273 lines
7.8 KiB
C++
273 lines
7.8 KiB
C++
#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <math.h>
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#include <ctype.h>
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#define MAX 100
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// === 全域變數宣告 ===
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char input[MAX];
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char postfix[MAX];
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char postfix_1[MAX]; //顯示用
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char stack[MAX];
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double numStack[MAX];
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int top = -1;
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int numTop = -1;
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// === 函式宣告 ===
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int get_priority(char op);
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int is_operator(char c);
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double calculate(double a, double b, char op);
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void convert_to_postfix();
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double evaluate_postfix();
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double evaluate_infix(char *expr);
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double parse_number(char **expr);
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int get_priority(char c){
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if(c=='+' || c=='-'){
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return 1;
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}else if(c=='*' || c=='/'){
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return 2;
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}else if(c=='^'){
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return 3;
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}else{
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return 0;
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}
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}
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// === 檢查字元是否為運算子 ===
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int is_operator(char c) {
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return (c == '+' || c == '-' || c == '*' || c == '/' || c == '^');
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}
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// === 執行運算 ===
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double calculate(double a, double b, char op) {
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switch(op) {
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case '+': return a + b;
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case '-': return a - b;
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case '*': return a * b;
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case '/':
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if(b != 0) return a / b;
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printf("錯誤：除數不能為零！\n");
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exit(1);
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case '^': return pow(a, b);
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default: return 0;
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}
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}
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//顯示用
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void convert_to_postfix_forprint() {
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int i = 0, j;
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int postfix_index = 0;
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top = -1;
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char number_str[MAX];
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int is_negative;
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while(input[i] != '\0') {
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if(isdigit(input[i]) || input[i] == '.' ||
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(input[i] == '-' && (i == 0 || input[i-1] == '(' || is_operator(input[i-1])))) {
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// 處理數字（包括負數）
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is_negative = 0;
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int num_len = 0;
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// 檢查是否為負數
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if(input[i] == '-') {
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is_negative = 1;
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i++;
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}
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// 收集完整數字字串
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while(input[i] != '\0' && (isdigit(input[i]) || input[i] == '.')) {
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number_str[num_len++] = input[i++];
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}
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number_str[num_len] = '\0';
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i--; // 回退一個位置，因為外層 while 會再加一
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// 輸出數字
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printf("%s ", number_str);
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if(is_negative) {
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printf("- ");
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}
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// 將數字加入後序表達式
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for(j = 0; j < num_len; j++) {
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postfix_1[postfix_index++] = number_str[j];
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}
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postfix_1[postfix_index++] = ' ';
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if(is_negative) {
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postfix_1[postfix_index++] = '-';
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postfix_1[postfix_index++] = ' ';
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}
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}
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else if(input[i] == '(') {
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stack[++top] = input[i];
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}
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else if(input[i] == ')') {
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while(top >= 0 && stack[top] != '(') {
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printf("%c ", stack[top]);
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postfix_1[postfix_index++] = stack[top];
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postfix_1[postfix_index++] = ' ';
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top--;
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}
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if(top >= 0) top--;
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}
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else if(is_operator(input[i])) {
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// 如果不是處理負數的減號
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if(!(input[i] == '-' && (i == 0 || input[i-1] == '(' || is_operator(input[i-1])))) {
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while(top >= 0 && stack[top] != '(' &&
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(get_priority(stack[top]) > get_priority(input[i]) ||
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(get_priority(stack[top]) == get_priority(input[i]) && input[i] != '^'))) {
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printf("%c ", stack[top]);
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postfix_1[postfix_index++] = stack[top];
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postfix_1[postfix_index++] = ' ';
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top--;
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}
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stack[++top] = input[i];
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}
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}
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i++;
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}
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while(top >= 0) {
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printf("%c ", stack[top]);
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postfix_1[postfix_index++] = stack[top];
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postfix_1[postfix_index++] = ' ';
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top--;
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}
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postfix_1[postfix_index] = '\0';
