{"id":620,"date":"2026-07-10T22:41:04","date_gmt":"2026-07-10T14:41:04","guid":{"rendered":"https:\/\/mitongxue.cn\/?p=620"},"modified":"2026-07-10T22:41:04","modified_gmt":"2026-07-10T14:41:04","slug":"%e7%a7%b0%e7%a0%9d%e7%a0%81","status":"publish","type":"post","link":"https:\/\/mitongxue.cn\/index.php\/2026\/07\/10\/%e7%a7%b0%e7%a0%9d%e7%a0%81\/","title":{"rendered":"\u79f0\u781d\u7801"},"content":{"rendered":"\n

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

<\/mspace><\/mrow><\/semantics><\/math>\u5bf9\u4e8e\u7ed9\u5b9a\u7684 n<\/mi><\/mrow><\/semantics><\/math>n<\/em> \u79cd\u781d\u7801\uff0c\u91cd\u91cf\u4e92\u4e0d\u76f8\u7b49\uff0c\u4f9d\u6b21\u4e3a m<\/mi>1<\/mn><\/msub>,<\/mo>m<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mo>,<\/mo>m<\/mi>n<\/mi><\/msub><\/mrow><\/semantics><\/math>m<\/em>1\u200b,m<\/em>2\u200b,\u2026,m<\/em>n<\/em>\u200b \uff0c\u6570\u91cf\u4f9d\u6b21\u4e3a x<\/mi>1<\/mn><\/msub>,<\/mo>x<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mo>,<\/mo>x<\/mi>n<\/mi><\/msub><\/mrow><\/semantics><\/math>x<\/em>1\u200b,x<\/em>2\u200b,\u2026,x<\/em>n<\/em>\u200b \uff0c
<\/mspace><\/mrow><\/semantics><\/math>\u73b0\u5728\u8981\u7528\u8fd9\u4e9b\u781d\u7801\u53bb\u79f0\u7269\u4f53\u7684\u91cd\u91cf\uff08\u653e\u5728\u540c\u4e00\u4fa7\uff09\uff0c\u95ee\u80fd\u79f0\u51fa\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u91cd\u91cf\u3002\u7279\u522b\u5730\uff0c\u79f0\u91cd\u91cd\u91cf\u5305\u62ec 0<\/mn><\/mrow><\/semantics><\/math>0 \u3002<\/p>\n\n\n\n

\u8f93\u5165\u63cf\u8ff0\uff1a<\/h3>\n\n\n\n

<\/mspace><\/mrow><\/semantics><\/math>\u7b2c\u4e00\u884c\u8f93\u5165\u4e00\u4e2a\u6574\u6570 n<\/mi>(<\/mo>1<\/mn>\u2266<\/mo>n<\/mi>\u2266<\/mo>10<\/mn>)<\/mo><\/mrow><\/mrow><\/semantics><\/math>n<\/em>(1\u2266n<\/em>\u226610) \u4ee3\u8868\u781d\u7801\u7684\u4e2a\u6570\u3002
<\/mspace><\/mrow><\/semantics><\/math>\u7b2c\u4e8c\u884c\u8f93\u5165 n<\/mi><\/mrow><\/semantics><\/math>n<\/em> \u4e2a\u6574\u6570 m<\/mi>1<\/mn><\/msub>,<\/mo>m<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mo>,<\/mo>m<\/mi>n<\/mi><\/msub>(<\/mo>1<\/mn>\u2266<\/mo>m<\/mi>i<\/mi><\/msub>\u2266<\/mo>2000<\/mn>)<\/mo><\/mrow><\/mrow><\/semantics><\/math>m<\/em>1\u200b,m<\/em>2\u200b,\u2026,m<\/em>n<\/em>\u200b(1\u2266m<\/em>i<\/em>\u200b\u22662000) \u4ee3\u8868\u6bcf\u79cd\u781d\u7801\u7684\u91cd\u91cf\u3002
<\/mspace><\/mrow><\/semantics><\/math>\u7b2c\u4e09\u884c\u8f93\u5165 n<\/mi><\/mrow><\/semantics><\/math>n<\/em> \u4e2a\u6574\u6570 x<\/mi>1<\/mn><\/msub>,<\/mo>x<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mo>,<\/mo>x<\/mi>n<\/mi><\/msub>(<\/mo>1<\/mn>\u2266<\/mo>x<\/mi>i<\/mi><\/msub>\u2266<\/mo>10<\/mn>)<\/mo><\/mrow><\/mrow><\/semantics><\/math>x<\/em>1\u200b,x<\/em>2\u200b,\u2026,x<\/em>n<\/em>\u200b(1\u2266x<\/em>i<\/em>\u200b\u226610) \u4ee3\u8868\u6bcf\u79cd\u781d\u7801\u7684\u6570\u91cf\u3002<\/p>\n\n\n\n

