{"id":109,"date":"2026-07-09T20:01:37","date_gmt":"2026-07-09T12:01:37","guid":{"rendered":"https:\/\/www.dashstar.cn\/?p=109"},"modified":"2026-07-09T20:01:38","modified_gmt":"2026-07-09T12:01:38","slug":"%e3%80%90%e5%96%9d%e5%89%8d%e6%91%87%e4%b8%80%e6%91%87%e3%80%91b%e6%a0%91%e4%b8%8eb%e6%a0%91","status":"publish","type":"post","link":"https:\/\/www.dashstar.cn\/?p=109","title":{"rendered":"\u3010\u559d\u524d\u6447\u4e00\u6447\u3011B\u6811\u4e0eB+\u6811"},"content":{"rendered":"\n
\n

\u672c\u7cfb\u5217\u4e3b\u8981\u5199\u4e00\u4e9b\u53ea\u9700\u8981\u8003\u524d\u8bb0\u4e00\u8bb0\u7684\u77e5\u8bc6\u70b9\uff0c\u4f9b\u81ea\u5df1\u4f7f\u7528\uff0c\u65f6\u95f4\u6709\u9650\u4e0d\u4fdd\u8bc1\u53ef\u8bfb\u6027<\/p>\n<\/blockquote>\n\n\n\n

B\u6811<\/h2>\n\n\n\n

B\u6811\u7684\u7279\u5f81<\/h3>\n\n\n\n

\u2460\u9664\u6839\u7ed3\u70b9\u5916\uff0c\u6bcf\u4e2a\u7ed3\u70b9\u7684\u5206\u53c9\u6570\u4e0d\u5c11\u4e8e\u2308<\/mo>m<\/mi>2<\/mn><\/mfrac>\u2309<\/mo><\/mrow>\\lceil\\frac{m}{2}\\rceil<\/annotation><\/semantics><\/math>\uff08\u4e00\u822cm\u9636\u8868\u793a\u6709m\u4e2a\u5206\u53c9\u7684\u610f\u601d\uff09<\/p>\n\n\n\n

\u2461\u5e73\u8861\u2014\u2014\u6bcf\u68f5\u5b50\u6811\u7684\u9ad8\u5ea6\u90fd\u76f8\u540c<\/p>\n\n\n\n

\u2462\u53f6\u5b50\u7ed3\u70b9\u4e0d\u5e26\u6709\u5173\u952e\u5b57\u4e0e\u4fe1\u606f\uff08\u88ab\u79f0\u4e3a\u5931\u8d25\u7ed3\u70b9\uff0c\u53f6\u5b50\u7ed3\u70b9\u7684\u7236\u7ed3\u70b9\u88ab\u79f0\u4e3a\u7ec8\u7aef\u7ed3\u70b9\uff09<\/p>\n\n\n\n

\u2463\u975e\u53f6\u7ed3\u70b9\u7684\u7ed3\u6784\uff1a <\/mspace>n<\/mi><\/mrow><\/mtd>P<\/mi>0<\/mn><\/msub><\/mtd>K<\/mi>1<\/mn><\/msub><\/mtd>P<\/mi>1<\/mn><\/msub><\/mtd>\u22ef<\/mo><\/mtd>K<\/mi>n<\/mi><\/msub><\/mtd>P<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtable>\\begin{array}{|c|c|c|c|c|c|c|} \\hline \\;n & P_0 & K_1 & P_1 & \\cdots & K_n & P_n \\\\ \\hline \\end{array} <\/annotation><\/semantics><\/math><\/p>\n\n\n\n

