# LeetCode parentheses matching

I came across this question from LeetCode OJ where I am given a string containing parentheses and I need to find out if the string contains valid matching parentheses or not.

Given a string containing just the characters '(', ')', '{', '}', '[' and ']', determine if the input string is valid.

The brackets must close in the correct order, "()" and "()[]{}" are all valid but "(]" and "([)]" are not.

This is the code I wrote (it got accepted and passed all the test cases.)

/** Java program to check if input string contains matching parameters
or not.
*  @author     :       Anish
*  @date       :       01-11-2017
*/
import java.util.Stack;

class Solution
{
public boolean isValid(String str)
{
Stack<Character> stack  =   new Stack<Character>();

char top    =   ' ';
int len     =   str.length();

for (int i = 0; i < len; i++)
{
char ch    =   str.charAt(i);

if (ch == '(')
stack.push(')');

else if (ch == '[')
stack.push(']');

else if (ch == '{')
stack.push('}');

else if (!stack.empty())
{
top   =   stack.peek();

if (top == ch)
stack.pop();
else
stack.push(ch);
}
else if (stack.empty())
{
stack.push(ch);
}
}
if (stack.empty())
{
return true;
}
return false;
}
}


ANALYSIS

Time Complexity : $O(n)$

Run Time : 9ms (on the leetcode OJ)

ISSUES

• Even though my time is $O(n)$, yet my percentile is 70.4 which effectively means there are better and faster solutions out there. In that case, how do I optimize the above code to make it faster?
• I have been using the Stack API provided by Java to solve the problem. Rather, if I were to redesign my own stack API and then use it to solve the problem, would I get faster runtime and better performance?
• If the above point is true, then does it mean that in general, user designed APIs are faster than what is provided by the Java libraries? (assuming the user designed API is clean and bug free)
• @Mat'sMug thanks for the update! m new here...thanks for the guidelines.. – enigma6174 Nov 2 '17 at 18:26

Usage of Stack

Don't use a Stack. This class is very old, it's thread safe (which you don't need) and achieves it by synchronizing the push and pop methods, which will have an impact in performance.

I would use ArrayDeque. By default it's initialized with size 16. To reduce number of re-allocations, allocate a larger size, perhaps ou can guess how many elements you'll need based on the size of the string. For example:

Queue<Character> queue = new ArrayDeque<>(str.size()/2);


Boxing of char

Note that each time you push/pop from the queue, you are boxing and unboxing char (to Character). For ultimate performance, create a char[] queue, but then you'll have to manage resizes and pointers to the top element yourself.

Fail fast

Consider that the input is {(])}. When finding ], your program can already know that the string is invalid and stop iterating. This will make the processing of invalid inputs potentially much faster. So what about replace this:

else if (!stack.empty())
{
top   =   stack.peek();
if (top == ch)
stack.pop();
else
stack.push(ch);
}
else if (stack.empty())
{
stack.push(ch);
}
}
else if (stack.empty())
{
stack.push(ch);
}


by:

else if (!stack.empty())
{
top   =   stack.peek();
if (top == ch)
stack.pop();
else
return false; // quit
}
}
else
{
return false; //quit
}


I didn't test and I might be missing something, but it looks that as soon as you have an char not matching the expected closing parenthesis, you can conclude that it's invalid.

## My suggestion

This has all the previous points applied and runs much faster:

public boolean isValid(String str) {
char[] stack = new char[str.length()];
int p = -1;

for (int i = 0; i < str.length(); i++) {
char ch = str.charAt(i);

if (ch == '(') {
stack[++p] = ')';
} else if (ch == '[') {
stack[++p] = ']';
} else if (ch == '{') {
stack[++p] = '}';
} else if (p >= 0) {
char top = stack[p];

if (top == ch) {
p--;
} else {
return false;
}
} else {
return false;
}
}

return p < 0;
}


## EDIT: Benchmarks

I'm adding the results of benchmarks done with JMH with some different solutions to show how performance is impacted.

I used one valid input: ([[{{([[{{[[[[]]]]}}]])}}]]) and one invalid input: ([[{{([[{{[[[[]]]]}}]]})}}]]).

Parameters of the benchmark:

# Warmup: 5 iterations, 1 s each
# Measurement: 5 iterations, 1 s each
# Benchmark mode: Average time, time/op (nanoseconds)


Results:

Benchmark               (input)  Mode  Cnt    Score    Error  Units
Benchmark.finalSolution   valid  avgt    5   67.468 ±  1.411  ns/op
Benchmark.finalSolution invalid  avgt    5   53.832 ±  1.543  ns/op

Benchmark.toCharArray     valid  avgt    5  241.692 ± 11.705  ns/op
Benchmark.toCharArray   invalid  avgt    5  261.955 ±  6.192  ns/op

Benchmark.original        valid  avgt    5  245.888 ±  3.329  ns/op
Benchmark.original      invalid  avgt    5  265.483 ±  3.312  ns/op

