王道数据结构之中缀转后缀并计算(栈)——考研复习笔记
所实现的算法:
- 括号匹配检查
- 中缀表达式转后缀表达式
- 计算转乘后缀后的表达式
数据类型
//用来转后缀表达式 typedef struct{ char data[MaxSize]; int top; }SqStack,SNode;
//用来计算后缀表达式 typedef struct{ float Num[MaxSize]; int top; }NuStack,NNode;
完整代码:
1 /* 中缀转后缀并计算 2 */ 3 #include <iostream> 4 #include <stdlib.h> 5 #include <string.h> 6 7 using namespace std; 8 #define MaxSize 100 9 10 typedef struct{ 11 char data[MaxSize]; 12 int top; 13 }SqStack,SNode; 14 15 16 typedef struct{ 17 float Num[MaxSize]; 18 int top; 19 }NuStack,NNode; 20 21 22 //运算符优先级 23 int Priority(char op){ 24 switch(op){ 25 case '+': 26 return 1; 27 case '-': 28 return 1; 29 case '*': 30 return 2; 31 case '/': 32 return 2; 33 default: 34 return 0; 35 } 36 } 37 38 void Init(SqStack &P){ 39 P.top=-1; 40 } 41 42 void Init_Nu(NuStack &S) 43 { 44 S.top=-1; 45 } 46 47 bool Empty(SqStack P){ 48 if (P.top==-1) return true; 49 return false; 50 } 51 52 bool Empty_Num(NuStack S){ 53 if (S.top==-1) return true; 54 return false; 55 } 56 57 bool Push(SqStack &P, char ch){ 58 P.data[++P.top]=ch; 59 return true; 60 } 61 62 bool Push_Nu(NuStack &S, float ch){ 63 //cout<<ch<<endl; 64 S.Num[++S.top]=ch; 65 return true; 66 } 67 68 bool Pop_1(SqStack &P){ 69 P.top--; 70 return true; 71 } 72 73 bool Pop_2(NuStack &S,float &x){ 74 x=S.Num[S.top--]; 75 return true; 76 } 77 78 char GetTop(SqStack S){ 79 return S.data[S.top]; 80 } 81 82 float GetNum(NuStack S){ 83 return S.Num[S.top]; 84 } 85 86 //转后缀并计算 87 void Convert(NuStack &S,SqStack &P,char ch[],int len){ 88 char Cov_ch[MaxSize]; 89 int cnt =0; 90 for(int i=0;i<len;i++){ 91 if(ch[i]<='9'&&ch[i]>='0'){ 92 Cov_ch[cnt++]=ch[i]; 93 }else{ 94 if(Empty(P)) Push(P,ch[i]); 95 else if(ch[i]=='(') Push(P,ch[i]); 96 else if(ch[i]==')'){ 97 while(GetTop(P)!='('){ 98 Cov_ch[cnt++]=GetTop(P); 99 Pop_1(P); 100 } 101 Pop_1(P); 102 } 103 else{ 104 while(Priority(ch[i])<=Priority(GetTop(P))){ 105 Cov_ch[cnt++]=GetTop(P); 106 Pop_1(P); 107 if(Empty(P)) break; 108 } 109 Push(P,ch[i]); 110 } 111 } 112 } 113 while(!Empty(P)){ 114 Cov_ch[cnt++]=GetTop(P); 115 Pop_1(P); 116 } 117 118 for(int i=0;i<cnt;i++){ 119 cout<<Cov_ch[i]; 120 } 121 puts(""); 122 float a,b; 123 for(int i=0;i<cnt;i++){ 124 if(Cov_ch[i]>='0'&&Cov_ch[i]<='9'){ 125 Push_Nu(S,Cov_ch[i]-'0'); 126 }else{ 127 switch(Cov_ch[i]){ 128 case '+': 129 Pop_2(S,a); 130 Pop_2(S,b); 131 Push_Nu(S,b+a); 132 break; 133 case '-': 134 Pop_2(S,a); 135 Pop_2(S,b); 136 Push_Nu(S,b-a); 137 break; 138 case '*': 139 Pop_2(S,a); 140 Pop_2(S,b); 141 Push_Nu(S,a*b); 142 break; 143 case '/': 144 Pop_2(S,a); 145 Pop_2(S,b); 146 Push_Nu(S,b/a); 147 break; 148 default: 149 break; 150 } 151 } 152 } 153 cout<<GetNum(S); 154 } 155 //括号检查 156 bool bracketCheck(char str[],int ll){ 157 SqStack Q; 158 Q.top=-1; 159 char x; 160 char bracket[MaxSize]; 161 int cnt=0; 162 for(int i=0;i<ll;i++){ 163 if(str[i]=='('||str[i]==')') bracket[cnt++]=str[i]; 164 } 165 for(int i=0;i<cnt;i++){ 166 if(bracket[i]=='('){ 167 Push(Q,bracket[i]); 168 } 169 else{ 170 if(Empty(Q)) return false; 171 x=GetTop(Q); 172 Pop_1(Q); 173 if((bracket[i]==')'&&x!='(')) 174 return false; 175 } 176 } 177 return Empty(Q); 178 } 179 180 int main(){ 181 SqStack P; 182 NuStack S; 183 Init(P); 184 Init_Nu(S); 185 char ch[MaxSize]; 186 cin>>ch; 187 int len = strlen(ch); 188 if(!bracketCheck(ch,len)){ 189 cout<<"It's a wrong expression"<<endl; 190 }else{ 191 Convert(S,P,ch,len); 192 } 193 return 0; 194 }