Check whether an arithmetic expression has balanced parentheses
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Suppose you are given an arithmetic expression. How will you check whether it has balanced parentheses or not?

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An arithmetic expression with balanced parentheses will have left and right parentheses in order. Since stack is implemented using LIFO (last in - first out), we can compare the last inserted parentheses in the stack with the current one and check whether they are a pair or not. The algorithm works as follows:

  • Convert the arithmetic expression into a character array.
  • PUSH the left parentheses into the stack.
  • For right parentheses check the status of the stack.

    • If the stack is empty, then the right parentheses has no left pair and return false (not balanced).
    • If the stack is not empty, POP the stack and match it with the right parentheses. If they do not match, return false (not balanced).

  • At the end check the status of the stack. If it is empty, return true (balanced), otherwise false (not balanced).

Example - For an arithmetic expression like ` } ([ ... ])', the algorithm will return false since no left pair of the first ` } ' is found.
For an arithmetic expression like `[{ ( ... }]', the algorithm will return false since the `}' does not match with ` ( '.

Time complexity = O(n) where n is the length of the arithmetic expression.

public boolean isExpressionBalanced(char[] expression){
/* Create a new stack */
Stack myStack = new Stack();
/* For each character in the array */
for(int i=0;i <expression.length;i++){
/* Check whether the character is left parentheses */
if(expression[i]=='(' || expression[i]=='{' || expression[i]=='[')
/* Push the left parentheses into the stack */
/* When it is the right parentheses */
if(expression[i]==')' || expression[i]=='}' || expression[i]==']'){
/* If the stack is empty */
/* No left pair :: hence not balanced */
return false;
/* Match the right parentheses with the last element of the stack :: not matched :: unbalanced*/
else if(!isParenthesesBalanced(myStack.pop(), expression[i]))
return false;
/* Check the status of the stack :: If empty, balanced parentheses, otherwise not */
return true;
return false;

public boolean isParenthesesBalanced(char c1, char c2){
if(c1=='(' && c2==')')
return true;
else if(c1=='{' && c2=='}')
return true;
else if(c1=='[' && c2==']')
return true;
return false;

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