├── README.md ├── pro1.xcodeproj ├── project.pbxproj ├── project.xcworkspace │ ├── contents.xcworkspacedata │ └── xcuserdata │ │ └── el1ven.xcuserdatad │ │ └── UserInterfaceState.xcuserstate └── xcuserdata │ └── el1ven.xcuserdatad │ ├── xcdebugger │ └── Breakpoints_v2.xcbkptlist │ └── xcschemes │ ├── pro1.xcscheme │ └── xcschememanagement.plist ├── pro1 ├── main.cpp └── pro1.1 └── result.png /README.md: -------------------------------------------------------------------------------- 1 | 中缀表达式转换为后缀表达式 2 | 3 | http://blog.csdn.net/sgbfblog/article/details/8001651 4 | 5 | 一、后缀表达式求值 6 | 后缀表达式也叫逆波兰表达式，其求值过程可以用到栈来辅助存储。假定待求值的后缀表达式为：6 5 2 3 + 8 * + 3 + *，则其求值过程如下： 7 | 1）遍历表达式，遇到的数字首先放入栈中，此时栈如下所示： 8 | 9 | 2）接着读到“+”，则弹出3和2，执行3+2，计算结果等于5，并将5压入到栈中。 10 | 11 | 3）读到8，将其直接放入栈中。 12 | 13 | 4）读到“*”，弹出8和5，执行8*5，并将结果40压入栈中。而后过程类似，读到“+”，将40和5弹出，将40+5的结果45压入栈...以此类推。最后求的值288。 14 | 15 | 16 | 二、中缀表达式转后缀表达式 17 | 2.1）规则 18 | 中缀表达式a + b*c + (d * e + f) * g，其转换成后缀表达式则为a b c * + d e * f + g * +。 19 | 转换过程需要用到栈，具体过程如下： 20 | 1）如果遇到操作数，我们就直接将其输出。 21 | 2）如果遇到操作符，则我们将其放入到栈中，遇到左括号时我们也将其放入栈中。 22 | 3）如果遇到一个右括号，则将栈元素弹出，将弹出的操作符输出直到遇到左括号为止。注意，左括号只弹出并不输出。 23 | 4）如果遇到任何其他的操作符，如（“+”， “*”，“（”）等，从栈中弹出元素直到遇到发现更低优先级的元素(或者栈为空)为止。弹出完这些元素后，才将遇到的操作符压入到栈中。有一点需要注意，只有在遇到" ) "的情况下我们才弹出" ( "，其他情况我们都不会弹出" ( "。 24 | 5）如果我们读到了输入的末尾，则将栈中所有元素依次弹出。 25 | 26 | 2.2）实例 27 | 规则很多，还是用实例比较容易说清楚整个过程。以上面的转换为例，输入为a + b * c + (d * e + f)*g，处理过程如下： 28 | 1）首先读到a，直接输出。 29 | 2）读到“+”，将其放入到栈中。 30 | 3）读到b，直接输出。 31 | 此时栈和输出的情况如下： 32 | 33 | 34 | 4）读到“*”，因为栈顶元素"+"优先级比" * " 低，所以将" * "直接压入栈中。 35 | 5）读到c，直接输出。 36 | 此时栈和输出情况如下： 37 | 38 | 39 | 6）读到" + "，因为栈顶元素" * "的优先级比它高，所以弹出" * "并输出， 同理，栈中下一个元素" + "优先级与读到的操作符" + "一样，所以也要弹出并输出。然后再将读到的" + "压入栈中。 40 | 此时栈和输出情况如下： 41 | 42 | 43 | 7）下一个读到的为"("，它优先级最高，所以直接放入到栈中。 44 | 8）读到d，将其直接输出。 45 | 此时栈和输出情况如下： 46 | 47 | 48 | 9）读到" * "，由于只有遇到" ) "的时候左括号"("才会弹出，所以" * "直接压入栈中。 49 | 10）读到e，直接输出。 50 | 此时栈和输出情况如下： 51 | 52 | 53 | 11）读到" + "，弹出" * "并输出，然后将"+"压入栈中。 54 | 12）读到f，直接输出。 55 | 此时栈和输出情况： 56 | 57 | 58 | 13）接下来读到“）”，则直接将栈中元素弹出并输出直到遇到"("为止。这里右括号前只有一个操作符"+"被弹出并输出。 59 | 60 | 61 | 14）读到" * "，压入栈中。读到g，直接输出。 62 | 63 | 64 | 15）此时输入数据已经读到末尾，栈中还有两个操作符“*”和" + "，直接弹出并输出。 65 | 66 | 至此整个转换过程完成。程序实现代码后续再补充了。 67 | 68 | 2.3）转换的另一种方法 69 | 1)先按照运算符的优先级对中缀表达式加括号，变成( ( a+(b*c) ) + ( ((d*e)+f) *g ) ) 70 | 2)将运算符移到括号的后面，变成((a(bc)*)+(((de)*f)+g)*)+ 71 | 3)去掉括号，得到abc*+de*f+g*+ -------------------------------------------------------------------------------- /pro1.xcodeproj/project.pbxproj: -------------------------------------------------------------------------------- 1 | // !$*UTF8*$! 2 | { 3 | archiveVersion = 1; 4 | classes = { 5 | }; 6 | objectVersion = 46; 7 | objects = { 8 | 9 | /* Begin PBXBuildFile section */ 10 | D93A21471941614000577967 /* main.cpp in Sources */ = {isa = PBXBuildFile; fileRef = D93A21461941614000577967 /* main.cpp */; }; 11 | D93A21491941614000577967 /* pro1.1 in CopyFiles */ = {isa = PBXBuildFile; fileRef = D93A21481941614000577967 /* pro1.1 */; }; 12 | /* End PBXBuildFile section */ 13 | 14 | /* Begin PBXCopyFilesBuildPhase section */ 15 | D93A21411941614000577967 /* CopyFiles */ = { 16 | isa = PBXCopyFilesBuildPhase; 17 | buildActionMask = 2147483647; 18 | dstPath = /usr/share/man/man1/; 19 | dstSubfolderSpec = 0; 20 | files = ( 21 | D93A21491941614000577967 /* pro1.1 in CopyFiles */, 22 | ); 23 | runOnlyForDeploymentPostprocessing = 1; 24 | }; 25 | /* End PBXCopyFilesBuildPhase section */ 26 | 27 | /* Begin PBXFileReference section */ 28 | D93A21431941614000577967 /* pro1 */ = {isa = PBXFileReference; explicitFileType = "compiled.mach-o.executable"; includeInIndex = 0; 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220 | defaultConfigurationIsVisible = 0; 221 | defaultConfigurationName = Release; 222 | }; 223 | D93A214C1941614000577967 /* Build configuration list for PBXNativeTarget "pro1" */ = { 224 | isa = XCConfigurationList; 225 | buildConfigurations = ( 226 | D93A214D1941614000577967 /* Debug */, 227 | D93A214E1941614000577967 /* Release */, 228 | ); 229 | defaultConfigurationIsVisible = 0; 230 | }; 231 | /* End XCConfigurationList section */ 232 | }; 233 | rootObject = D93A213B1941614000577967 /* Project object */; 234 | } 235 | -------------------------------------------------------------------------------- /pro1.xcodeproj/project.xcworkspace/contents.xcworkspacedata: -------------------------------------------------------------------------------- 1 | 2 | 4 | 6 | 7 | 8 | -------------------------------------------------------------------------------- /pro1.xcodeproj/project.xcworkspace/xcuserdata/el1ven.xcuserdatad/UserInterfaceState.xcuserstate: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/el1ven/infixConvertPostfix/9ab07b8b5a4bc32977ddf2649cdcdd2f80d3b282/pro1.xcodeproj/project.xcworkspace/xcuserdata/el1ven.xcuserdatad/UserInterfaceState.xcuserstate -------------------------------------------------------------------------------- /pro1.xcodeproj/xcuserdata/el1ven.xcuserdatad/xcdebugger/Breakpoints_v2.xcbkptlist: -------------------------------------------------------------------------------- 1 | 2 | 5 | 6 | 8 | 18 | 19 | 20 | 21 | 22 | -------------------------------------------------------------------------------- /pro1.xcodeproj/xcuserdata/el1ven.xcuserdatad/xcschemes/pro1.xcscheme: -------------------------------------------------------------------------------- 1 | 2 | 5 | 8 | 9 | 15 | 21 | 22 | 23 | 24 | 25 | 30 | 31 | 32 | 33 | 39 | 40 | 41 | 42 | 51 | 52 | 58 | 59 | 60 | 61 | 62 | 63 | 69 | 70 | 76 | 77 | 78 | 79 | 81 | 82 | 85 | 86 | 87 | -------------------------------------------------------------------------------- /pro1.xcodeproj/xcuserdata/el1ven.xcuserdatad/xcschemes/xcschememanagement.plist: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | SchemeUserState 6 | 7 | pro1.xcscheme 8 | 9 | orderHint 10 | 0 11 | 12 | 13 | SuppressBuildableAutocreation 14 | 15 | D93A21421941614000577967 16 | 17 | primary 18 | 19 | 20 | 21 | 22 | 23 | -------------------------------------------------------------------------------- /pro1/main.cpp: -------------------------------------------------------------------------------- 1 | // 2 | // main.cpp 3 | // pro1 4 | // 5 | // Created by el1ven on 14-6-6. 6 | // Copyright (c) 2014年 el1ven. All rights reserved. 