\u7279\u60271\uff1aP<\/mi>0<\/mn><\/msub>\u6240<\/mtext>\u6307<\/mtext>\u5b50<\/mtext>\u6811<\/mtext>\u5173<\/mtext>\u952e<\/mtext>\u5b57<\/mtext><<\/mo>k<\/mi>1<\/mn><\/msub><<\/mo>P<\/mi>1<\/mn><\/msub>\u6240<\/mtext>\u6307<\/mtext>\u5b50<\/mtext>\u6811<\/mtext>\u5173<\/mtext>\u952e<\/mtext>\u5b57<\/mtext><<\/mo>\u22ef<\/mo><<\/mo>k<\/mi>n<\/mi><\/msub><<\/mo>P<\/mi>n<\/mi><\/msub>\u6240<\/mtext>\u6307<\/mtext>\u5b50<\/mtext>\u6811<\/mtext>\u5173<\/mtext>\u952e<\/mtext>\u5b57<\/mtext><\/mrow>P_0\u6240\u6307\u5b50\u6811\u5173\u952e\u5b57<k_1<P_1\u6240\u6307\u5b50\u6811\u5173\u952e\u5b57<\\cdots<k_n<P_n\u6240\u6307\u5b50\u6811\u5173\u952e\u5b57<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

\u7279\u60272\uff1a\u5173\u952e\u5b57\u6570\u91cf\u59cb\u7ec8\u6bd4\u5206\u53c9\u6570\uff08\u9636\u6570\uff09\u5c111<\/p>\n\n\n\n

\u4e00\u68f5n\u4e2a\u7ed3\u70b9\u7684m\u9636B\u6811\u7684\u9ad8\u5ea6\u8303\u56f4\uff1a<\/p>\n\n\n\n

l<\/mi>o<\/mi>g<\/mi>m<\/mi><\/msub>(<\/mo>n<\/mi>+<\/mo>1<\/mn>)<\/mo>\u2264<\/mo>h<\/mi>\u2264<\/mo>l<\/mi>o<\/mi>g<\/mi>\u2308<\/mo>m<\/mi>2<\/mn><\/mfrac>\u2309<\/mo><\/mrow><\/msub>n<\/mi>+<\/mo>1<\/mn><\/mrow>2<\/mn><\/mfrac>+<\/mo>1<\/mn><\/mrow> log_m(n+1) \\le h \\le log_{\\lceil\\frac{m}{2}\\rceil}\\frac{n+1}{2}+1<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

B\u6811\u7684\u63d2\u5165\uff08\u4ee55\u9636B\u6811\u4e3a\u4f8b\uff09<\/h3>\n\n\n\n

5\u9636B\u6811\u4e00\u4e2a\u7ed3\u70b9\u53ef\u4ee5\u5bb9\u7eb3\u2308<\/mo>m<\/mi>2<\/mn><\/mfrac>\u2309<\/mo>\u2212<\/mo>1<\/mn>\u2264<\/mo>k<\/mi>\u2264<\/mo>m<\/mi>\u2212<\/mo>1<\/mn><\/mrow>\\lceil\\frac{m}{2}\\rceil -1 \\le k \\le m-1<\/annotation><\/semantics><\/math>\u4e2a\u5173\u952e\u5b57\uff08\u6839\u7ed3\u70b9\u65e0\u4e0b\u9650\uff09\uff0c\u53732<\/mn>\u2264<\/mo>k<\/mi>\u2264<\/mo>4<\/mn><\/mrow>2 \\le k \\le 4<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

\u5f53\u63d2\u5165\u64cd\u4f5c\u5bfc\u81f4\u5173\u952e\u5b57\u8d85\u8fc7\u8fd9\u4e2a\u7ed3\u70b9\u7684\u4e0a\u9650\u540e\uff0c\u9700\u8981\u5c06\u8be5\u7ed3\u70b9\u5206\u88c2\u3002<\/p>\n\n\n\n

