Q. Explain what are the stacks? How can we use the stacks to check whether an expression is correctly parentheses or not. For example (()) is well formed but (() or )()( is not well formed.
Ans:
The stack is a data structure that organizes data in a similar way one organizes a pile of coins. The new coin is all the time placed on the top and the oldest is on the bottom of the stack. When we are accessing coins, the last coin on the pile is the first coin which was removed from the stack. If we want to reach the third coin, we should remove the first two coins from the top of the stack first so that the third coin comes on the top of the stack and we can easily remove it. There is no way at all to remove a coin from anywhere other than the top of the stack.
A stack is useful whenever we need to store data and retrieve data in last in, first out order. Let us take an example the computer processes instructions using a stack in which the next instruction to execute is at the top of the stack.
To determine whether an expression is well parentheses or not:- the two conditions should be fulfilled while pushing an expression into a stack. At first, whenever an opening bracket is pushed inside a stack, there should be an occurrence a closing bracket before we reach the last symbol. Whenever a closing bracket is encountered, the top of the stack is popped until the opening bracket is popped out and discarded. If no such type of opening bracket is found and stack is made empty, then this means that the expression is not well parentheses designed.
An algorithm to check that whether an expression is correctly parenthized or not is written below:
flag=TRUE;
clear the stack;
Read a symbol from input string;
while not end of input string and flag do
{
if(symbol= '( ' or symbol= '[' or symbol = '{' )
push(symbol,stack);
else if(symbol= ') ' or symbol= '[' or symbol =
'{' )
if stack is empty flag=false;
printf("More right parenthesis than left
parenthises");
else c=pop(stack);
match c and the input symbol; If not matched
{ flag=false;
printf("Mismatched
parenthesis");
}
Read the next input symbol;
}
if stack is empty then
printf("parentheses are balanced properly");
else
printf(" More number of left parentheses than right parentheses");