{"id":75056,"date":"2026-02-11T09:57:30","date_gmt":"2026-02-11T01:57:30","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/75056.html"},"modified":"2026-02-11T09:57:30","modified_gmt":"2026-02-11T01:57:30","slug":"gesp2025%e5%b9%b46%e6%9c%88%e8%ae%a4%e8%af%81c%e4%ba%8c%e7%ba%a7-%e7%ac%ac%e4%b8%89%e9%83%a8%e5%88%86%e7%bc%96%e7%a8%8b%e9%a2%98-2%e3%80%81%e5%b9%82%e5%92%8c%e6%95%b0%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/75056.html","title":{"rendered":"GESP2025\u5e746\u6708\u8ba4\u8bc1C++\u4e8c\u7ea7( \u7b2c\u4e09\u90e8\u5206\u7f16\u7a0b\u9898 2\u3001\u5e42\u548c\u6570\uff09"},"content":{"rendered":"

\"\"\"\"\"\"<\/p>\n

\n

\u300a\u5e42\u548c\u6570\u738b\u56fd\u7684\u79d8\u5bc6\u300b<\/h2>\n
\n

📖 \u4e00\u3001\u6545\u4e8b\u80cc\u666f：\u5e42\u548c\u6570\u738b\u56fd 🏰<\/h2>\n

1\u3001\u5728\u6570\u5b57\u5927\u9646\u4e0a，\u6709\u4e00\u79cd\u7279\u522b\u795e\u5947\u7684\u6570\u5b57，\u53eb\u505a\u2014\u2014<\/h4>\n

\u2728 \u5e42\u548c\u6570<\/p>\n

\n

2\u3001\u56fd\u738b\u89c4\u5b9a：<\/h4>\n

\u5982\u679c\u4e00\u4e2a\u6570 N
\n\u53ef\u4ee5\u5199\u6210
\n\u4e24\u4e2a 2 \u7684\u5e42\u76f8\u52a0<\/p>\n

\u6bd4\u5982：
\nN = 2^a + 2^b<\/p>\n

\u90a3\u4e48，N \u5c31\u662f\u5e42\u548c\u6570！<\/p>\n

\n

3\u3001\u4f60\u7684\u4efb\u52a1\u662f：<\/h4>\n

🎯 \u5728\u4e00\u4e2a\u8303\u56f4 [L, R] \u91cc，\u627e\u51fa\u4e00\u5171\u6709\u591a\u5c11\u4e2a\u5e42\u548c\u6570<\/p>\n

\n

🧠 \u4e8c\u3001\u5148\u628a\u201c\u5e42\u201d\u8bb2\u660e\u767d（\u8d85\u7ea7\u5173\u952e）<\/h2>\n

1\u3001\u4ec0\u4e48\u662f 2 \u7684\u5e42？<\/h4>\n

\u5c31\u662f\u4e00\u76f4\u4e58 2：<\/p>\n\n\u5199\u6cd5\u6570\u5b57<\/tr>\n\n\n\n\n\n\n\n
2\u2070<\/td>\n1<\/td>\n<\/tr>\n
2\u00b9<\/td>\n2<\/td>\n<\/tr>\n
2\u00b2<\/td>\n4<\/td>\n<\/tr>\n
2\u00b3<\/td>\n8<\/td>\n<\/tr>\n
2\u2074<\/td>\n16<\/td>\n<\/tr>\n
2\u2075<\/td>\n32<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

2\u3001📌 \u8bb0\u4f4f\u4e00\u53e5\u8bdd：<\/h4>\n

\u4ece 1 \u5f00\u59cb，\u4e00\u76f4 \u00d72<\/p>\n

\n

🧩 \u4e09\u3001\u5e42\u548c\u6570\u5230\u5e95\u957f\u4ec0\u4e48\u6837？<\/h2>\n

🌟 \u4e3e\u51e0\u4e2a\u4f8b\u5b50<\/h4>\n
    \n
  • \n

    3 = 1 + 2 \u2192 \u2714 \u5e42\u548c\u6570<\/p>\n<\/li>\n

  • \n

    5 = 1 + 4 \u2192 \u2714<\/p>\n<\/li>\n

  • \n

    6 = 2 + 4 \u2192 \u2714<\/p>\n<\/li>\n

  • \n

    7 \u274c（\u4e0d\u662f\u4e24\u4e2a 2 \u7684\u5e42\u76f8\u52a0）<\/p>\n<\/li>\n<\/ul>\n

    \n

    🧠 \u56db\u3001\u9898\u76ee\u771f\u6b63\u8ba9\u4f60\u5e72\u4ec0\u4e48？<\/h2>\n

    1\u3001\u9898\u76ee\u8f93\u5165：<\/h4>\n

    L R<\/p>\n

    \n

    2\u3001\u610f\u601d\u662f：<\/h4>\n

    👉 \u4ece L \u5230 R
    \n👉 \u6570\u4e00\u6570
    \n👉 \u6709\u591a\u5c11\u4e2a\u6570
    \n👉 \u53ef\u4ee5\u5199\u6210 2^a + 2^b<\/p>\n

