Stack & Queue • Expression Parsing

Infix Expressions

Infix is the standard mathematical notation we learn in school, where operators are placed in between their operands. For example: A + B * C.

The Challenge

While Infix is easy for humans to read, it is very difficult for computers to evaluate natively. It requires understanding order of operations (BODMAS/PEMDAS) and handling parentheses.

Operator Precedence

In the expression `2 + 3 * 4`, a computer cannot simply process left-to-right. It must realize that `*` has higher precedence than `+` and must evaluate `3 * 4` first.

The Computer's Solution

Instead of building complex recursive trees just to evaluate math, compilers usually convert Infix expressions into Postfix or Prefix notation using a Stack, and then evaluate the simpler notation directly.

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Stack & Queue • Expression Parsing

Infix Expressions

Infix is the standard mathematical notation we learn in school, where operators are placed in between their operands. For example: A + B * C.

The Challenge

While Infix is easy for humans to read, it is very difficult for computers to evaluate natively. It requires understanding order of operations (BODMAS/PEMDAS) and handling parentheses.

Operator Precedence

In the expression `2 + 3 * 4`, a computer cannot simply process left-to-right. It must realize that `*` has higher precedence than `+` and must evaluate `3 * 4` first.