc5b4\ub5a4 \uc591\uc758 \uc815\uc218 n(n>3)\uc5d0 \ub300\ud558\uc5ec I[n]\uc774 \uc54c\ub824\uc838 \uc788\ub2e4\uace0 \ud558\uc790.
\n
\n I[n+1] = ??
\n
\n \uc5b4\ub5a4 \uc810\ud654\uc2dd\uc774 \uc874\uc7ac\ud560 \uac83\uc774\ub2e4.<\/p>\n

4.
\n
\n I\uc5d0 \ub300\ud55c 3\uc758 \ub0b4\uc6a9\uc744 D\uc5d0 \ub300\ud574\uc11c\ub3c4 \ub9c8\ucc2c\uac00\uc9c0\ub85c \uc99d\uba85\ud560 \uc218 \uc788\ub2e4.<\/p>\n

5.
\n
\n 1, 2, 3, 4\ub97c \uc815\ub9ac\ud558\uba74 B(10^100)\uc744 \uacc4\uc0b0\ud560 \uc218 \uc788\ub2e4.<\/p>\n

*\ud63c\uc790 \ud480\uace0 \uc788\ub294 \uc911\uc785\ub2c8\ub2e4.
\n <\/p>\n

\n
\n
\n\"\uc2e0\uace0\"
\n<\/a>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

10\uc9c4\uc218\ub85c \ud558\uc790. \uc5b4\ub290 \uc218\ub97c 10\uc9c4 \uae30\uc218\ubc95\uc73c\ub85c \uc368 \ub193\uace0 \uc67c\ucabd\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c \uc77d\uc73c\uba74\uc11c, \uc5b4\ub290 \uc790\ub9bf\uc218\uc758 \uc22b\uc790\ub77c\ub3c4 \uadf8 \uc67c\ucabd\uc5d0 \uc788\ub294 \uc22b\uc790\ub97c \ucd08\uacfc\ud558\uc9c0 \uc54a\uc73c\uba74 \uadf8 \uc218\ub294 \uac10\uc18c\ud558\ub294 \uc218\uc774\ub2e4. \ubc18\ub300\ub85c, \ud56d\uc0c1 \uac19\uac70\ub098 \ud06c\ub2e4\uba74 \uadf8 \uc218\ub294 \uc99d\uac00\ud558\ub294 \uc218\uc774\ub2e4. \uc99d\uac00\ud558\uc9c0\ub3c4 \uc54a\uace0 \uac10\uc18c\ud558\uc9c0\ub3c4 \uc54a\ub294 \uc218\ub294 bouncy number\ub77c\uace0 \ud55c\ub2e4. 10^6\uc774\ud558\uc758 \uc218 \uc911\uc5d0\ub294 12951\uac1c\uc758 bouncy number\uac00 \uc788\uace0, 10^10\uc774\ud558\uc758 \uc218 \uc911\uc5d0\ub294 277032\uac1c\uac00 \uc788\ub2e4\uace0 \ud55c\ub2e4. \uad6c\uace8(10^100)\uc774\ud558\uc758 \uc218 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-9894","post","type-post","status-publish","format-standard","hentry","category-academic"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8o6gA-2zA","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/9894","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9894"}],"version-history":[{"count":0,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/9894\/revisions"}],"wp:attachment":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9894"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9894"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9894"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}