\u2460\u5bf9\u4e8e\u6839\u7ed3\u70b9\uff1a\u5c06\u2308<\/mo>m<\/mi>2<\/mn><\/mfrac>\u2309<\/mo>=<\/mo>2<\/mn>\uff08<\/mtext>\u4ece<\/mtext>0<\/mn>\u5f00<\/mtext>\u59cb<\/mtext>\u6570<\/mtext>\uff09<\/mtext><\/mrow>\\lceil\\frac{m}{2}\\rceil = 2\uff08\u4ece0\u5f00\u59cb\u6570\uff09<\/annotation><\/semantics><\/math>\u5904\u7684\u5173\u952e\u5b57\u63d0\u51fa\uff0c\u52a0\u5165\u65b0\u7684\u6839\u7ed3\u70b9<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n

\u2461\u5bf9\u4e8e\u975e\u6839\u7ed3\u70b9\uff1a\u540c\u6837\u5c06\u2308<\/mo>m<\/mi>2<\/mn><\/mfrac>\u2309<\/mo><\/mrow>\\lceil\\frac{m}{2}\\rceil<\/annotation><\/semantics><\/math>\u5904\u7684\u5173\u952e\u5b57\u63d0\u51fa\uff0c\u5e76\u5c06\u5176\u585e\u5165\u7236\u7ed3\u70b9\uff0c\u82e5\u7236\u7ed3\u70b9\u4e5f\u6ee1\u4e86\u5c31\u91cd\u590d\u8fd9\u4e24\u4e2a\u64cd\u4f5c\u76f4\u81f3\u6240\u6709\u7ed3\u70b9\u7684\u5173\u952e\u5b57\u6570\u91cf\u90fd\u7b26\u5408\u8981\u6c42<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n

B\u6811\u7684\u5220\u9664<\/h3>\n\n\n\n

\u5bf9\u4e8e\u975e\u7ec8\u7aef\u7ed3\u70b9\uff1a\u5220\u9664\u4e00\u4e2a\u5173\u952e\u5b57\u901a\u5e38\u5220\u9664\u4ed6\u7684\u524d\u9a71\u6216\u8005\u540e\u7ee7\u7684\u5173\u952e\u5b57\uff0c\u8f6c\u6362\u4e3a\u5220\u9664\u7ec8\u7aef\u7ed3\u70b9\u7684\u5173\u952e\u5b57<\/p>\n\n\n\n

\u5bf9\u4e8e\u7ec8\u7aef\u7ed3\u70b9\uff1a\u5f53\u5220\u9664\u64cd\u4f5c\u4e0d\u4f1a\u5bfc\u81f4\u5173\u952e\u5b57\u4e2a\u6570\u4e0d\u4f4e\u4e8e\u4e0b\u9650\u65f6\uff0c\u76f4\u63a5\u5220\u9664\uff1b\u82e5\u4f4e\u4e8e\u4e0b\u9650\u5219\u6709\u4ee5\u4e0b3\u4e2a\u65b9\u6cd5\uff1a<\/p>\n\n\n\n

\u2460\u540e\u7ee7\u524d\u79fb\uff1a\u53f3\u5144\u5f1f\u5173\u952e\u8bcd\u5197\u4f59\uff0c\u5c06\u540e\u7ee7\u548c\u540e\u7ee7\u7684\u540e\u7ee7\u524d\u79fb<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u2461\u524d\u9a71\u540e\u79fb\uff1a\u5de6\u5144\u5f1f\u5173\u952e\u8bcd\u6709\u5197\u4f59\uff0c\u5c06\u524d\u9a71\u548c\u524d\u9a71\u7684\u524d\u9a71\u540e\u79fb<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u2462\u7ed3\u70b9\u5408\u5e76\uff1a\u5de6\u3001\u53f3\u5144\u5f1f\u5173\u952e\u8bcd\u5747\u5df2\u8fbe\u5230\u4e0b\u9650\uff0c\u8fdb\u884c\u7ed3\u70b9\u5408\u5e76\uff0c\u5c06\u7236\u7ed3\u70b9\u4e2d\u7684\u5173\u952e\u8bcd\u63d0\u51fa\uff0c\u5c06\u4e24\u4e2a\u7ed3\u70b9\u5408\u5e76\u4e3a\u4e00\u4e2a\u7ed3\u70b9\uff0c\u82e5\u7236\u7ed3\u70b9\u6b64\u65f6\u5173\u952e\u8bcd\u8fbe\u5230\u4e0b\u9650\uff0c\u91cd\u590d\u64cd\u4f5c<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