\u8f93\u51fa\u63cf\u8ff0\uff1a<\/h3>\n\n\n\n

<\/mspace><\/mrow><\/semantics><\/math>\u8f93\u51fa\u4e00\u4e2a\u6574\u6570\uff0c\u4ee3\u8868\u5229\u7528\u7ed9\u5b9a\u7684\u781d\u7801\u53ef\u4ee5\u79f0\u51fa\u7684\u4e0d\u540c\u7684\u91cd\u91cf\u6570\u3002<\/p>\n\n\n\n

\u793a\u4f8b1<\/h2>\n\n\n\n

\u8f93\u5165\uff1a<\/p>\n\n\n\n

2\n1 2\n2 1<\/code><\/pre>\n\n\n\n
\u8f93\u51fa\uff1a<\/p>\n\n\n\n
5<\/code><\/pre>\n\n\n\n
\u8bf4\u660e\uff1a<\/p>\n\n\n\n
<\/mspace><\/mrow><\/semantics><\/math>\u5728\u8fd9\u4e2a\u6837\u4f8b\u4e2d\uff0c\u6709 2<\/mn><\/mrow><\/semantics><\/math>2 \u4e2a\u91cd\u91cf\u4e3a 1<\/mn><\/mrow><\/semantics><\/math>1 \u7684\u781d\u7801\uff0c1<\/mn><\/mrow><\/semantics><\/math>1 \u4e2a\u91cd\u91cf\u4e3a 2<\/mn><\/mrow><\/semantics><\/math>2 \u7684\u781d\u7801\u3002\u79f0\u91cd\u65b9\u5f0f\u5982\u4e0b\uff1a
<\/mspace>\u2219<\/mo>\u2009<\/mtext><\/mrow><\/semantics><\/math>\u2219\u4e0d\u653e\u781d\u7801\uff0c\u79f0\u91cd\u91cd\u91cf\u4e3a 0<\/mn><\/mrow><\/semantics><\/math>0 \uff1b
<\/mspace>\u2219<\/mo>\u2009<\/mtext><\/mrow><\/semantics><\/math>\u2219\u653e 1<\/mn><\/mrow><\/semantics><\/math>1 \u4e2a\u91cd\u91cf\u4e3a 1<\/mn><\/mrow><\/semantics><\/math>1 \u7684\u781d\u7801\uff0c\u79f0\u91cd\u91cd\u91cf\u4e3a 1<\/mn><\/mrow><\/semantics><\/math>1 \uff1b
<\/mspace>\u2219<\/mo>\u2009<\/mtext><\/mrow><\/semantics><\/math>\u2219\u653e 2<\/mn><\/mrow><\/semantics><\/math>2 \u4e2a\u91cd\u91cf\u4e3a 1<\/mn><\/mrow><\/semantics><\/math>1 \u7684\u781d\u7801\uff0c\u79f0\u91cd\u91cd\u91cf\u4e3a 2<\/mn><\/mrow><\/semantics><\/math>2 \uff1b
<\/mspace>\u2219<\/mo>\u2009<\/mtext><\/mrow><\/semantics><\/math>\u2219\u653e 1<\/mn><\/mrow><\/semantics><\/math>1 \u4e2a\u91cd\u91cf\u4e3a 1<\/mn><\/mrow><\/semantics><\/math>1 \u7684\u781d\u7801\u30011<\/mn><\/mrow><\/semantics><\/math>1 \u4e2a\u91cd\u91cf\u4e3a 2<\/mn><\/mrow><\/semantics><\/math>2 \u7684\u781d\u7801\uff0c\u79f0\u91cd\u91cd\u91cf\u4e3a 3<\/mn><\/mrow><\/semantics><\/math>3 \uff1b
<\/mspace>\u2219<\/mo>\u2009<\/mtext><\/mrow><\/semantics><\/math>\u2219\u653e 2<\/mn><\/mrow><\/semantics><\/math>2 \u4e2a\u91cd\u91cf\u4e3a 1<\/mn><\/mrow><\/semantics><\/math>1 \u7684\u781d\u7801\u30011<\/mn><\/mrow><\/semantics><\/math>1 \u4e2a\u91cd\u91cf\u4e3a 2<\/mn><\/mrow><\/semantics><\/math>2 \u7684\u781d\u7801\uff0c\u79f0\u91cd\u91cd\u91cf\u4e3a 4<\/mn><\/mrow><\/semantics><\/math>4 \u3002
<\/mspace><\/mrow><\/semantics><\/math>\u56e0\u6b64\uff0c\u80fd\u79f0\u51fa\u7684\u4e0d\u540c\u91cd\u91cf\u6709 5<\/mn><\/mrow><\/semantics><\/math>5 \u79cd\uff0c\u5206\u522b\u662f 0<\/mn>,<\/mo>1<\/mn>,<\/mo>2<\/mn>,<\/mo>3<\/mn>,<\/mo>4<\/mn><\/mrow><\/semantics><\/math>0,1,2,3,4 \u3002<\/code><\/pre>\n\n\n\n
<\/p>\n\n\n\n
