{"id":1795,"date":"2017-02-18T08:42:52","date_gmt":"2017-02-18T00:42:52","guid":{"rendered":"http:\/\/cn.hostease.com\/xueyuan\/?p=1795"},"modified":"2025-01-13T19:07:51","modified_gmt":"2025-01-13T11:07:51","slug":"%e7%bb%8f%e5%85%b8%e7%ae%97%e6%b3%95%e9%a2%98%e6%af%8f%e6%97%a5%e6%bc%94%e7%bb%83-%e7%ac%ac%e5%8d%81%e9%a2%98-%e6%a0%91%e7%8a%b6%e6%95%b0%e7%bb%84","status":"publish","type":"post","link":"https:\/\/cn.hostease.com\/xueyuan\/jishu\/%e7%bb%8f%e5%85%b8%e7%ae%97%e6%b3%95%e9%a2%98%e6%af%8f%e6%97%a5%e6%bc%94%e7%bb%83-%e7%ac%ac%e5%8d%81%e9%a2%98-%e6%a0%91%e7%8a%b6%e6%95%b0%e7%bb%84\/","title":{"rendered":"\u7ecf\u5178\u7b97\u6cd5\u9898\u6bcf\u65e5\u6f14\u7ec3\u2014\u2014\u7b2c\u5341\u9898 \u6811\u72b6\u6570\u7ec4"},"content":{"rendered":"\n

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\u4e00\uff1a\u6982\u5e8f<\/p>\n\n\n\n

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\u6d89\u7684\u6570\u636e\u592a\u591a\u4e86\uff0c\u90a3\u4e48\u95ee\u9898\u6765\u4e86\uff0c\u6211\u80fd\u4e0d\u80fd\u5728\u76f8\u5e94\u7684sum[i]\u4e2d\u53ea\u4fdd\u5b58\u67d0\u4e9ba[i]\u7684\u503c\u5462\uff1f\u597d\u5427\uff0c\u4e0b\u9762\u6211\u4eec\u770b\u5f20\u56fe\u3002<\/p>\n\n\n\n

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\u4ece\u56fe\u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u5230S[]\u7684\u5206\u5e03\u53d8\u6210\u4e86\u4e00\u9897\u6811\uff0c\u6709\u610f\u601d\u5427\uff0c\u4e0b\u9762\u6211\u4eec\u770b\u770bS[i]\u4e2d\u5230\u5e95\u5b58\u653e\u7740\u54ea\u4e9ba[i]\u7684\u503c\u3002<\/p>\n\n\n\n

S[1]=a[1];<\/p>\n\n\n\n

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S[4]=a[1]+a[2]+a[3]+a[4];<\/p>\n\n\n\n

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\u5176\u4e2d\uff1a2k<\/sup> \u4e2d\u7684k\u8868\u793a\u5f53\u524dS[i]\u5728\u6811\u4e2d\u7684\u5c42\u6570\uff0c\u5b83\u7684\u503c\u5c31\u662fi\u7684\u4e8c\u8fdb\u5236\u4e2d\u672b\u5c3e\u8fde\u7eed0\u7684\u4e2a\u6570\uff0c2k<\/sup>\u4e5f\u5c31\u662f\u8868\u793aS[i]\u4e2d\u5305\u542b\u4e86\u54ea\u4e9ba[]\uff0c<\/p>\n\n\n\n

\u4e3e\u4e2a\u4f8b\u5b50:  i=610<\/sub>=01102 <\/sub>\uff1b\u53ef\u4ee5\u53d1\u73b0\u672b\u5c3e\u8fde\u7eed\u76840\u6709\u4e00\u4e2a\uff0c\u5373k=1\uff0c\u5219\u8bf4\u660eS[6]\u662f\u5728\u6811\u4e2d\u7684\u7b2c\u4e8c\u5c42\uff0c\u5e76\u4e14S[6]\u4e2d\u670921<\/sup>\u9879\uff0c\u968f\u540e\u6211\u4eec\u6c42\u51fa\u4e86\u8d77\u59cb\u9879\uff1a<\/p>\n\n\n\n

a[6-21<\/sup>+1]=a[5]\uff0c\u4f46\u662f\u5728\u7f16\u7801\u4e2d\u6c42\u51fak\u7684\u503c\u8fd8\u662f\u6709\u70b9\u9ebb\u70e6\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u91c7\u7528\u66f4\u7075\u5de7\u7684Lowbit\u6280\u672f\uff0c\u5373\uff1a2k<\/sup>=i&-i \u3002<\/p>\n\n\n\n

