The best data structure to check whether an arithmetic expression has balanced parentheses is a (GATE CS 2004)
(A) queue
(B) stack
(C) tree
(D) list
Answer: (B)
Explanation: There are three types of parentheses [ ] { } (). Below is an arbit c code segment which has parentheses of all three types.
void func(int c, int a[]) {    return ((c +2) + arr[(c-2)]) ; } |
Stack is a straightforward choice for checking if left and right parentheses are balanced. Here is a algorithm to do the same.
/*Return 1 if expression has balanced parentheses */bool areParenthesesBalanced(expression ) {    for each character in expression    {       if(character == ’(’ || character == ’{’ || character == ’[’)         push(stack, character);       if(character == ’)’ || character == ’}’ || character == ’]’)       {          if(isEmpty(stack))             return 0; /*We are seeing a right parenthesis                         without a left pair*/           /* Pop the top element from stack, if it is not a pair              bracket of character then there is a mismatch.              This will happen for expressions like {(}) */         else if (! isMatchingPair(pop(stack), character) )            return 0;         }    }        if(isEmpty(stack))      return 1; /*balanced*/   else       return 0; /*not balanced*/   } /* End of function to check parentheses */  /* Returns 1 if character1 and character2 are matching left    and right parentheses */bool isMatchingPair(character1, character2) {    if(character1 == ‘(‘ && character2 == ‘)’)      return 1;    else If(character1 == ‘{‘ && character2 == ‘}’)      return 1;    else If(character1 == ‘[‘ && character2 == ‘]’)      return 1;    else      return 0; } |
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