\u7b2c\u4e00\u7248\u601d\u8def<\/p>\n\n\n\n
    \n
  1. \u5c06\u6240\u6709\u781d\u7801\u5165\u6808<\/li>\n\n\n\n
  2. \u901a\u8fc7\u6ed1\u52a8\u7a97\u53e3\u7684\u65b9\u5f0f\u8ba1\u7b97\u6240\u6709\u781d\u7801\u7684\u548c\uff0c\u53bb\u6389\u91cd\u590d\u7684<\/li>\n<\/ol>\n\n\n\n
    void async function () {\n    \/\/ Write your code here\n    const res = [];\n    const num = (await readline());\n    const list = (await readline()).split(\" \");\n    const listNum = (await readline()).split(\" \");\n    \/\/console.log(listNum);\n    for(let i=0; i< num;i++){\n        for(let j =0; j<listNum[i]; j++){\n            res.push(list[i]*1);\n        }\n    }\n   \n    \/\/\u5b50\u5e8f\u5217\n    \/\/console.log(res);\n    const total = [0];\n    const child=()=>{\n        \/\/\u83b7\u53d6\u4e0d\u540c\u7684\u7ec4\u5408\uff1a\u653e\u5355\u4e2a\u781d\u7801\uff0c...n\u4e2a\u781d\u7801\n        for(let i=1;i<=res.length;i++){\n            \/\/\u63a7\u5236\u7a97\u53e3\n            for(let j=0;j<res.length;j++){\n                const temp = res.slice(j,j+i);\n                let sum = 0;\n                for(const v of temp){\n                    sum += v;\n                }\n                if(!total.includes(sum)){\n                    total.push(sum);\n                }\n            }\n        }\n    }\n    child();\n    console.log(total.length)\n\n}()<\/code><\/pre>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
    \u53e6\u4e00\u79cd\u65b9\u5f0f<\/p>\n\n\n\n
    void (async function () {\n    \/\/ Write your code here\n   const n = parseInt(await readline());\n    const category = (await readline()).split(\" \").map(Number);\n    const cnt = (await readline()).split(\" \").map(Number);\n    \/\/\u5e8f\u5217\u5316\u781d\u7801\uff0c\u6bd4\u5982\u4e24\u4e2a1g\u548c\u4e00\u4e2a2g\u7684\u781d\u7801\u7528[1,1,2]\u8868\u793a\n    const nums = [];\n    for (let i = 0; i < n; i++) {\n        for (let j = 0; j < cnt[i]; j++) {\n            nums.push(category[i]);\n        }\n    }\n    \/\/ \u8ba1\u7b97\u79cd\u6570\n    const set = new Set([0]);\n    for(let i = 0; i < nums.length; i++){\n        let arr = [...set];\n        for(const k of arr){\n            set.add(k+nums[i]);\n        }\n    }\n    console.log(set.size);\n})();<\/code><\/pre>\n\n\n\n
    \u4e0a\u9762\u7684\u4ee3\u7801\u6709\u95ee\u9898\uff0c\u53ea\u8003\u8651\u4e86\u781d\u7801\u653e\u540c\u4fa7\u7684\u60c5\u51b5\uff0c\u8fd8\u9700\u8981\u8003\u8651\u781d\u7801\u653e\u5bf9\u4fa7\u7684\u60c5\u51b5\u3002<\/p>\n\n\n\n
    \u52a8\u6001\u89c4\u5212<\/h2>\n\n\n\n
    \u4e00\u3001\u4e8c\u7ef4 DP \u8868\u5b9a\u4e49<\/h2>\n\n\n\n
    \u7eb5\u5411\uff08\u884c i\uff09<\/h3>\n\n\n\n
    i = \u5df2\u7ecf\u5904\u7406\u5b8c\u524d i \u4e2a\u781d\u7801<\/p>\n\n\n\n