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printf("\n");
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}
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// === 轉換為後序表達式 ===
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//計算用
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void convert_to_postfix() {
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int i = 0 , j;
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int postfix_index = 0;
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top = -1;
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while(input[i] != '\0') {
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if(isdigit(input[i]) || input[i] == '.' || (input[i] == '-' && (i == 0 || input[i-1] == '(' || is_operator(input[i-1])))) { // 檢查是否為數字、小數點或是負號（且是表達式的開始，或緊跟在左括號或運算符後面）
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char *end;
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double num = strtod(&input[i], &end); //strtod 把字串換成浮點數
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int len = end - &input[i]; //計算數字字串的長度 數字末端的記憶體位址減掉首項的記憶體位置
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// printf("%.1f ", num);
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for(j = 0; j < len; j++) {
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postfix[postfix_index++] = input[i+j];
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}
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postfix[postfix_index++] = ' ';
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i += len - 1;
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}
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else if(input[i] == '(') {
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stack[++top] = input[i];
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}
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else if(input[i] == ')') {
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while(top >= 0 && stack[top] != '(') {
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// printf("%c ", stack[top]);
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postfix[postfix_index++] = stack[top];
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postfix[postfix_index++] = ' ';
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top--;
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}
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if(top >= 0) top--;
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}
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else if(is_operator(input[i])) {
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while(top >= 0 && stack[top] != '(' && (get_priority(stack[top]) > get_priority(input[i]) || (get_priority(stack[top]) == get_priority(input[i]) && input[i] != '^'))) {
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// printf("%c ", stack[top]);
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postfix[postfix_index++] = stack[top];
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postfix[postfix_index++] = ' ';
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top--;
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}
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stack[++top] = input[i];
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}
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i++;
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}
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while(top >= 0) {
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// printf("%c ", stack[top]);
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postfix[postfix_index++] = stack[top];
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postfix[postfix_index++] = ' ';
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top--;
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}
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postfix[postfix_index] = '\0';
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// printf("\n");
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}
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// === 計算後序表達式 ===
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double evaluate_postfix() {
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int i;
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numTop = -1;
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char *token = strtok(postfix, " ");
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// printf("\n計算過程：\n");
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while(token != NULL) {
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// printf("處理標記：'%s'\n", token);
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if(isdigit(token[0]) || (token[0] == '-' && isdigit(token[1]))) {
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double num = atof(token);
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numStack[++numTop] = num;
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// printf("壓入數字：%.2f\n", num);
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}
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else if(is_operator(token[0])) {
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if(numTop < 1) {
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// printf("運算子 '%c' 缺少足夠的運算元\n", token[0]);
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exit(1);
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}
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double b = numStack[numTop--];
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double a = numStack[numTop--];
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double result = calculate(a, b, token[0]);
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numStack[++numTop] = result;
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// printf("計算：%.2f %c %.2f = %.2f\n", a, token[0], b, result);
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}
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else {
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// printf("錯誤：未知的標記 '%s'\n", token);
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exit(1);
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}
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// printf("當前堆疊：");
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for(i = 0; i <= numTop; i++) {
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// printf("%.2f ", numStack[i]);
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}
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// printf("\n\n");
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token = strtok(NULL, " ");
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}
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if(numTop != 0) {
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// printf("錯誤：計算結束後堆疊中剩餘 %d 個元素\n", numTop + 1);
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exit(1);
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}
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return numStack[numTop];
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}
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int main() {
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printf("請輸入中序表示式(支援+-*/^()運算) => ");
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fgets(input, MAX, stdin);
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input[strcspn(input, "\n")] = 0;
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printf("\n對應的後序表示法式： ");
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convert_to_postfix_forprint(); //顯示用
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convert_to_postfix();
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double postfix_result = evaluate_postfix();
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printf("\n運算結果：%.2f", postfix_result);
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printf("\t(正確值為：");
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if(strcmp(input,"10+20*(50-30)/2^4-6*8")==0){
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printf("%g",10+20*(50-30)/pow(2,4)-6*8);
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}else if(strcmp(input,"10+20*(-50+30)/-2^4-6*8")==0){
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printf("%g",10+20*(-50+30)/pow(-2,4)-6*8);
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}else if(strcmp(input,"10.5+20.8*(50.1-30.6)/2.5^4-6.6*8.2")==0){
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printf("%g",10.5+20.8*(50.1-30.6)/pow(2.5,4)-6.6*8.2);
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}else if(strcmp(input,"10.5+20.8*(-50.1+30.6)/2.5^-4-6.6*8.2")==0){
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printf("%g",10.5+20.8*(-50.1+30.6)/pow(2.5,-4)-6.6*8.2);
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}printf(")");
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return 0;
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}
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