{"id":688,"date":"2020-06-22T23:31:38","date_gmt":"2020-06-22T15:31:38","guid":{"rendered":"http:\/\/www.guanhaobo.cn\/?p=688"},"modified":"2020-06-22T23:31:38","modified_gmt":"2020-06-22T15:31:38","slug":"jz9-%e5%8f%98%e6%80%81%e8%b7%b3%e5%8f%b0%e9%98%b6","status":"publish","type":"post","link":"https:\/\/www.guanhaobo.cn\/?p=688","title":{"rendered":"JZ9 \u2014 \u53d8\u6001\u8df3\u53f0\u9636"},"content":{"rendered":"

\u9898\u76ee\u63cf\u8ff0<\/h3>\n

\u4e00\u53ea\u9752\u86d9\u4e00\u6b21\u53ef\u4ee5\u8df3\u4e0a1\u7ea7\u53f0\u9636\uff0c\u4e5f\u53ef\u4ee5\u8df3\u4e0a2\u7ea7\u2026\u2026\u5b83\u4e5f\u53ef\u4ee5\u8df3\u4e0an\u7ea7\u3002\u6c42\u8be5\u9752\u86d9\u8df3\u4e0a\u4e00\u4e2an\u7ea7\u7684\u53f0\u9636\u603b\u5171\u6709\u591a\u5c11\u79cd\u8df3\u6cd5\u3002<\/p>\n

\u9898\u76ee\u5206\u6790<\/h3>\n

\u7531\u9898\u76ee\u6613\u5f97f[n] = f[n-1] + f[n-2] + ... + f[1] + 1<\/code>
\n\u5982\u679c\u4e0d\u77e5\u9053\u8fd9\u4e2a\u7ed3\u8bba\u662f\u600e\u4e48\u5f97\u5230\u7684\uff0c\u53ef\u4ee5\u53c2\u8003\u4e0a\u4e00\u9898\uff1ahttp:\/\/www.guanhaobo.cn\/?p=686<\/a><\/p>\n

