{"id":52,"date":"2023-10-22T22:21:00","date_gmt":"2023-10-22T14:21:00","guid":{"rendered":"http:\/\/www.cmd137blog.top\/?p=52"},"modified":"2024-03-31T22:25:39","modified_gmt":"2024-03-31T14:25:39","slug":"%e3%80%90%e6%b4%9b%e8%b0%b7%e5%88%b7%e9%a2%98%e7%ac%94%e8%ae%b0%e3%80%91p1601-ab-problem%ef%bc%88%e9%ab%98%e7%b2%be%ef%bc%89%ef%bc%9a%e9%ab%98%e7%b2%be%e5%ba%a6%e5%8a%a0%e6%b3%95","status":"publish","type":"post","link":"http:\/\/www.cmd137blog.top\/?p=52","title":{"rendered":"\u3010\u6d1b\u8c37\u5237\u9898\u7b14\u8bb0\u3011P1601 A+B Problem\uff08\u9ad8\u7cbe\uff09\uff1a\u9ad8\u7cbe\u5ea6\u52a0\u6cd5"},"content":{"rendered":"\n

\u4e00\u3001\u539f\u9898\uff1a<\/h1>\n\n\n\n

A+B Problem\uff08\u9ad8\u7cbe\uff09<\/h1>\n\n\n\n

\u9898\u76ee\u63cf\u8ff0<\/h2>\n\n\n\n

\u9ad8\u7cbe\u5ea6\u52a0\u6cd5\uff0c\u76f8\u5f53\u4e8e a+b problem\uff0c\u4e0d\u7528\u8003\u8651\u8d1f\u6570<\/strong>\u3002<\/p>\n\n\n\n

\u8f93\u5165\u683c\u5f0f<\/h2>\n\n\n\n

\u5206\u4e24\u884c\u8f93\u5165\u3002$a,b \\leq 10^{500}$\u3002<\/p>\n\n\n\n

\u8f93\u51fa\u683c\u5f0f<\/h2>\n\n\n\n

\u8f93\u51fa\u53ea\u6709\u4e00\u884c\uff0c\u4ee3\u8868 $a+b$ \u7684\u503c\u3002<\/p>\n\n\n\n

