前缀到中缀的转换
中缀:如果运算符出现在表达式中的操作数之间，则该表达式称为中缀表达式。简单的形式(操作符 1 操作符 2)。 例:(甲+乙)*(丙-丁)
前缀:如果运算子出现在运算对象之前的表达式中，则该表达式称为前缀表达式。简单的形式(操作符 1 操作符 2)。 例:*+AB-CD(中缀:(A+B) * (C-D))
给定前缀表达式，将其转换为中缀表达式。 计算机通常用前缀或后缀(通常是后缀)进行计算。但是对于人类来说，理解一个中缀表达式比理解一个前缀更容易。因此转换是人类理解的需要。
示例:
Input : Prefix : *+AB-CD
Output : Infix : ((A+B)*(C-D))
Input : Prefix : *-A/BC-/AKL
Output : Infix : ((A-(B/C))*((A/K)-L))
前缀到中缀的算法:
- 按照相反的顺序(从右到左)阅读前缀表达式
- 如果符号是一个操作数，则将它推到堆栈上
- 如果符号是运算符，则从堆栈中弹出两个操作数 通过连接两个操作数和它们之间的运算符来创建一个字符串。 字符串=(操作符 1 +操作符 2) 并将结果字符串推回堆栈
- 重复以上步骤，直到前缀表达式结束。
C++
// C++ Program to convert prefix to Infix
#include <iostream>
#include <stack>
using namespace std;
// function to check if character is operator or not
bool isOperator(char x) {
switch (x) {
case '+':
case '-':
case '/':
case '*':
return true;
}
return false;
}
// Convert prefix to Infix expression
string preToInfix(string pre_exp) {
stack<string> s;
// length of expression
int length = pre_exp.size();
// reading from right to left
for (int i = length - 1; i >= 0; i--) {
// check if symbol is operator
if (isOperator(pre_exp[i])) {
// pop two operands from stack
string op1 = s.top(); s.pop();
string op2 = s.top(); s.pop();
// concat the operands and operator
string temp = "(" + op1 + pre_exp[i] + op2 + ")";
// Push string temp back to stack
s.push(temp);
}
// if symbol is an operand
else {
// push the operand to the stack
s.push(string(1, pre_exp[i]));
}
}
// Stack now contains the Infix expression
return s.top();
}
// Driver Code
int main() {
string pre_exp = "*-A/BC-/AKL";
cout << "Infix : " << preToInfix(pre_exp);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to convert prefix to Infix
import java.util.Stack;
class GFG{
// Function to check if character
// is operator or not
static boolean isOperator(char x)
{
switch(x)
{
case '+':
case '-':
case '*':
case '/':
return true;
}
return false;
}
// Convert prefix to Infix expression
public static String convert(String str)
{
Stack<String> stack = new Stack<>();
// Length of expression
int l = str.length();
// Reading from right to left
for(int i = l - 1; i >= 0; i--)
{
char c = str.charAt(i);
if (isOperator(c))
{
String op1 = stack.pop();
String op2 = stack.pop();
// Concat the operands and operator
String temp = "(" + op1 + c + op2 + ")";
stack.push(temp);
}
else
{
// To make character to string
stack.push(c + "");
}
}
return stack.pop();
}
// Driver code
public static void main(String[] args)
{
String exp = "*-A/BC-/AKL";
System.out.println("Infix : " + convert(exp));
}
}
// This code is contributed by abbeyme
Python 3
# Python Program to convert prefix to Infix
def prefixToInfix(prefix):
stack = []
# read prefix in reverse order
i = len(prefix) - 1
while i >= 0:
if not isOperator(prefix[i]):
# symbol is operand
stack.append(prefix[i])
i -= 1
else:
# symbol is operator
str = "(" + stack.pop() + prefix[i] + stack.pop() + ")"
stack.append(str)
i -= 1
return stack.pop()
def isOperator(c):
if c == "*" or c == "+" or c == "-" or c == "/" or c == "^" or c == "(" or c == ")":
return True
else:
return False
# Driver code
if __name__=="__main__":
str = "*-A/BC-/AKL"
print(prefixToInfix(str))
# This code is contributed by avishekarora
C
// C# program to convert prefix to Infix
using System;
using System.Collections;
class GFG{
// Function to check if character
// is operator or not
static bool isOperator(char x)
{
switch(x)
{
case '+':
case '-':
case '*':
case '/':
return true;
}
return false;
}
// Convert prefix to Infix expression
public static string convert(string str)
{
Stack stack = new Stack();
// Length of expression
int l = str.Length;
// Reading from right to left
for(int i = l - 1; i >= 0; i--)
{
char c = str[i];
if (isOperator(c))
{
string op1 = (string)stack.Pop();
string op2 = (string)stack.Pop();
// Concat the operands and operator
string temp = "(" + op1 + c + op2 + ")";
stack.Push(temp);
}
else
{
// To make character to string
stack.Push(c + "");
}
}
return (string)stack.Pop();
}
// Driver code
public static void Main(string[] args)
{
string exp = "*-A/BC-/AKL";
Console.Write("Infix : " + convert(exp));
}
}
// This code is contributed by rutvik_56
java 描述语言
<script>
// Javascript program to convert prefix to Infix
// Function to check if character
// is operator or not
function isOperator(x)
{
switch(x)
{
case '+':
case '-':
case '*':
case '/':
return true;
}
return false;
}
// Convert prefix to Infix expression
function convert(str)
{
let stack = [];
// Length of expression
let l = str.length;
// Reading from right to left
for(let i = l - 1; i >= 0; i--)
{
let c = str[i];
if (isOperator(c))
{
let op1 = stack[stack.length - 1];
stack.pop()
let op2 = stack[stack.length - 1];
stack.pop()
// Concat the operands and operator
let temp = "(" + op1 + c + op2 + ")";
stack.push(temp);
}
else
{
// To make character to string
stack.push(c + "");
}
}
return stack[stack.length - 1];
}
let exp = "*-A/BC-/AKL";
document.write("Infix : " + convert(exp));
// This code is contributed by suresh07.
</script>
Output:
Infix : ((A-(B/C))*((A/K)-L))
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