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[No Audio]

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Hello and welcome back again in the course.

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In the previous tutorial, we looked at how to

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convert a given expression to a postfix

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expression. In this tutorial now, we will be

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looking at how to evaluate the final result

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from a postfix expression. Once we understand

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the process, we will be in a better position

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to implement the underlying algorithm in the

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upcoming tutorial. As announced already, this

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tutorial will be comparatively short. There

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are two basic and simple rules that we need

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to remember for converting a postfix

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expression into an infix expression.

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Again, we will be scanning a given expression from

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left to right, and while doing so, the first

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rule is that, if we encounter an operand, then

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simply push it onto the stack. Let me write

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this rule, so that we can easily remember it.

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I will write if operand then push.

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[No Audio]

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The second rule is that, if we encounter an

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operation, then pop up two elements from the

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stack and perform the operations, and then

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push the result back onto the stack.

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Let me write this rule also. I will write if operation

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then pop two elements and perform operation

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and then push.

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[No Audio]

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Now, let us apply the two

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rules on the expression that we have obtained

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in postfix form from the previous tutorial.

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I have written the expression already, and now

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we will be scanning this expression from left

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to right, and we'll apply the two rules on

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each symbol that we encountered to evaluate

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the final result. For ease of work, I have

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already made a table with two columns

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indicating the symbols and the stack.

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The first symbol in the expression is an operand.

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So under the symbol, I will write 33. Since it

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is an operand, so therefore we will push it

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onto the stack. The next symbol is 45. It is

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again an operand, so I will push it onto the

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stack by writing the already contained

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element of 33 followed by 45 under the stack column.

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Please note that the top of the stack

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in this case, is indicated by the element at

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the right most position, and the stack is in

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horizontal direction. The next symbol is

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3, which is operand, and we'll add

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it to the stack. So under the stack, I will

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write the updated status of stack. The

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next symbol is divides. Since this is an

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operation, so therefore we will pop up two

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elements from the stack, and we'll perform the

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operation on it. Please note that the element

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which is popped first, will be our second

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operand, and element which is being popped up

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second, will be our first operand. This means

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that in this case the value of three will be

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popped first, which is going to be the second operand.

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[No Audio]

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Next, the value of 45 will be popped,

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which is going to be our first operand.

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Let me also draw it.

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[No Audio]

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Finally, we will do the

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operation of divides, which will be operand1

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divided by operand 2. So let me

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indicate this by writing, op1/op2 = 45/3.

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The result of this division which has a value

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of 15, will be pushed onto the stack. So under

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the stack, I will indicate the new status of

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the stack. The next symbol is 2, which is

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operand, so we will push it on to the stack.

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Let me update the symbol and the stack

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columns accordingly.

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The next symbol is 9,

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which is operand, so we will push it on to the stack.

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Let me update the symbol and the stack

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columns again. Next, we have the symbol of

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addition, this is an operation. So again, we

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will be popping up the two elements, and we'll

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perform the operations on them, and the result

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will be pushed back onto the stack. In this

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case, we will pop 9 and 2, and we'll add them.

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The result of addition which is 11, will be

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pushed onto the stack. So let me update the

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status of the stack.

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[No Audio]

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Next we have multiplication operation, so let me write it

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under symbol. Again, we will be popping two

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elements and we'll perform the operation on them.

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In this case, the value of 11 and 15

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will be popped, and will be multiplied

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together, resulting in a value of 165, which

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will, which will be pushed onto the stack.

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So let me update the status of the stack.

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[No Audio]

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Next is the addition symbol, so let me write it.

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Again, we will be popping two elements which

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are 165 and 33 in this case, and we will add

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them together, which will result in a value of

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198, which will be pushed onto the stack.

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So, let me update the status of the stack again.

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[No Audio]

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Next, is the symbol of 50, which will be pushed

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onto the stack. So, let me update the status.

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[No Audio]

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Finally, we have the symbol indicating the

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subtraction operation. Again the two elements

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will be popped. Please note again the element

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which is popped first is going to be the

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second operand, and the element which is

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popped a second, will be the first operand.

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So, I will do op1- op2,

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that is 198 - 50, resulting in a value of 148

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which will be pushed back onto the stack.

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Now, when there is no more symbols to scan,

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then anything which is left behind in the

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stack is being popped out. And that is the

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final answer, which in this case has a value of 148.

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Okay, let us quickly check if we have

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computed the result correctly or not. I have

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already written the original expression. In

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maths, when we have an expression like this

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one, we will first compute anything which is

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inside the parentheses. If there are more

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than one operation inside the parentheses,

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then we will apply the operation precedence

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rule, according to which the divides has the

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highest precedence, followed by multiplication,

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followed by addition, and finally subtraction.

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So, in this case, the value of 2 + 9

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will be first computed, resulting in a value of 11.

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So, I will write the simplified expression again.

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Next inside the outer

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brackets, there are many operations. So we

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will apply the operation precedence according

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to which the divides has the highest priority.

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So, we will divide 45/3 which has a value of 15.

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Next, we will do the

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multiplication operation, because it has the

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highest precedence. So let me write the updated expression.

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[No Audio]

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Next, we will perform the addition, which will

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result in a value of 198. Let me write new updated expression.

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Finally, when we will do

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the subtraction operation, which will result

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in a value of 148. You may have noted, that we

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have computed the value of 148 in our

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example, which confirms that our result is correct.

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Okay, great. Now in the next

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tutorial, we will be looking at the

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implementation details of Expression

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Evaluation in Rust. That is going to be fun

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and interesting. So do come back for learning

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that, and until next tutorial, happy Rust programming.

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[No Audio]