{"id":87057,"date":"2026-07-29T18:24:52","date_gmt":"2026-07-29T10:24:52","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/87057.html"},"modified":"2026-07-29T18:24:52","modified_gmt":"2026-07-29T10:24:52","slug":"c%e5%9f%ba%e7%a1%80%e7%ae%97%e6%b3%95%e3%80%90%e5%80%8d%e5%a2%9e%e6%80%9d%e6%83%b3-%e5%bf%ab%e9%80%9f%e5%b9%82%e3%80%91%e6%b5%81%e9%a3%9f%e8%88%ac%e6%8a%95%e5%96%82","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/87057.html","title":{"rendered":"C++\u57fa\u7840\u7b97\u6cd5\u3010\u500d\u589e\u601d\u60f3-\u5feb\u901f\u5e42\u3011\u6d41\u98df\u822c\u6295\u5582"},"content":{"rendered":"

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

\u672c\u7f16\u8981\u6c42\u5e26\u7740\u7406\u89e3\u8bb0\u4f4f\u5feb\u901f\u5e42\u7684\u6a21\u677f，\u5bf9\u500d\u589e\u601d\u60f3-\u5feb\u901f\u5e42\u6709\u5e95\u5c42\u7406\u89e3\u3002<\/p>\n

\u500d\u589e\u601d\u60f3-\u5feb\u901f\u5e42：<\/h4>\n

🧀\u8fd9\u4e2a\u7b97\u6cd5\u662f \u4e0d\u8d85\u65f6\u3001\u4e0d\u8d85\u7c7b\u578b\u5b58\u50a8\u6570\u636e\u8303\u56f4\u00a0\u5feb\u901f\u6c42\u89e3\u4e00\u4e2a\u5e42\u3002<\/p>\n

\n

\u500d\u589e\u601d\u60f3\u7684\u4f53\u73b0：<\/h5>\n

📌\u4e0d\u65ad\u901a\u8fc7\u81ea\u5df1\u548c\u81ea\u5df1\u76f8\u4e58，\u8fbe\u5230\u500d\u589e\u6548\u679c\u3002<\/p>\n\n\n\n\n\n\n\n\n
\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2^2 = 2^1 * 2^1<\/p>\n<\/td>\n<\/tr>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02^4 = 2^2 * 2^2<\/td>\n<\/tr>\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02^8 = 2^4 * 2^4<\/td>\n<\/tr>\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02^16 = 2^8 * 2^8<\/td>\n<\/tr>\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02^32 = 2^16 * 2^16<\/td>\n<\/tr>\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02^64 = 2^32 * 2^32<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

📌\u6b64\u65f6，\u8fd9\u4e2a\u53ea\u80fd\u7528\u4e8e\u5feb\u901f\u6c42\u89e3 "a^\u7279\u5b9a\u5076\u6570\u6b21\u65b9" \u7684\u6570\u3002<\/p>\n

\n
\u501f\u52a9 "\u4e8c\u8fdb\u5236"\u89e3\u51b3\u8d85\u65f6\u95ee\u9898：<\/h5>\n

🧀\u501f\u52a9 "\u4e8c\u8fdb\u5236" \u662f\u505a\u5230\u4e0d\u8d85\u65f6\u3002<\/p>\n

🍞\u501f\u52a9 "\u4e8c\u8fdb\u5236" \u53ef\u4ee5\u5728\u7ed3\u5408\u4e0a\u6587\u6240\u4f53\u73b0\u7684\u500d\u589e\u601d\u60f3，\u505a\u5230\u5feb\u901f\u6c42\u89e3 "a^\u4efb\u610f\u6b21\u65b9" \u7684\u6570\u3002<\/p>\n

📌\u4e8c\u8fdb\u5236\u7528\u4e8e\u5e42\u7684\u6307\u6570\u90e8\u5206\u3002<\/p>\n

    \n
  • \u4f8b\u5982 "2^11" \u8fd9\u4e2a\u6570，\u501f\u52a9\u4e8c\u8fdb\u5236\u62c6\u89e3\u4ed6\u7684\u6307\u6570\u90e8\u5206：<\/li>\n<\/ul>\n