    \n

    🧩 \u4e94\u3001\u5343\u4e07\u4e0d\u8981\u7528\u201c\u7b28\u65b9\u6cd5\u201d！<\/h2>\n

    \u274c \u9519\u8bef\u601d\u8def（\u540c\u5b66\u4eec\u6700\u5bb9\u6613\u60f3\u5230）<\/h4>\n

    \u5bf9\u6bcf\u4e2a\u6570 N
    \n\u518d\u53bb\u8bd5\u6240\u6709 a\u3001b
    \n\u770b\u80fd\u4e0d\u80fd\u62fc\u51fa\u6765<\/p>\n

    \u274c \u592a\u6162！
    \n\u274c \u592a\u4e71！
    \n\u274c \u5bb9\u6613\u5199\u70b8！<\/p>\n

    \n

    🌟 \u516d\u3001\u806a\u660e\u9b54\u6cd5\u5e08\u7684\u601d\u8def<\/h2>\n

    🎯 \u6362\u4e2a\u89d2\u5ea6\u60f3！<\/h4>\n

    👉 \u4e0d\u662f\u53bb\u731c N
    \n👉 \u800c\u662f：<\/p>\n

    \u5148\u751f\u6210\u6240\u6709\u7684 2^a + 2^b<\/p>\n

    \u518d\u770b\u770b\u5b83\u843d\u4e0d\u843d\u5728 [L, R] \u91cc<\/p>\n

    \n

    🧠 \u4e03\u3001\u600e\u4e48\u751f\u6210\u6240\u6709\u7684 2^a + 2^b？<\/h2>\n

    \u9b54\u6cd5\u89c4\u5219<\/h4>\n
      \n
    • \n

      a \u4ece 1 \u5f00\u59cb，\u4e00\u76f4 \u00d72 （\u5916\u5faa\u73af）<\/p>\n<\/li>\n

    • \n

      b \u4ece a \u5f00\u59cb，\u4e00\u76f4 \u00d72\u00a0（\u5185\u5faa\u73af）<\/p>\n<\/li>\n

    • \n

      \u53ea\u8981\u548c <= R，\u5c31\u7ee7\u7eed<\/p>\n<\/li>\n<\/ul>\n

      <\/h2>\n
      \n

      🧮 \u516b\u3001\u7528\u5c0f\u4f8b\u5b50\u8d70\u4e00\u904d（\u65b9\u4fbf\u7406\u89e3）<\/h2>\n

      1\u3001\u5047\u8bbe\u8f93\u5165：<\/h4>\n

      L = 2, R = 10<\/p>\n

      \n

      2\u3001\u6240\u6709 2 \u7684\u5e42：<\/p>\n

      1, 2, 4, 8<\/p>\n

      \n

      3\u3001\u7ec4\u6210\u5e42\u548c\u6570：<\/p>\n\naba+b<\/tr>\n\n\n\n\n\n\n\n\n\n
      1<\/td>\n1<\/td>\n2<\/td>\n<\/tr>\n
      1<\/td>\n2<\/td>\n3<\/td>\n<\/tr>\n
      1<\/td>\n4<\/td>\n5<\/td>\n<\/tr>\n
      1<\/td>\n8<\/td>\n9<\/td>\n<\/tr>\n
      2<\/td>\n2<\/td>\n4<\/td>\n<\/tr>\n
      2<\/td>\n4<\/td>\n6<\/td>\n<\/tr>\n
      2<\/td>\n8<\/td>\n10<\/td>\n<\/tr>\n
      4<\/td>\n4<\/td>\n8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
      \n
      \n

      4\u3001👉 \u5728 [2,10] \u91cc\u7684\u6709：
      \n2,3,4,5,6,8,9,10<\/h4>\n

      👉 \u4e00\u5171 8 \u4e2a<\/p>\n

      \n

      💻 \u4e5d\u3001\u53c2\u8003\u7a0b\u5e8f<\/h2>\n

      #include <iostream>
      \nusing namespace std;<\/p>\n

      int main() {
      \n int L, R;
      \n cin >> L >> R;<\/p>\n

      int cnt = 0;<\/p>\n

      \/\/ \u7b2c\u4e00\u4e2a 2 \u7684\u5e42
      \n for (int a = 1; a <= R; a *= 2) {
      \n \/\/ \u7b2c\u4e8c\u4e2a 2 \u7684\u5e42（\u4ece a \u5f00\u59cb，\u9632\u6b62\u91cd\u590d）
      \n for (int b = a; b <= R; b *= 2) {
      \n int sum = a + b;<\/p>\n