7 | // 8 | 9 | #include 10 | #include 11 | #include 12 | #include 13 | #include 14 | #include 15 | 16 | using namespace std; 17 | 18 | //中缀表达式转化为后缀表达式, RSP代表逆波兰表达式 19 | 20 | bool isOptMark(char op){//判断是否为运算符 21 | switch(op){ 22 | case '+': 23 | return 1; 24 | break; 25 | case '-': 26 | return 1; 27 | break; 28 | case '*': 29 | return 1; 30 | break; 31 | case '/': 32 | return 1; 33 | break; 34 | case '(': 35 | return 1; 36 | break; 37 | default: 38 | return 0; 39 | } 40 | } 41 | 42 | int prior(char op){//求运算符优先级 43 | switch (op) { 44 | case '#': 45 | return -1; 46 | break; 47 | case '(': 48 | return 0; 49 | break; 50 | case '+': 51 | case '-': 52 | return 1; 53 | break; 54 | case '*': 55 | case '/': 56 | return 2; 57 | break; 58 | default: 59 | return -1; 60 | } 61 | } 62 | 63 | string convert(string infixExp,string &RSP){//中缀表达式转后缀表达式 64 | 65 | stack stk;//存储操作符栈 66 | 67 | stk.push('#');//必须要有这个末尾识别符号，否则栈为空的话，会报错！！！ 68 | 69 | int length = (int)infixExp.length();//获取表达式的长度 70 | for(int i = 0; i < length; i++){ 71 | if(infixExp[i] >= '0' && infixExp[i] <= '9'){ 72 | //读入数字的话，直接输出 73 | RSP += infixExp[i]; 74 | }else if(infixExp[i] == '('){ 75 | //遇到左括号直接入栈 76 | stk.push(infixExp[i]); 77 | }else if(infixExp[i] == ')'){ 78 | //如果遇到右括号的话，就把一直到最近的左括号之间的都弹出来加入RPN中 79 | while(stk.top() != '('){ 80 | RSP += stk.top(); 81 | stk.pop(); 82 | } 83 | stk.pop();//把左括号弹出栈 84 | }else if(isOptMark(infixExp[i])){ 85 | //用空格把数字和运算符分开，这样就可以计算多位数字了 86 | RSP += ' '; 87 | //如果是运算符的话，比较他们的优先级再决定是否入栈 88 | while( prior(infixExp[i]) <= prior(stk.top()) ){ 89 | //如果当前的优先级小于等于栈顶操作符的话，栈顶操作符弹出，加入RSP 90 | RSP += stk.top(); 91 | stk.pop(); 92 | } 93 | //如果当前的优先级大于栈顶操作符的话，入栈 94 | 95 | stk.push(infixExp[i]); 96 | 97 | 98 | } 99 | } 100 | //如果已经扫描到中缀表达式的末尾，就把栈中的操作符都弹出来加入到RSP中 101 | while(!stk.empty()){ 102 | RSP += stk.top(); 103 | stk.pop(); 104 | } 105 | 106 | return RSP; 107 | } 108 | 109 | int readNum(string exp, int &i){ 110 | int result = 0; 111 | while(exp[i] >= '0' && exp[i] <= '9'){ 112 | result = result * 10 + (exp[i] - '0'); 113 | i++; 114 | } 115 | return result; 116 | } 117 | 118 | int calulate(string RSP){//计算后缀表达式(逆波兰表达式)的最终数值 119 | 120 | int i = 0; 121 | stack optNum;//操作数栈 122 | int x1,x2 = 0; 123 | 124 | while(RSP[i] != '#'){//没有遇到结束标志#，即进行表达式的计算 125 | if(RSP[i] >= '0' && RSP[i] <= '9'){ 126 | optNum.push(readNum(RSP, i));//字符串转整数 127 | }else if(RSP[i] == ' '){ 128 | i++; 129 | }else if(RSP[i] == '+'){ 130 | x1 = optNum.top(); 131 | optNum.pop(); 132 | x2 = optNum.top(); 133 | optNum.pop(); 134 | optNum.push(x1+x2); 135 | i++; 136 | }else if(RSP[i] == '-'){ 137 | x1 = optNum.top(); 138 | optNum.pop(); 139 | x2 = optNum.top(); 140 | optNum.pop(); 141 | optNum.push(x2-x1); 142 | i++; 143 | }else if(RSP[i] == '*'){ 144 | x1 = optNum.top(); 145 | optNum.pop(); 146 | x2 = optNum.top(); 147 | optNum.pop(); 148 | optNum.push(x1*x2); 149 | i++; 150 | }else if(RSP[i] == '/'){ 151 | x1 = optNum.top(); 152 | optNum.pop(); 153 | x2 = optNum.top(); 154 | optNum.pop(); 155 | optNum.push(x2/x1); 156 | i++; 157 | } 158 | } 159 | return optNum.top();//返回最终的计算结果 160 | } 161 | 162 | 163 | int main(){ 164 | string infixExp = ""; 165 | while(cin>>infixExp){ 166 | string RSP = ""; 167 | string postFix = convert(infixExp, RSP);//后缀表达式 168 | cout<<"RSP为: "<