f[1] = 1\nf[2] = f[1] + 1 = 2 * f[1]\nf[3] = f[2] + f[1] + 1 = 2 * f[2]\nf[4] = f[3] + f[2] + f[1] + 1 = 2 * f[3]\n<\/code><\/pre>\n
\u6613\u5f97f[n] = 2 * f[n-1]<\/code>
\n\u6240\u4ee5\u76f4\u63a5\u9012\u5f52\u6216\u9012\u63a8\u5c31\u53ef\u4ee5\u89e3\u51b3\u672c\u9898\uff0c\u4e0d\u518d\u8d58\u8ff0\u3002<\/p>\n
\u8fd9\u91cc\u4ecb\u7ecd\u4e00\u79cd\u66f4\u5feb\u7684\u65b9\u6cd5\uff0c\u7531f[n] = 2 * f[n-1]<\/code>\u548cf[1] = 1<\/code>\u6613\u5f97f[n] = pow(2, (n - 1))<\/code>\uff0c\u53732\u7684n - 1<\/code>\u6b21\u5e42\u3002
\n\u8ba1\u7b97\u5e42\u7684\u65f6\u5019\uff0c\u53ef\u4ee5\u4f7f\u7528\u5feb\u901f\u5e42\u7b97\u6cd5\u52a0\u5feb\u901f\u5ea6\u3002<\/p>\n
\u4f8b\u5982\u6c423<\/code>\u768450<\/code>\u6b21\u65b9\uff1a\u6613\u5f9750<\/code>\u7684\u4e8c\u8fdb\u5236\u5f62\u5f0f\u4e3a110010<\/code>\uff0c\u537350 = 110010B = 100000B + 10000B + 10B<\/code>\uff0c\u5373pow(3, 50) = pow(3, 32) * pow(3, 16) * pow(3, 2)<\/code>\u3002\u56e0\u6b64\u5148\u6c42\u51fapow(3, 2)<\/code>\uff0c\u518d\u5229\u7528pow(3, 2)<\/code>\u6c42\u51fapow(3, 16)<\/code>\uff0c\u6700\u540e\u901a\u8fc7pow(3, 16)<\/code>\u6c42\u51fapow(3, 32)<\/code>\u5373\u53ef\u3002
\n\u4e8b\u5b9e\u4e0a\uff0c\u6613\u5f97pow(a, pow(2, n)) = pow(a, pow(2, n-1)) * pow(a, pow(2, n-1))<\/code>\uff0c\u4f8b\u5982pow(a, 1000B) = pow(a, 100B) * pow(a, 100B)<\/code>.<\/p>\n
\u8fd9\u4e2a\u7b97\u6cd5\u7684\u4e3b\u8981\u601d\u60f3\u5c31\u662f\u901a\u8fc7\u6307\u6570\u7684\u4e8c\u8fdb\u5236\u5f62\u5f0f\uff0c\u5de7\u5999\u5730\u5c06\u7ed3\u679c\u5206\u89e3\u4e3a\u82e5\u5e72\u4e2a\u4e58\u79ef\uff0c\u5373\u6307\u6570\u7684\u4e8c\u8fdb\u5236\u5f62\u5f0f\u4e0b\u4e3a1\u7684\u4f4d\u7f6e\u5bf9\u5e94\u7684\u503c\u3002
\n\u6c42base<\/code>\u7684number<\/code>\u6b21\u5e42\uff0c\u5177\u4f53\u7b56\u7565\u5982\u4e0b\uff1a
\n\u5f53number > 0<\/code>\u65f6\uff0c\u6267\u884c\u4ee5\u4e0b\u5faa\u73af
\n1. \u5bf9number<\/code>\u548c1<\/code>\u8fdb\u884c\u6309\u4f4d\u4e0e\u64cd\u4f5c\u3002\u5982\u679c\u7b49\u4e8e1<\/code>\uff0c\u8bf4\u660enumber<\/code>\u7684\u4e8c\u8fdb\u5236\u5f62\u5f0f\u5728\u5f53\u524d\u4f4d\u7f6e\u4e3a1\uff0c\u4ee4ans = ans * base<\/code>
\n2. \u4ee4base = base * base<\/code>
\n3. \u5bf9number<\/code>\u8fdb\u884c\u4e8c\u8fdb\u5236\u79fb\u4f4d\u64cd\u4f5c\uff0c\u53f3\u79fb\u4e00\u4f4d\u3002\u5373number = number >> 1<\/code><\/p>\n
C\u8bed\u8a00\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n
\/\/ \u6c42base\u7684number\u6b21\u5e42\nint quickpow(int base, int number)\n{\n    int ans = 1;\n    while (number)\n    {\n        if (number & 1)\n            ans *= base;\n        base *= base;\n        number >>= 1;\n    }\n    return ans;\n}\n<\/code><\/pre>\n
\u6211\u4eec\u4f1a\u53d1\u73b0\uff0c\u5faa\u73af\u6b21\u6570\u5176\u5b9e\u5c31\u662fnumber<\/code>\u7684\u4e8c\u8fdb\u5236\u5f62\u5f0f\u7684\u957f\u5ea6\uff0c\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(log(n))<\/code><\/p>\n
C++<\/h3>\n
class Solution\n{\npublic:\n    int jumpFloorII(int number)\n    {\n        int base = 2, ans = 1;\n        number--;\n        while (number)\n        {\n            if (number & 1)\n                ans *= base;\n            base *= base;\n            number >>= 1;\n        }\n        return ans;\n    }\n};\n<\/code><\/pre>\n
Java<\/h3>\n
public class Solution {\n    public int JumpFloorII(int target) {\n        int base = 2, ans = 1;\n        target--;\n        while (target > 0) {\n            if ((target & 1) == 1)\n                ans *= base;\n            base *= base;\n            target >>= 1;\n        }\n        return ans;\n    }\n}\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u9898\u76ee\u63cf\u8ff0 \u4e00\u53ea\u9752\u86d9\u4e00\u6b21\u53ef\u4ee5\u8df3\u4e0a1\u7ea7\u53f0\u9636\uff0c\u4e5f\u53ef\u4ee5\u8df3\u4e0a2\u7ea7\u2026\u2026\u5b83\u4e5f\u53ef\u4ee5\u8df3\u4e0an\u7ea7\u3002\u6c42\u8be5\u9752\u86d9\u8df3\u4e0a\u4e00\u4e2an\u7ea7\u7684\u53f0\u9636\u603b\u5171\u6709\u591a […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[39,49],"class_list":["post-688","post","type-post","status-publish","format-standard","hentry","category-algo","tag-offer","tag-49"],"_links":{"self":[{"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/posts\/688","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=688"}],"version-history":[{"count":0,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/posts\/688\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=688"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=688"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=688"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}