      \/\/ \u5982\u679c\u5728\u8303\u56f4\u5185，\u5c31\u8ba1\u6570
      \n if (sum >= L && sum <= R) {
      \n cnt++;
      \n }
      \n }
      \n }<\/p>\n

      cout << cnt << endl;
      \n return 0;
      \n}<\/p>\n

      \n

      🧩 \u5341\u3001\u9010\u53e5\u62c6\u89e3<\/h2>\n

      1\u3001🔹 \u4e3a\u4ec0\u4e48 a *= 2？<\/h4>\n

      for (int a = 1; a <= R; a *= 2)<\/p>\n

      👉 \u8868\u793a：
      \n1 \u2192 2 \u2192 4 \u2192 8 \u2192 16 \u2026<\/p>\n

      \n

      2\u3001🔹 \u4e3a\u4ec0\u4e48 b = a \u5f00\u59cb？<\/h4>\n

      for (int b = a; b <= R; b *= 2)<\/p>\n

      👉 \u9632\u6b62：<\/p>\n

        \n
      • \n

        1 + 2<\/p>\n<\/li>\n

      • \n

        2 + 1<\/p>\n<\/li>\n<\/ul>\n

        \u88ab\u7b97\u4e24\u6b21 \u2757<\/p>\n

        \n

        🚨 \u5341\u4e00\u3001\u8003\u573a\u6700\u5bb9\u6613\u6263\u5206\u7684 4 \u4e2a\u5751<\/h2>\n

        \u274c \u5199\u6210 a++（\u76f4\u63a5\u9519）
        \n\u274c b \u4ece 1 \u5f00\u59cb（\u4f1a\u91cd\u590d）
        \n\u274c \u5fd8\u4e86\u5224\u65ad sum <= R
        \n\u274c \u7528 pow()（\u6d6e\u70b9\u6570，\u5371\u9669）<\/p>\n

        \n

        🏆 \u5341\u4e8c\u3001\u672c\u9898\u603b\u7ed3<\/h3>\n

        📌<\/p>\n

          \n
        • \n

          \u5e42 = \u4ece 1 \u5f00\u59cb \u00d72<\/p>\n<\/li>\n

        • \n

          \u5e42\u548c\u6570 = \u4e24\u4e2a\u5e42\u76f8\u52a0<\/p>\n<\/li>\n

        • \n

          \u601d\u8def：\u5148\u9020，\u518d\u7b5b<\/p>\n<\/li>\n

        • \n

          \u9632\u91cd\u590d：\u7b2c\u4e8c\u4e2a\u4ece\u7b2c\u4e00\u4e2a\u5f00\u59cb<\/p>\n<\/li>\n<\/ul>\n

          \n","protected":false},"excerpt":{"rendered":"

          \u300a\u5e42\u548c\u6570\u738b\u56fd\u7684\u79d8\u5bc6\u300b📖 \u4e00\u3001\u6545\u4e8b\u80cc\u666f：\u5e42\u548c\u6570\u738b\u56fd 🏰1\u3001\u5728\u6570\u5b57\u5927\u9646\u4e0a，\u6709\u4e00\u79cd\u7279\u522b\u795e\u5947\u7684\u6570\u5b57，\u53eb\u505a\u2014\u2014\u2728 \u5e42\u548c\u65702\u3001\u56fd\u738b\u89c4\u5b9a：\u5982\u679c\u4e00\u4e2a\u6570 N
          \n\u53ef\u4ee5\u5199\u6210
          \n\u4e24\u4e2a 2 \u7684\u5e42\u76f8\u52a0\u6bd4\u5982：
          \nN 2^a 2^b\u90a3\u4e48，N \u5c31\u662f\u5e42\u548c\u6570！3\u3001\u4f60\u7684\u4efb\u52a1\u662f：🎯 \u5728\u4e00\u4e2a\u8303\u56f4 [L, R] \u91cc，\u627e\u51fa\u4e00\u5171\u6709\u591a\u5c11\u4e2a\u5e42\u548c\u6570&#x1f9e<\/p>\n","protected":false},"author":2,"featured_media":75053,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[7919,7920,7949,7950,55,427],"topic":[],"class_list":["post-75056","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-gesp2","tag-gesp","tag-7949","tag-7950","tag-c","tag-427"],"yoast_head":"\nGESP2025\u5e746\u6708\u8ba4\u8bc1C++\u4e8c\u7ea7( \u7b2c\u4e09\u90e8\u5206\u7f16\u7a0b\u9898 2\u3001\u5e42\u548c\u6570\uff09 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/75056.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GESP2025\u5e746\u6708\u8ba4\u8bc1C++\u4e8c\u7ea7( \u7b2c\u4e09\u90e8\u5206\u7f16\u7a0b\u9898 2\u3001\u5e42\u548c\u6570\uff09 - 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