\u6837\u4f8b #1<\/h2>\n\n\n\n

\u6837\u4f8b\u8f93\u5165 #1<\/h3>\n\n\n\n
1\n1<\/code><\/pre>\n\n\n\n
\u6837\u4f8b\u8f93\u51fa #1<\/h3>\n\n\n\n
2<\/code><\/pre>\n\n\n\n
\u6837\u4f8b #2<\/h2>\n\n\n\n
\u6837\u4f8b\u8f93\u5165 #2<\/h3>\n\n\n\n
1001\n9099<\/code><\/pre>\n\n\n\n
\u6837\u4f8b\u8f93\u51fa #2<\/h3>\n\n\n\n
10100<\/code><\/pre>\n\n\n\n
\u63d0\u793a<\/h2>\n\n\n\n
$20\\%$ \u7684\u6d4b\u8bd5\u6570\u636e\uff0c$0\\le a,b \\le10^9$\uff1b<\/p>\n\n\n\n
$40\\%$ \u7684\u6d4b\u8bd5\u6570\u636e\uff0c$0\\le a,b \\le10^{18}$\u3002<\/p>\n\n\n\n
\u4e8c\u3001\u89e3\u51b3\uff1a<\/h1>\n\n\n\n
\u9ad8\u7cbe\u5ea6\u8ba1\u7b97\uff08Arbitrary-Precision Arithmetic\uff09\uff0c\u4e5f\u88ab\u79f0\u4f5c\u5927\u6574\u6570\uff08bignum\uff09\u8ba1\u7b97\uff0c\u8fd0\u7528\u4e86\u4e00\u4e9b\u7b97\u6cd5\u7ed3\u6784\u6765\u652f\u6301\u66f4\u5927\u6574\u6570\u95f4\u7684\u8fd0\u7b97\uff08\u6570\u5b57\u5927\u5c0f\u8d85\u8fc7\u8bed\u8a00\u5185\u5efa\u6574\u578b\uff09—\u6458\u81eaOI Wiki<\/p>\n\n\n\n
1.\u5b58\u50a8\uff1a<\/h2>\n\n\n\n
\u5728\u4f7f\u7528\u9ad8\u7cbe\u5ea6\u8ba1\u7b97\u65f6\uff0c\u6211\u4eec\u5e38\u7528\u5b57\u7b26\u4e32\u6765\u4fdd\u5b58\u3002
\u5b9a\u4e49char s1[500],s2[500],\uff08500\u662f\u4e3a\u4e86\u9632\u6b62\u8d8a\u754c\uff0c501\uff0c499\u90fd\u884c\uff09
\u800c\u5728\u5b9e\u9645\u64cd\u4f5c\u65f6\uff0c\u6211\u4eec\u9700\u8981\u53cd\u8f6c\u5b58\u50a8\uff0c\u4f7f\u6570\u5b57\u7684\u6700\u4f4e\u4e3a\u5c31\u662f\u4e0b\u6807\u6700\u5c0f\u7684\u4f4d\u7f6e\uff0c\u540c\u65f6\u4f7f\u6570\u5b57\u7684\u76f8\u540c\u6743\u503c\u4f4d\u5bf9\u9f50\uff0c\u4ee5\u4fbf\u8fd0\u7b97\u3002
\u7528\u6570\u7ec4a\uff0cb\u4fdd\u5b58\u53cd\u8f6c\u540e\u7684\u4e24\u7ec4\u6570\uff0cc[500]\u6765\u4fdd\u5b58\u7ed3\u679c\u3002
\u7279\u522b\u6ce8\u610f\uff0c\u6b64\u65f6\u4e2a\u4f4d\u4e0b\u6807\u4e3a1\u800c\u975e0\uff1b
\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n
<\/circle><\/circle><\/circle><\/g><\/svg><\/span><\/path><\/path><\/svg><\/span>
    <\/span>char<\/span> <\/span>s1<\/span>[<\/span>500<\/span>],<\/span>s2<\/span>[<\/span>500<\/span>]<\/span>;<\/span><\/span>\n    <\/span>int<\/span> <\/span>a<\/span>[<\/span>500<\/span>],<\/span>b<\/span>[<\/span>500<\/span>],<\/span>c<\/span>[<\/span>500<\/span>]<\/span>;<\/span><\/span>\n    \/\/\u6ce8\u610f\u521d\u59cb\u5316<\/span><\/span>\n    <\/span>memset<\/span>(<\/span>a<\/span>,<\/span> <\/span>0<\/span>,<\/span> <\/span>sizeof<\/span>(<\/span>a<\/span>))<\/span>;<\/span><\/span>\n    <\/span>memset<\/span>(<\/span>b<\/span>,<\/span> <\/span>0<\/span>,<\/span> <\/span>sizeof<\/span>(<\/span>b<\/span>))<\/span>;<\/span><\/span>\n    <\/span>memset<\/span>(<\/span>c<\/span>,<\/span> <\/span>0<\/span>,<\/span> <\/span>sizeof<\/span>(<\/span>c<\/span>))<\/span>;<\/span><\/span>\n<\/span>\n    <\/span>int<\/span> la<\/span>=<\/span>0<\/span>,<\/span>lb<\/span>=<\/span>0<\/span>,<\/span>lc<\/span>=<\/span>0<\/span>;<\/span><\/span>\n    cin<\/span>>><\/span>s1<\/span>>><\/span>s2<\/span>;<\/span><\/span>\n<\/span>\n    la<\/span>=<\/span>strlen<\/span>(<\/span>s1<\/span>)<\/span>;<\/span><\/span>\n    