{"id":86,"date":"2014-01-06T08:40:12","date_gmt":"2014-01-06T00:40:12","guid":{"rendered":"http:\/\/www.lixiaodong.com\/?p=86"},"modified":"2014-02-03T07:32:05","modified_gmt":"2014-02-02T23:32:05","slug":"%e7%ae%97%e6%9c%af%e8%a1%a8%e8%be%be%e5%bc%8f%e8%bd%ac%e6%8d%a2%e6%88%90%e9%80%86%e6%b3%a2%e5%85%b0%e8%a1%a8%e8%be%be%e5%bc%8freverse-polish-notation%e4%b9%8bjava%e5%ae%9e%e7%8e%b0","status":"publish","type":"post","link":"https:\/\/www.lixiaodong.com\/?p=86","title":{"rendered":"\u7b97\u672f\u8868\u8fbe\u5f0f\u8f6c\u6362\u6210\u9006\u6ce2\u5170\u8868\u8fbe\u5f0f(Reverse Polish notation)\u4e4bjava\u5b9e\u73b0"},"content":{"rendered":"

\u9006\u6ce2\u5170\u8868\u8fbe\u5f0f\u5c06\u64cd\u4f5c\u7b26\u7f6e\u4e8e\u64cd\u4f5c\u6570\u7684\u540e\u9762\u3002\u6bd4\u5982\uff0c3+4\u7528\u9006\u6ce2\u5170\u8868\u793a\u6cd5\u5219\u662f \u201c3 4 +\u201d\u3002 \u66f4\u590d\u6742\u7684\uff0c7+8*2 \u5219\u662f “7 8 2 * +”\u3002<\/p>\n

\u5c06\u7b97\u672f\u8868\u8fbe\u5f0f\u8f6c\u6362\u6210\u9006\u6ce2\u5170\u8868\u8fbe\u5f0f\u7684\u7b97\u6cd5\u5982\u4e0b\uff1a<\/p>\n

1. \u5206\u914d2\u4e2a\u6808\uff0c\u6808s1\u7528\u4e8e\u4e34\u65f6\u5b58\u50a8\u8fd0\u7b97\u7b26\uff08\u542b\u4e00\u4e2a\u7ed3\u675f\u7b26\u53f7\uff09\uff1b\u6808s2\u7528\u4e8e\u8f93\u5165\u9006\u6ce2\u5170\u5f0f\uff0c\u4e3a\u65b9\u4fbf\u8d77\u89c1\uff0c\u6808s1\u9700\u5148\u653e\u5165\u4e00\u4e2a\u4f18\u5148\u7ea7\u6700\u4f4e\u7684\u8fd0\u7b97\u7b26\uff0c\u5728\u8fd9\u91cc\u5047\u5b9a\u4e3a’#’\uff1b<\/p>\n

2.\u00a0\u4ece\u7b97\u672f\u8868\u8fbe\u5f0f\u7684\u5de6\u7aef\u5f00\u59cb\u9010\u4e2a\u8bfb\u53d6\u5b57\u7b26x\uff0c\u9010\u5e8f\u8fdb\u884c\u5982\u4e0b\u6b65\u9aa4\uff1a<\/p>\n

\uff081\uff09\u82e5x\u662f\u64cd\u4f5c\u6570\uff0c\u5219\u5206\u6790\u51fa\u5b8c\u6574\u7684\u8fd0\u7b97\u6570\uff08\u5728\u8fd9\u91cc\u4e3a\u65b9\u4fbf\uff0c\u7528\u5b57\u6bcd\u4ee3\u66ff\u6570\u5b57\uff09\uff0c\u5c06x\u76f4\u63a5\u538b\u5165\u6808s2\uff1b<\/p>\n

\uff082\uff09\u82e5x\u662f\u8fd0\u7b97\u7b26\uff0c\u5219\u5206\u60c5\u51b5\u8ba8\u8bba\uff1a<\/p>\n