\u5219\uff1aS[6]=a[6-21<\/sup>+1]=a[6-(6&-6)+1]=a[5]+a[6]\u3002<\/p>\n\n\n\n

\u4e8c\uff1a\u4ee3\u7801<\/p>\n\n\n\n

1:\u795e\u5947\u7684Lowbit\u51fd\u6570<\/p>\n\n\n\n

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 1 #region \u5f53\u524d\u7684sum\u6570\u5217\u7684\u8d77\u59cb\u4e0b\u6807\n 2         \/\/\/ <summary>\n 3         \/\/\/ \u5f53\u524d\u7684sum\u6570\u5217\u7684\u8d77\u59cb\u4e0b\u6807\n 4         \/\/\/ <\/summary>\n 5         \/\/\/ <param name=\"i\"><\/param>\n 6         \/\/\/ <returns><\/returns>\n 7         public static int Lowbit(int i)\n 8         {\n 9             return i & -i;\n10         }\n11         #endregion<\/pre>\n
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2:\u6c42\u524dn\u9879\u548c<\/p>\n\n\n\n
\u6bd4\u5982\u4e0a\u56fe\u4e2d\uff0c\u5982\u4f55\u6c42Sum(6)\uff0c\u5f88\u663e\u7136Sum(6)=S4<\/sub>+S6\uff0c<\/sub>\u90a3\u4e48\u5982\u4f55\u5bfb\u627eS4\u5462\uff1f\u5373\u627e\u52306\u4ee5\u524d\u7684\u6240\u6709\u6700\u5927\u5b50\u6811\uff0c\u5f88\u663e\u7136\u8fd9\u4e2a\u6c42\u548c\u7684\u590d\u6742\u5ea6\u4e3alogN\u3002<\/p>\n\n\n\n
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 1         #region \u6c42\u524dn\u9879\u548c\n 2         \/\/\/ <summary>\n 3         \/\/\/ \u6c42\u524dn\u9879\u548c\n 4         \/\/\/ <\/summary>\n 5         \/\/\/ <param name=\"x\"><\/param>\n 6         \/\/\/ <returns><\/returns>\n 7         public static int Sum(int x)\n 8         {\n 9             int ans = 0;\n10 \n11             var i = x;\n12 \n13             while (i > 0)\n14             {\n15                 ans += sumArray[i - 1];\n16 \n17                 \/\/\u5f53\u524d\u9879\u7684\u6700\u5927\u5b50\u6811\n18                 i -= Lowbit(i);\n19             }\n20 \n21             return ans;\n22         }\n23         #endregion<\/pre>\n
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3\uff1a\u4fee\u6539<\/p>\n\n\n\n
\u5982\u4e0a\u56fe\u4e2d\uff0c\u5982\u679c\u6211\u4fee\u6539\u4e86a[5]\u7684\u503c\uff0c\u90a3\u4e48\u5305\u542ba[5]\u7684S[5]\uff0cS[6]\uff0cS[8]\u7684\u533a\u95f4\u503c\u90fd\u9700\u8981\u540c\u6b65\u4fee\u6539,\u6211\u4eec\u770b\u5230\u53ea\u8981\u6cbf\u7740S[5]\u4e00\u76f4\u56de\u6eaf\u5230\u6839\u5373\u53ef\uff0c<\/p>\n\n\n\n
\u540c\u6837\u5b83\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e5f\u4e3alogN\u3002<\/p>\n\n\n\n
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 1         public static void Modify(int x, int newValue)\n 2         {\n 3             \/\/\u62ff\u51fa\u539f\u6570\u7ec4\u7684\u503c\n 4             var oldValue = arr[x];\n 5 \n 6             for (int i = x; i < arr.Length; i += Lowbit(i + 1))\n 7             {\n 8                 \/\/\u51cf\u53bb\u8001\u503c\uff0c\u6362\u4e00\u4e2a\u65b0\u503c\n 9                 sumArray[i] = sumArray[i] - oldValue + newValue;\n10             }\n11         }<\/pre>\n
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\u6700\u540e\u4e0a\u603b\u7684\u4ee3\u7801:<\/p>\n\n\n\n