lb <\/span>=<\/span>strlen<\/span>(<\/span>s2<\/span>)<\/span>;<\/span><\/span>\n<\/span>\n    \/\/\u53cd\u8f6c\u5b58\u50a8<\/span><\/span>\n    <\/span>for<\/span>(<\/span>int<\/span> i <\/span>=<\/span>0<\/span>;<\/span>i<\/span><<\/span>la<\/span>;<\/span>i<\/span>++<\/span>){<\/span><\/span>\n        <\/span>a<\/span>[<\/span>la<\/span>-<\/span>i<\/span>]<\/span>=<\/span>s1<\/span>[<\/span>i<\/span>]<\/span>-<\/span>'<\/span>0<\/span>'<\/span>;<\/span>\/\/\u5c06\u5b57\u7b26\u8f6c\u4e3a\u6570\u5b57<\/span><\/span>\n    <\/span>}<\/span><\/span>\n    <\/span>for<\/span>(<\/span>int<\/span> i <\/span>=<\/span>0<\/span>;<\/span>i<\/span><<\/span>lb<\/span>;<\/span>i<\/span>++<\/span>){<\/span><\/span>\n        <\/span>a<\/span>[<\/span>lb<\/span>-<\/span>i<\/span>]<\/span>=<\/span>s2<\/span>[<\/span>i<\/span>]<\/span>-<\/span>'<\/span>0<\/span>'<\/span>;<\/span><\/span>\n    <\/span>}<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n
2.\u8ba1\u7b97\uff1a<\/h2>\n\n\n\n
\u9996\u5148\u8ba1\u7b97\u8f93\u51fa\u7ed3\u679c\u7684\u957f\u5ea6lc\uff08 \u52a0\u4e00\u662f\u4e3a\u4e86\u8ba1\u7b97a,b\u6700\u5927\u4f4d\u76f8\u52a0\u540e\u7684\u8fdb\u4e00\uff09
\u800c\u540e\u9010\u4f4d\u8ba1\u7b97\uff0c\u7279\u522b\u6ce8\u610f\u201cc[i]+=a[i]+b[i];\u201d\u4e2d\u7684\u201c+=\u201d\uff0c\u662f\u4e3a\u4e86\u8ba1\u7b97\u524d\u4e00\u4f4d\u8ba1\u7b97\u65f6\u8fdb\u76841\u3002<\/p>\n\n\n\n
<\/circle><\/circle><\/circle><\/g><\/svg><\/span><\/path><\/path><\/svg><\/span>
lc <\/span>=<\/span> <\/span>max<\/span>(<\/span>la<\/span>,<\/span> lb<\/span>)<\/span> <\/span>+<\/span> <\/span>1<\/span>;<\/span><\/span>\n<\/span>\n    <\/span>for<\/span>(<\/span>int<\/span> i <\/span>=<\/span> <\/span>1<\/span>;<\/span>i<\/span><=<\/span>lc<\/span>;<\/span>i<\/span>++<\/span>){<\/span><\/span>\n        <\/span>c<\/span>[<\/span>i<\/span>]<\/span>+=<\/span>a<\/span>[<\/span>i<\/span>]<\/span>+<\/span>b<\/span>[<\/span>i<\/span>]<\/span>;<\/span>\/\/\u7279\u522b\u6ce8\u610f+=<\/span><\/span>\n        <\/span>c<\/span>[<\/span>i<\/span>+<\/span>1<\/span>]<\/span>=<\/span>c<\/span>[<\/span>i<\/span>]<\/span>\/<\/span>10<\/span>;<\/span><\/span>\n        <\/span>c<\/span>[<\/span>i<\/span>]<\/span>=<\/span>c<\/span>[<\/span>i<\/span>]<\/span>%<\/span>10<\/span>;<\/span><\/span>\n    <\/span>}<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n
3.\u8f93\u51fa\uff1a<\/h2>\n\n\n\n
\u9996\u5148\u5224\u65ad\u8f93\u51fa\u7684\u4f4d\u6570\uff0c\u5373\u5904\u7406\u524d\u5bfc0\uff1b\uff08&&lc>0\u662f\u4e3a\u4e86\u4e0d\u5220\u9664\u7ed3\u679c\u4e3a0\u76840\uff09
\u540e\u9010\u4f4d\u8f93\u51fa\uff08\u6ce8\u610f\u9006\u5e8f\uff09\u3002<\/p>\n\n\n\n
<\/circle><\/circle><\/circle><\/g><\/svg><\/span><\/path><\/path><\/svg><\/span>