\u82e5x\u662f'(‘\uff0c\u5219\u76f4\u63a5\u538b\u5165\u6808s1\uff1b<\/p>\n

\u82e5x\u662f’)’\uff0c\u5219\u5c06\u8ddd\u79bb\u6808s1\u6808\u9876\u7684\u6700\u8fd1\u7684'(‘\u4e4b\u95f4\u7684\u8fd0\u7b97\u7b26\uff0c\u9010\u4e2a\u51fa\u6808\uff0c\u4f9d\u6b21\u538b\u5165\u6808s2\uff0c\u6b64\u65f6\u629b\u5f03'(‘\uff1b<\/p>\n

\u82e5x\u662f\u9664'(‘\u548c’)’\u5916\u7684\u8fd0\u7b97\u7b26\uff0c\u5219\u518d\u5206\u5982\u4e0b\u60c5\u51b5\u8ba8\u8bba\uff1a<\/p>\n

\u82e5\u5f53\u524d\u6808s1\u7684\u6808\u9876\u5143\u7d20\u4e3a'(‘\uff0c\u5219\u5c06x\u76f4\u63a5\u538b\u5165\u6808s1\uff1b<\/p>\n

\u82e5\u5f53\u524d\u6808s1\u7684\u6808\u9876\u5143\u7d20\u4e0d\u4e3a'(‘\uff0c\u5219\u5c06x\u4e0e\u6808s1\u7684\u6808\u9876\u5143\u7d20\u6bd4\u8f83\uff0c\u82e5x\u7684\u4f18\u5148\u7ea7\u5927\u4e8e\u6808s1\u6808\u9876\u8fd0\u7b97\u7b26\u4f18\u5148\u7ea7\uff0c\u5219\u5c06x\u76f4\u63a5\u538b\u5165\u6808s1\u3002\u5426\u8005\uff0c\u5c06\u6808s1\u7684\u6808\u9876\u8fd0\u7b97\u7b26\u5f39\u51fa\uff0c\u538b\u5165\u6808s2\u4e2d\uff0c\u76f4\u5230\u6808s1\u7684\u6808\u9876\u8fd0\u7b97\u7b26\u4f18\u5148\u7ea7\u522b\u4f4e\u4e8e\uff08\u4e0d\u5305\u62ec\u7b49\u4e8e\uff09x\u7684\u4f18\u5148\u7ea7\uff0c\u6216\u6808s1\u7684\u6808\u9876\u8fd0\u7b97\u7b26\u4e3a'(‘\u6216”#”\u3002\u6700\u540e\u518d\u5219\u5c06x\u538b\u5165\u6808s1;<\/p>\n

3. \u5728\u8fdb\u884c\u5b8c2\u540e\uff0c\u68c0\u67e5\u6808s1\u662f\u5426\u4e3a\u7a7a\uff0c\u82e5\u4e0d\u4e3a\u7a7a\uff0c\u5219\u5c06\u6808\u4e2d\u5143\u7d20\u4f9d\u6b21\u5f39\u51fa\u5e76\u538b\u5165\u6808s2\u4e2d\uff08\u4e0d\u5305\u62ec’#’\uff09\uff1b<\/p>\n

4. \u5b8c\u6210\u4e0a\u8ff0\u6b65\u9aa4\u540e\uff0c\u6808s2\u4fbf\u4e3a\u9006\u6ce2\u5170\u5f0f\u8f93\u51fa\u7ed3\u679c\u3002\u4f46\u662f\u6808s2\u5e94\u505a\u4e00\u4e0b\u9006\u5e8f\u5904\u7406\uff0c\u56e0\u4e3a\u6b64\u65f6\u8868\u8fbe\u5f0f\u7684\u9996\u5b57\u7b26\u4f4d\u4e8e\u6808\u5e95\u3002<\/p>\n