B+\u6811<\/h2>\n\n\n\n

B+\u6811\u7279\u5f81\uff08\u4e0d\u8003\u63d2\u5165\u5220\u9664\uff09<\/h3>\n\n\n\n

\u2460\u9636\u6570\u4e3am\u7684B+\u6811\u6700\u5927\u5206\u53c9\u6570\u548c\u7ed3\u70b9\u6570\u5747\u4e3am<\/p>\n\n\n\n

\u2461\u975e\u53f6\u6839\u7ed3\u70b9\uff08\u4e0d\u662f\u53f6\u5b50\u7684\u6839\u7ed3\u70b9\uff0c\u5373\u6811\u9ad8\u5927\u4e8e1\u65f6\uff09\u81f3\u5c11\u67092\u68f5\u5b50\u6811\uff08\u4e3a\u4e86\u4fdd\u6301\u5e73\u8861\uff09\uff0c\u5176\u4ed6\u7ed3\u70b9\u4e0d\u5c11\u4e8e\u2308<\/mo>m<\/mi>2<\/mn><\/mfrac>\u2309<\/mo><\/mrow>\\lceil\\frac{m}{2}\\rceil<\/annotation><\/semantics><\/math>\u68f5<\/p>\n\n\n\n

\u2462\u53f6\u5b50\u7ed3\u70b9\u5373\u4e3a\u6709\u6548\u7ed3\u70b9\uff0c\u5305\u542b\u5168\u90e8\u5173\u952e\u5b57\u53ca\u6307\u5411\u8bb0\u5f55\u7684\u6307\u9488<\/p>\n\n\n\n

\u2464\u53f6\u7ed3\u70b9\u6309\u7167\u5173\u952e\u5b57\u5927\u5c0f\u6392\u5e8f\uff0c\u76f8\u90bb\u7684\u7ed3\u70b9\u4e92\u76f8\u94fe\u63a5\uff08\u652f\u6301\u987a\u5e8f\u67e5\u627e\uff09<\/p>\n\n\n\n

\u2465\u5176\u4ed6\u5206\u652f\u7ed3\u70b9\u4ec5\u5305\u542b\u5b50\u7ed3\u70b9\u4e2d\u7684\u6700\u5927\u503c<\/p>\n\n\n\n