if<\/span> <\/span>(<\/span>c<\/span>[<\/span>lc<\/span>]<\/span> <\/span>==<\/span> <\/span>0<\/span> <\/span>&&<\/span> lc <\/span>><\/span> <\/span>0<\/span>)<\/span><\/span>\n        lc<\/span>--;<\/span><\/span>\n<\/span>\n    <\/span>for<\/span> <\/span>(<\/span>int<\/span> i <\/span>=<\/span> lc<\/span>;<\/span> i <\/span>><\/span> <\/span>0<\/span>;<\/span> i<\/span>--<\/span>)<\/span> <\/span>{<\/span><\/span>\n        cout <\/span><<<\/span> <\/span>c<\/span>[<\/span>i<\/span>]<\/span>;<\/span><\/span>\n    <\/span>}<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n
———————————————–<\/h2>\n\n\n\n
\u5168\u90e8\u6e90\u4ee3\u7801<\/h4>\n\n\n\n
<\/circle><\/circle><\/circle><\/g><\/svg><\/span><\/path><\/path><\/svg><\/span>
#<\/span>include<\/span> <\/span><<\/span>iostream<\/span>><\/span><\/span>\n#<\/span>include<\/span> <\/span><<\/span>string.h<\/span>><\/span><\/span>\n#<\/span>include<\/span> <\/span><<\/span>algorithm<\/span>><\/span><\/span>\nusing<\/span> <\/span>namespace<\/span> std<\/span>;<\/span><\/span>\n<\/span>\n<\/span>\n<\/span>\nint<\/span> <\/span>main<\/span>()<\/span> <\/span>{<\/span><\/span>\n\t<\/span>char<\/span> <\/span>s1<\/span>[<\/span>500<\/span>],<\/span> <\/span>s2<\/span>[<\/span>500<\/span>]<\/span>;<\/span><\/span>\n\t<\/span>int<\/span> <\/span>a<\/span>[<\/span>500<\/span>],<\/span> <\/span>b<\/span>[<\/span>500<\/span>],<\/span> <\/span>c<\/span>[<\/span>500<\/span>]<\/span>;<\/span><\/span>\n<\/span>\n\t<\/span>memset<\/span>(<\/span>a<\/span>,<\/span> <\/span>0<\/span>,<\/span> <\/span>sizeof<\/span>(<\/span>a<\/span>))<\/span>;<\/span><\/span>\n\t<\/span>memset<\/span>(<\/span>b<\/span>,<\/span> <\/span>0<\/span>,<\/span> <\/span>sizeof<\/span>(<\/span>b<\/span>))<\/span>;<\/span><\/span>\n\t<\/span>memset<\/span>(<\/span>c<\/span>,<\/span> <\/span>0<\/span>,<\/span> <\/span>sizeof<\/span>(<\/span>c<\/span>))<\/span>;<\/span><\/span>\n<\/span>\n\t<\/span>int<\/span> la<\/span>,<\/span> lb<\/span>,<\/span> lc<\/span>;<\/span><\/span>\n\tcin <\/span>>><\/span> s1 <\/span>>><\/span> s2<\/span>;<\/span><\/span>\n<\/span>\n\tla <\/span>=<\/span> <\/span>strlen<\/span>(<\/span>s1<\/span>)<\/span>;<\/span><\/span>\n\tlb <\/span>=<\/span> <\/span>strlen<\/span>(<\/span>s2<\/span>)<\/span>;<\/span><\/span>\n<\/span>\n\t\/\/\u53cd\u8f6c\u5b58\u50a8<\/span><\/span>\n\t<\/span>for<\/span> <\/span>(<\/span>int<\/span> i <\/span>=<\/span> <\/span>0<\/span>;<\/span> i <\/span><<\/span> la<\/span>;<\/span> i<\/span>++<\/span>)<\/span> <\/span>{<\/span><\/span>\n\t\t<\/span>a<\/span>[<\/span>la <\/span>-<\/span> i<\/span>]<\/span> <\/span>=<\/span> <\/span>s1<\/span>[<\/span>i<\/span>]<\/span> <\/span>-<\/span> <\/span>'<\/span>0<\/span>'<\/span>;<\/span> \/\/\u5c06\u5b57\u7b26\u8f6c\u4e3a\u6570\u5b57<\/span><\/span>\n\t<\/span>}<\/span><\/span>\n\t<\/span>for<\/span> <\/span>(<\/span>int<\/span> i <\/span>=<\/span> <\/span>0<\/span>;<\/span> i <\/span><<\/span> lb<\/span>;<\/span> i<\/span>++<\/span>)<\/span> <\/span>{<\/span><\/span>\n\t\t<\/span>b<\/span>[<\/span>lb <\/span>-<\/span> i<\/span>]<\/span> <\/span>=<\/span> <\/span>s2<\/span>[<\/span>i<\/span>]<\/span> <\/span>-<\/span> <\/span>'<\/span>0<\/span>'<\/span>;<\/span><\/span>\n\t<\/span>}<\/span><\/span>\n<\/span>\n\tlc <\/span>=<\/span> <\/span>max<\/span>(<\/span>la<\/span>,<\/span> lb<\/span>)<\/span> <\/span>+<\/span> <\/span>1<\/span>;<\/span><\/span>\n<\/span>\n\t<\/span>for<\/span> <\/span>(<\/span>int<\/span> i <\/span>=<\/span> <\/span>1<\/span>;<\/span> i <\/span><=<\/span> lc<\/span>;<\/span> i<\/span>++<\/span>)<\/span> <\/span>{<\/span><\/span>\n\t\t<\/span>c<\/span>[<\/span>i<\/span>]<\/span> <\/span>+=<\/span> <\/span>a<\/span>[<\/span>i<\/span>]<\/span> <\/span>+<\/span> <\/span>b<\/span>[<\/span>i<\/span>]<\/span>;<\/span> \/\/\u7279\u522b\u6ce8\u610f+=<\/span><\/span>\n\t\t<\/span>c<\/span>[<\/span>i <\/span>+<\/span> <\/span>1<\/span>]<\/span> <\/span>=<\/span> <\/span>c<\/span>[<\/span>i<\/span>]<\/span> <\/span>\/<\/span> <\/span>10<\/span>;<\/span><\/span>\n\t\t<\/span>c<\/span>[<\/span>i<\/span>]<\/span> <\/span>=<\/span> <\/span>c<\/span>[<\/span>i<\/span>]<\/span> <\/span>%<\/span> <\/span>10<\/span>;<\/span><\/span>\n\t<\/span>}<\/span><\/span>\n<\/span>\n\t<\/span>if<\/span> <\/span>(<\/span>c<\/span>[<\/span>lc<\/span>]<\/span> <\/span>==<\/span> <\/span>0<\/span> <\/span>&&<\/span> lc <\/span>><\/span> <\/span>0<\/span>)<\/span><\/span>\n\t\tlc<\/span>--;<\/span><\/span>\n<\/span>\n\t<\/span>for<\/span> <\/span>(<\/span>int<\/span> i <\/span>=<\/span> lc<\/span>;<\/span> i <\/span>><\/span> <\/span>0<\/span>;<\/span> i<\/span>--<\/span>)<\/span> <\/span>{<\/span><\/span>\n\t\tcout <\/span><<<\/span> <\/span>c<\/span>[<\/span>i<\/span>]<\/span>;<\/span><\/span>\n\t<\/span>}<\/span><\/span>\n<\/span>\n}<\/span><\/span><\/code><\/pre><\/div>\n","protected":false},"excerpt":{"rendered":"
\u4e00\u3001\u539f\u9898\uff1a A+B Problem\uff08\u9ad8\u7cbe\uff09 \u9898\u76ee\u63cf\u8ff0 \u9ad8\u7cbe\u5ea6\u52a0\u6cd5\uff0c\u76f8\u5f53\u4e8e a+b problem\uff0c\u4e0d\u7528\u8003\u8651\u8d1f\u6570 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[7,6,8],"class_list":["post-52","post","type-post","status-publish","format-standard","hentry","category-3","tag-7","tag-6","tag-8"],"_links":{"self":[{"href":"http:\/\/www.cmd137blog.top\/index.php?rest_route=\/wp\/v2\/posts\/52","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.cmd137blog.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.cmd137blog.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.cmd137blog.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.cmd137blog.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=52"}],"version-history":[{"count":1,"href":"http:\/\/www.cmd137blog.top\/index.php?rest_route=\/wp\/v2\/posts\/52\/revisions"}],"predecessor-version":[{"id":53,"href":"http:\/\/www.cmd137blog.top\/index.php?rest_route=\/wp\/v2\/posts\/52\/revisions\/53"}],"wp:attachment":[{"href":"http:\/\/www.cmd137blog.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=52"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.cmd137blog.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=52"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.cmd137blog.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=52"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}