\u4e0b\u9762\u662fjava\u5b9e\u73b0\u3002<\/p>\n

\r\n\r\n\r\nimport java.util.ArrayList;\r\nimport java.util.List;\r\nimport java.util.Stack;\r\n\r\npublic class ReversePolishNotation {\r\n\tprivate final static String PLUS = "+";\r\n\r\n\tprivate final static String MINUS = "-";\r\n\r\n\tprivate final static String MULTIPLY = "*";\r\n\r\n\tprivate final static String DIVIDE = "\/";\r\n\r\n\tprivate final static String POINT = ".";\r\n\r\n\tprivate final static String OPSTART = "(";\r\n\r\n\tprivate final static String OPEND = ")";\r\n\r\n\tprivate final static String NUMBER_SIGN = "#";\r\n\r\n\tprivate String exp;\r\n\r\n\tprivate List<String> expList = new ArrayList<String>();\r\n\r\n\tprivate List<String> rpnList = new ArrayList<String>();\r\n\r\n\tpublic ReversePolishNotation(String exp) {\r\n\t\tthis.exp = exp;\r\n\t}\r\n\r\n\tprivate boolean isDigit(String str) {\r\n\t\treturn str.equals("0") || str.equals("1") || str.equals("2")\r\n\t\t\t\t|| str.equals("3") || str.equals("4") || str.equals("5")\r\n\t\t\t\t|| str.equals("6") || str.equals("7") || str.equals("8")\r\n\t\t\t\t|| str.equals("9");\r\n\t}\r\n\r\n\t\/**\r\n\t * \u662f\u5426\u662f\u8d1f\u53f7\r\n\t * \r\n\t * @param exp\r\n\t * @param ch\r\n\t * @param index\r\n\t * @return\r\n\t *\/\r\n\tprivate boolean isNegativeSign(String exp, String ch, int index) {\r\n\t\tif (ch.equals("-")) {\r\n\t\t\tif (index == 0) {\r\n\t\t\t\treturn true;\r\n\t\t\t} else {\r\n\t\t\t\tString previous = exp.substring(index - 1, index);\r\n\t\t\t\tif ((!isDigit(previous)) && (!(previous.equals(OPEND)))) {\r\n\t\t\t\t\treturn true;\r\n\t\t\t\t} else {\r\n\t\t\t\t\treturn false;\r\n\t\t\t\t}\r\n\t\t\t}\r\n\t\t}\r\n\t\treturn false;\r\n\t}\r\n\r\n\tprivate void parse() {\r\n\t\tint length = exp.length();\r\n\r\n\t\tString tempStr = "";\r\n\t\tfor (int i = 0; i < length; i++) {\r\n\t\t\tString tempChar = exp.substring(i, i + 1);\r\n\t\t\tif (isDigit(tempChar) || tempChar.equals(POINT)\r\n\t\t\t\t\t|| isNegativeSign(exp, tempChar, i)) {\r\n\t\t\t\ttempStr += tempChar;\r\n\t\t\t} else {\r\n\t\t\t\tif (!tempStr.equals("")) {\r\n\t\t\t\t\texpList.add(tempStr);\r\n\t\t\t\t}\r\n\t\t\t\texpList.add(tempChar);\r\n\t\t\t\ttempStr = "";\r\n\t\t\t}\r\n\t\t}\r\n\t\tif (!tempStr.equals("")) {\r\n\t\t\texpList.add(tempStr);\r\n\t\t}\r\n\r\n\t}\r\n\r\n\tprivate boolean isNumber(String str) {\r\n\t\ttry {\r\n\t\t\tDouble.parseDouble(str);\r\n\t\t\treturn true;\r\n\t\t} catch (NumberFormatException e) {\r\n\t\t\treturn false;\r\n\t\t}\r\n\t}\r\n\r\n\t\/**\r\n\t * \u8fd0\u7b97\u7b26str1 \u662f\u5426\u6bd4str2\u4f18\u5148\u7ea7\u9ad8\r\n\t * \r\n\t * @param str1\r\n\t * @param str2\r\n\t * @return\r\n\t *\/\r\n\tprivate boolean prior(String str1, String