B\u6811\u4e0eB+\u6811\u5bf9\u6bd4<\/h3>\n\n\n\n
\n
\n
<\/td>B\u6811<\/strong><\/td>B+\u6811<\/strong><\/td><\/tr>
\u7ed3\u70b9\u4e2d\u5173\u952e\u5b57\u4e2a\u6570
\u4e0e\u5b50\u6811\u6570\u91cf\uff08\u5206\u53c9\u6570\u91cf\uff09<\/td>		k\u4e2a\u5173\u952e\u5b57\u5bf9\u5e94k+1\u68f5\u5b50\u6811<\/td>k\u4e2a\u5173\u952e\u5b57\u5bf9\u5e94k\u68f5\u5b50\u6811<\/td><\/tr>
m\u9636\u6811\u7684\u7ed3\u70b9\u5173\u952e\u5b57\u4e2a\u6570\u8303\u56f4<\/td>\u6839\uff1ak<\/mi>\u2208<\/mo>[<\/mo>1<\/mn>,<\/mo>m<\/mi>\u2212<\/mo>1<\/mn>]<\/mo><\/mrow>k\\in [ 1,m-1 ]<\/annotation><\/semantics><\/math>
\u975e\u6839\uff1ak<\/mi>\u2208<\/mo>[<\/mo>\u2308<\/mo>m<\/mi>2<\/mn><\/mfrac>\u2309<\/mo>\u2212<\/mo>1<\/mn>,<\/mo>m<\/mi>\u2212<\/mo>1<\/mn>]<\/mo><\/mrow>k\\in [ \\lceil \\frac{m}{2} \\rceil -1,m-1 ]<\/annotation><\/semantics><\/math><\/td>		\u6839\uff1ak<\/mi>\u2208<\/mo>[<\/mo>1<\/mn>,<\/mo>m<\/mi>]<\/mo><\/mrow>k\\in [ 1,m]<\/annotation><\/semantics><\/math>
\u975e\u6839\uff1ak<\/mi>\u2208<\/mo>[<\/mo>\u2308<\/mo>m<\/mi>2<\/mn><\/mfrac>\u2309<\/mo>,<\/mo>m<\/mi>]<\/mo><\/mrow>k\\in [ \\lceil \\frac{m}{2} \\rceil, m]<\/annotation><\/semantics><\/math><\/td><\/tr>
\u7ed3\u70b9\u4fe1\u606f<\/td>\u5173\u952e\u5b57\u4e0d\u91cd\u590d\uff0c\u7ed3\u70b9\u4e2d\u5305\u542b\u5168\u90e8\u4fe1\u606f<\/td>\u975e\u53f6\u7ed3\u70b9\u4ec5\u4e3a\u7d22\u5f15\uff0c\u4e0d\u5305\u542b\u5168\u90e8\u4fe1\u606f\uff1b\u53f6\u7ed3\u70b9\u5305\u542b\u5168\u90e8\u4fe1\u606f<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n

\u76f8\u540c\u70b9\uff1a\u9664\u4e86\u6839\u7ed3\u70b9\u5916\u90fd\u9700\u8981\u6709\u2308<\/mo>m<\/mi>2<\/mn><\/mfrac>\u2309<\/mo><\/mrow>\\lceil \\frac{m}{2} \\rceil<\/annotation><\/semantics><\/math>\u68f5\u5b50\u6811\uff0c\u4e14\u5b50\u6811\u9ad8\u5ea6\u5fc5\u987b\u76f8\u540c\uff08\u5e73\u8861\uff09<\/p>\n\n\n\n

\u62d3\u5c55<\/h2>\n\n\n\n

Q\uff1a<\/strong>\u5982\u4f55\u7406\u89e3B+\u6811\u53ef\u4f7f\u5f97\u4e00\u4e2a\u78c1\u76d8\u5757\u53ef\u5305\u542b\u66f4\u591a\u5173\u952e\u5b57\uff0c\u4f7f\u5f97B+\u6811\u9636\u6570\u66f4\u5927\uff0c\u6811\u9ad8\u66f4\u77ee\uff0c\u8bfb\u78c1\u76d8\u6b21\u6570\u66f4\u5c11\uff1f<\/p>\n\n\n\n

A\uff1a<\/strong>\u8fd9\u9898\u597d\u50cf\u6709\u70b9\u8d85\u7eb2<\/s><\/p>\n\n\n\n

\u4e00\u822c\u4e00\u4e2a\u78c1\u76d8\u5757\u5927\u5c0f\u5bf9\u5e94\u4e00\u4e2a\u7ed3\u70b9\u3002\u67e5\u8be2\u65f6\uff0c\u65e0\u8bbaB\u6811\u8fd8\u662fB+\u6811\uff0c\u90fd\u662f\u628a\u6574\u4e2a\u7ed3\u70b9\uff08\u4e00\u6574\u4e2a\u78c1\u76d8\u5757\uff09\u4e00\u6b21\u6027\u8bfb\u5165\u4e3b\u5b58\u3002<\/p>\n\n\n\n

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