    2^3 2^2 2^1 2^0
    \n | | | |
    \n 8 4 2 1
    \n | | | |
    \n 1 0 1 1
    \n\u5373 11 = (1011)\u4e8c\u8fdb\u5236 = 1*8 + 0*4 + 1*2 + 1*1
    \n 2^11 = 2^(1011)\u4e8c\u8fdb\u5236 = 2^(8 + 0 + 2 + 1) = 2^8 * 2^0 * 2^2 * 2^1
    \n = 2^8 * 1 * 2^2 * 2^1
    \n🧀\u6307\u6570\u7531\u5341\u8fdb\u5236->\u4e8c\u8fdb\u5236->\u5341\u8fdb\u5236，
    \n \u76ee\u7684\u662f：\u628a\u4e00\u4e2a\u6307\u6570\u5f88\u5927\u7684\u5e42，\u901a\u8fc7\u5176\u6027\u8d28，\u62c6\u89e3\u6210\u591a\u4e2a\u6307\u6570\u5c0f\u7684\u5e42\u76f8\u4e58，
    \n \u800c\u8fd9\u4e9b\u591a\u4e2a\u6307\u6570\u5c0f\u7684\u5e42，\u53ef\u4ee5\u5728\u81ea\u5df1\u548c\u81ea\u5df1\u76f8\u4e58\u7684\u500d\u589e\u4e2d\u627e\u5230\u3002
    \n📌\u6307\u6570\u62c6\u89e3\u6210\u4e8c\u8fdb\u5236\u6570\u540e，\u4e8c\u8fdb\u5236\u65f6，\u4e8c\u8fdb\u5236\u4f4d\u4e3a 1 \u7684，\u8981\u627e，\u5c31\u5728 ret \u4e58\u4e0a\u5bf9\u5e94\u6743\u503c，
    \n \u4e3a 0，\u4e0d\u8981\u627e，\u5c31\u5728\u7edf\u8ba1\u7ed3\u679c\u7684 ret \u4e0a\u4e58 1\u3002<\/p>\n

    \n
    \u53d6\u6a21\u89e3\u51b3\u8d85\u7c7b\u578b\u5b58\u50a8\u8303\u56f4\u53ca\u5176\u6269\u5c55：<\/h5>\n
  • \u5728\u8ba1\u7b97\u7684\u8868\u8fbe\u5f0f\u4e2d，\u53ea\u6709 "\u52a0\u51cf\u4e58" \u8fd0\u7b97\u7b26\u65f6，\u53ef\u4ee5\u5904\u5904\u53d6\u6a21；\n

    (a + b + c + d) % p
    \n=(((a + b) % p + c) % p + d) % p <\/p>\n<\/li>\n

  • \u5728\u53d6\u6a21\u65f6，\u7ed3\u679c\u4e0d\u80fd\u4e3a\u8d1f\u6570，\u53ef\u91c7\u7528 "\u6a21\u52a0\u6a21" \u7684\u6280\u5de7；\n

    ((a % p) + p) % p
    \n |
    \n \u8981\u4e3a\u8d1f\u6570， 📌\u52a0\u4e0a\u4e00\u4e2a\u6a21\u6570p,\u4fdd\u8bc1\u4e0d\u662f\u8d1f\u6570
    \n \u4e5f\u662f\u5c0f\u4e8e\u6a21\u6570p\u7684\u8d1f\u6570 \u518d\u6a21p，\u4fdd\u8bc1\u8fd8\u6709\u53d6\u6a21\u6548\u679c<\/p>\n<\/li>\n

  • \u9047\u5230\u8ba1\u7b97\u7684\u8868\u8fbe\u5f0f\u4e2d，\u5b58\u5728\u9664\u6570\u7684，\u7528\u3010\u6570\u5b66-\u6570\u8bba\u3011\u7684\u9006\u5143\u77e5\u8bc6\u70b9\u3002<\/li>\n
    \n
    \u7b97\u6cd5\u601d\u60f3\u8f6c\u5316\u4e58\u4ee3\u7801\u5b9e\u73b0：<\/h5>\n

    #include<iostream><\/p>\n

    using namespace std;<\/p>\n

    typedef long long LL;<\/p>\n

    \/\/ a^b % p \u7684\u503c
    \nLL qpow(LL a, LL b)
    \n{
    \n LL ret = 1;
    \n while(b)
    \n {
    \n if (b & 1) ret = ret * a % p;
    \n a = a * a % p;
    \n b >>= 1;
    \n }
    \n}<\/p>\n

    int main()
    \n{
    \n \/\/…<\/p>\n

    return 0;
    \n}<\/p>\n","protected":false},"excerpt":{"rendered":"

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