str2) {\r\n\t\tif ((str1.equals(MULTIPLY) || str1.equals(DIVIDE))\r\n\t\t\t\t&& (str2.equals(PLUS) || str2.equals(MINUS))) {\r\n\t\t\treturn true;\r\n\t\t} else if ((str1.equals(PLUS) || str1.equals(MINUS)\r\n\t\t\t\t|| str1.equals(MULTIPLY) || str1.equals(DIVIDE))\r\n\t\t\t\t&& str2.equals(NUMBER_SIGN)) {\r\n\t\t\treturn true;\r\n\t\t}\r\n\t\treturn false;\r\n\t}\r\n\r\n\t\/**\r\n\t * \u8fd0\u7b97\u7b26str1 \u662f\u5426\u6bd4str2\u4f18\u5148\u7ea7\u4f4e\r\n\t * \r\n\t * @param str1\r\n\t * @param str2\r\n\t * @return\r\n\t *\/\r\n\tprivate boolean posterior(String str1, String str2) {\r\n\t\tif ((str1.equals(PLUS) || str1.equals(MINUS))\r\n\t\t\t\t&& (str2.equals(MULTIPLY) || str2.equals(DIVIDE))) {\r\n\t\t\treturn true;\r\n\t\t} else if (str1.equals(NUMBER_SIGN)\r\n\t\t\t\t&& (str2.equals(PLUS) || str2.equals(MINUS)\r\n\t\t\t\t\t\t|| str2.equals(MULTIPLY) || str2.equals(DIVIDE))) {\r\n\t\t\treturn true;\r\n\t\t}\r\n\t\treturn false;\r\n\t}\r\n\r\n\tprivate void generateRPN() {\r\n\t\tStack<String> s1 = new Stack<String>();\r\n\t\ts1.push(NUMBER_SIGN);\r\n\t\tStack<String> s2 = new Stack<String>();\r\n\t\tfor (int i = 0; i < expList.size(); i++) {\r\n\t\t\tString item = expList.get(i);\r\n\t\t\tif (isNumber(item)) {\r\n\t\t\t\ts2.push(item);\r\n\t\t\t} else if (item.equals(OPSTART)) {\r\n\t\t\t\ts1.push(item);\r\n\t\t\t} else if (item.equals(OPEND)) {\r\n\t\t\t\tString c;\r\n\t\t\t\tdo {\r\n\t\t\t\t\tc = s1.pop();\r\n\t\t\t\t\tif (!c.equals(OPSTART)) {\r\n\t\t\t\t\t\ts2.push(c);\r\n\t\t\t\t\t}\r\n\t\t\t\t} while (!c.equals(OPSTART));\r\n\t\t\t} else {\r\n\t\t\t\tString top = s1.peek();\r\n\t\t\t\tif (top.equals("(")) {\r\n\t\t\t\t\ts1.push(item);\r\n\t\t\t\t} else {\r\n\t\t\t\t\tif (prior(item, top)) {\r\n\t\t\t\t\t\ts1.push(item);\r\n\t\t\t\t\t} else {\r\n\t\t\t\t\t\tString c;\r\n\t\t\t\t\t\tdo {\r\n\t\t\t\t\t\t\tc = s1.pop();\r\n\t\t\t\t\t\t\ts2.push(c);\r\n\t\t\t\t\t\t\tif (posterior(s1.peek(), item)\r\n\t\t\t\t\t\t\t\t\t|| s1.peek().equals("(")\r\n\t\t\t\t\t\t\t\t\t|| s1.peek().equals(NUMBER_SIGN)) {\r\n\t\t\t\t\t\t\t\tbreak;\r\n\t\t\t\t\t\t\t}\r\n\r\n\t\t\t\t\t\t} while (true);\r\n\t\t\t\t\t\ts1.push(item);\r\n\t\t\t\t\t}\r\n\t\t\t\t}\r\n\t\t\t}\r\n\t\t}\r\n\r\n\t\twhile (!s1.isEmpty()) {\r\n\t\t\tString c = s1.pop();\r\n\t\t\tif (!c.equals(NUMBER_SIGN)) {\r\n\t\t\t\ts2.push(c);\r\n\t\t\t}\r\n\t\t}\r\n\t\trpnList = new ArrayList<String>();\r\n\t\trpnList.addAll(s2);\r\n\r\n\t}\r\n\r\n\tpublic List<String> getRPN() {\r\n\t\tparse();\r\n\t\tgenerateRPN();\r\n\t\treturn rpnList;\r\n\t}\r\n\r\n\t\/**\r\n\t * @param args\r\n\t *\/\r\n\tpublic static void main(String[] args) {\r\n\t\tString exp = "7+8*2";\r\n\t\tReversePolishNotation rpn = new ReversePolishNotation(exp);\r\n\t\tList<String> rpnExp = rpn.getRPN();\r\n\t\tSystem.out.println("\u7b97\u672f\u8868\u8fbe\u5f0f\uff1a" + exp);\r\n\t\tSystem.out.println("\u9006\u6ce2\u5170\u8868\u8fbe\u5f0f\uff1a" + rpnExp);\r\n\r\n\t\texp = "(30-4*5)*(3+5)-5";\r\n\t\trpn = new ReversePolishNotation(exp);\r\n\t\trpnExp = rpn.getRPN();\r\n\t\tSystem.out.println("\u7b97\u672f\u8868\u8fbe\u5f0f\uff1a" + exp);\r\n\t\tSystem.out.println("\u9006\u6ce2\u5170\u8868\u8fbe\u5f0f\uff1a" + rpnExp);\r\n\r\n\t\texp = "(8-4)*(88\/2\/11)";\r\n\t\trpn = new ReversePolishNotation(exp);\r\n\t\trpnExp = rpn.getRPN();\r\n\t\tSystem.out.println("\u7b97\u672f\u8868\u8fbe\u5f0f\uff1a" + exp);\r\n\t\tSystem.out.println("\u9006\u6ce2\u5170\u8868\u8fbe\u5f0f\uff1a" + rpnExp);\r\n\t}\r\n\r\n}\r\n<\/pre>\n
\u63a7\u5236\u53f0\u8f93\u51fa\u5982\u4e0b\uff1a<\/p>\n
\u7b97\u672f\u8868\u8fbe\u5f0f\uff1a7+8*2
\n\u9006\u6ce2\u5170\u8868\u8fbe\u5f0f\uff1a[7, 8, 2, *, +]
\n\u7b97\u672f\u8868\u8fbe\u5f0f\uff1a(30-4*5)*(3+5)-5
\n\u9006\u6ce2\u5170\u8868\u8fbe\u5f0f\uff1a[30, 4, 5, *, -, 3, 5, +, *, 5, -]
\n\u7b97\u672f\u8868\u8fbe\u5f0f\uff1a(8-4)*(88\/2\/11)
\n\u9006\u6ce2\u5170\u8868\u8fbe\u5f0f\uff1a[8, 4, -, 88, 2, \/, 11, \/, *]<\/p>\n
 <\/p>\n","protected":false},"excerpt":{"rendered":"
\u9006\u6ce2\u5170\u8868\u8fbe\u5f0f\u5c06\u64cd\u4f5c\u7b26\u7f6e\u4e8e\u64cd\u4f5c\u6570\u7684\u540e\u9762\u3002\u6bd4\u5982\uff0c3+4\u7528\u9006\u6ce2\u5170\u8868\u793a\u6cd5\u5219\u662f \u201c3 4  … \u7ee7\u7eed\u9605\u8bfb →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[42,32],"class_list":["post-86","post","type-post","status-publish","format-standard","hentry","category-8","tag-java","tag-32"],"_links":{"self":[{"href":"https:\/\/www.lixiaodong.com\/index.php?rest_route=\/wp\/v2\/posts\/86","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lixiaodong.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lixiaodong.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lixiaodong.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lixiaodong.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=86"}],"version-history":[{"count":12,"href":"https:\/\/www.lixiaodong.com\/index.php?rest_route=\/wp\/v2\/posts\/86\/revisions"}],"predecessor-version":[{"id":134,"href":"https:\/\/www.lixiaodong.com\/index.php?rest_route=\/wp\/v2\/posts\/86\/revisions\/134"}],"wp:attachment":[{"href":"https:\/\/www.lixiaodong.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=86"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lixiaodong.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=86"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lixiaodong.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=86"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}