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  1 using System;\n  2 using System.Collections.Generic;\n  3 using System.Linq;\n  4 using System.Text;\n  5 using System.Diagnostics;\n  6 using System.Threading;\n  7 using System.IO;\n  8 \n  9 namespace ConsoleApplication2\n 10 {\n 11     public class Program\n 12     {\n 13         static int[] sumArray = new int[8];\n 14 \n 15         static int[] arr = new int[8];\n 16 \n 17         public static void Main()\n 18         {\n 19             Init();\n 20 \n 21             Console.WriteLine(\"A\u6570\u7ec4\u7684\u503c:{0}\", string.Join(\",\", arr));\n 22             Console.WriteLine(\"S\u6570\u7ec4\u7684\u503c:{0}\", string.Join(\",\", sumArray));\n 23 \n 24             Console.WriteLine(\"\u4fee\u6539A[1]\u7684\u503c\u4e3a3\");\n 25             Modify(1, 3);\n 26 \n 27             Console.WriteLine(\"A\u6570\u7ec4\u7684\u503c:{0}\", string.Join(\",\", arr));\n 28             Console.WriteLine(\"S\u6570\u7ec4\u7684\u503c:{0}\", string.Join(\",\", sumArray));\n 29 \n 30             Console.Read();\n 31         }\n 32 \n 33         #region \u521d\u59cb\u5316\u4e24\u4e2a\u6570\u7ec4\n 34         \/\/\/ <summary>\n 35         \/\/\/ \u521d\u59cb\u5316\u4e24\u4e2a\u6570\u7ec4\n 36         \/\/\/ <\/summary>\n 37         public static void Init()\n 38         {\n 39             for (int i = 1; i <= 8; i++)\n 40             {\n 41                 arr[i - 1] = i;\n 42 \n 43                 \/\/\u8bbe\u7f6e\u5176\u5b9e\u5750\u6807\uff1ai=1\u5f00\u59cb\n 44                 int start = (i - Lowbit(i));\n 45 \n 46                 var sum = 0;\n 47 \n 48                 while (start < i)\n 49                 {\n 50                     sum += arr[start];\n 51 \n 52                     start++;\n 53                 }\n 54 \n 55                 sumArray[i - 1] = sum;\n 56             }\n 57         }\n 58         #endregion\n 59 \n 60         public static void Modify(int x, int newValue)\n 61         {\n 62             \/\/\u62ff\u51fa\u539f\u6570\u7ec4\u7684\u503c\n 63             var oldValue = arr[x];\n 64 \n 65             arr[x] = newValue;\n 66 \n 67             for (int i = x; i < arr.Length; i += Lowbit(i + 1))\n 68             {\n 69                 \/\/\u51cf\u53bb\u8001\u503c\uff0c\u6362\u4e00\u4e2a\u65b0\u503c\n 70                 sumArray[i] = sumArray[i] - oldValue + newValue;\n 71             }\n 72         }\n 73 \n 74         #region \u6c42\u524dn\u9879\u548c\n 75         \/\/\/ <summary>\n 76         \/\/\/ \u6c42\u524dn\u9879\u548c\n 77         \/\/\/ <\/summary>\n 78         \/\/\/ <param name=\"x\"><\/param>\n 79         \/\/\/ <returns><\/returns>\n 80         public static int Sum(int x)\n 81         {\n 82             int ans = 0;\n 83 \n 84             var i = x;\n 85 \n 86             while (i > 0)\n 87             {\n 88                 ans += sumArray[i - 1];\n 89 \n 90                 \/\/\u5f53\u524d\u9879\u7684\u6700\u5927\u5b50\u6811\n 91                 i -= Lowbit(i);\n 92             }\n 93 \n 94             return ans;\n 95         }\n 96         #endregion\n 97 \n 98         #region \u5f53\u524d\u7684sum\u6570\u5217\u7684\u8d77\u59cb\u4e0b\u6807\n 99         \/\/\/ <summary>\n100         \/\/\/ \u5f53\u524d\u7684sum\u6570\u5217\u7684\u8d77\u59cb\u4e0b\u6807\n101         \/\/\/ <\/summary>\n102         \/\/\/ <param name=\"i\"><\/param>\n103         \/\/\/ <returns><\/returns>\n104         public static int Lowbit(int i)\n105         {\n106             return i & -i;\n107         }\n108         #endregion\n109     }\n110 }<\/pre>\n
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\u6587\u7ae0\u6765\u81ea\u7f51\u7edc\u535a\u5ba2https:\/\/www.cnblogs.com\/huangxincheng\/archive\/2012\/12\/05\/2802858.html<\/p>\n","protected":false},"excerpt":{"rendered":"
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