Benchmark.useArrayDeque   valid  avgt    5  100.597 ±  1.621  ns/op
Benchmark.useArrayDeque invalid  avgt    5  102.695 ±  0.659  ns/op

Benchmark.useLinkedList   valid  avgt    5  180.679 ±  4.395  ns/op
Benchmark.useLinkedList invalid  avgt    5  190.591 ±  4.010  ns/op

• Another possible optimization: if(p > str.length()-i) return false;. There's no need to process further if there aren't enough characters left to properly close all parentheses currently on the stack. Also: if(str.length() % 2 == 1) return false;: An odd length string of only parentheses can not be balanced. – hoffmale Nov 2 '17 at 16:09
• @hoffmale good points! – Duarte Meneses Nov 6 '17 at 16:30
• @DuarteMeneses Yes, I finally created a stack of char using char[ ]. Also, I made a lot of changes to my code, added some optimization techniques for early return (much of it very similar to yours) and the fastest speed I got from that code was 98% faster than the rest! So yes, char[ ] gave me a huge bump in performance! It saved me from unnecessary boxing/unboxing operations. Thanks a lot! :) – enigma6174 Nov 7 '17 at 14:59
• @hoffmale Yes, those optimization tricks do speed up the process a lot! I added those and some more and it did make considerable difference. Thanks :) – enigma6174 Nov 7 '17 at 15:03

One thing that will definitely speed up your code is switching from a Stack<Character> to a char[]. Every time you push and pop a value from a Stack, it's boxed and unboxed to and from its primitive representation, and this is a somewhat expensive operation to do many times in a tight loop. I measured about a 5x speed-up in a pretty unscientific micro-benchmark.

Another smaller optimization you can do is check if the stack grows to over half the length of the input string. If this is ever the case, you know that the string is unbalanced, and you don't have to keep checking.

• thanks so much for your suggestion. What you said is completely true. That wrapper class is definitely slowing things down. Alternatively, I tried designing my own stack API and the solution was accepted but with horrible results!! :P I tried using char[] but my implementations were wrong!! :P On a side note, I realized if I put the following code as a check it speeds thins up : if (len %2 != 0) {return false}. Nevertheless, I would update again once I get a score > 70% using char[] – enigma6174 Nov 5 '17 at 13:10

## Changes

• Move the early declaration of top. Push it into the else-if block, where it's used, to have it as close as possible to it's usage.

• Always put braces around your blocks. Java code is compiled, so more braces don't slow the code down, while preventing bugs.

• If the stack is empty when you just read a closing paren, the string is unbalanced. The final else-if can be an early-return, which saves you a minuscle factor of time.

• Instead of using an indexed for-loop and charAt(i) it would be cleaner (and more idiomatic) to use a for-each loop:

for (char ch : str.toCharArray()) {
if (ch == '(') {
// ...
}


I don't know exactly how this impacts runtime, but it shouldn't make a huge difference either way.

• Instead of if (condition) return true; else return false; one can just return condition. This applies for your code too:

    }
return stack.empty();
}

• Wow dude!! that for each loop made a huge difference! it reduced runtime A LOT!! I followed the other suggestions also and now my code is much cleaner! Here is a trick I used for optimization : if (len % 2 != 0) {return false;}. Just one thing : how does the placement of braces affect runtime? I checked online resources but could not come up with much conclusive data. BTW, my score currently beats 88.9% of Java submissions!! Thanks so much!! :) – enigma6174 Nov 5 '17 at 14:09
• braces placement shouldn't affect runtime at all. that's why I'm advocating to always place braces – Vogel612 Nov 5 '17 at 14:58
• @enigma6174 are you sure it's the for-each loop that made a big difference? I would expect the technique to minimize autoboxing as in Duarte's answer is much more likely to make a significant difference. – janos Nov 6 '17 at 8:57
• @janos Yes I actually verified it!! I used for loop and and submitted my code and saw it was 70% faster than other submissions. Then, keeping everything else same i just modified the indexed for loop into for each loop and submitted it again. This time the code was 89% faster than other submissions. However, I guess one has to expect LeetCode to run the exact same test cases on both the codes to get a much clearer picture. Also I haven't tried out Duarte's answer yet and that is why I didn't say anything. I got so overwhelmed by the responses, I got busy trying each and every answer! :P – enigma6174 Nov 6 '17 at 11:01
• @enigma6174 keep in mind that there can be variation in the execution time on leetcode, even when you submit the exact same code multiple times – janos Nov 6 '17 at 12:43

you may use Deque which gives you the best performance always.

Deque<Character> stack = new LinkedList<Character>();


for pushing:

stack.offerFirst(temp);


for popping:

Charcter temp = stack.pollFirst();

• A linked list does not have always a better performance over Collections based on an array. In this particular case you will have much better performance with an ArrayDeque than with a LinkedList. – Duarte Meneses Nov 5 '17 at 21:29
• @DuarteMeneses i agree! in order to check if I could modify my code into a better solution, I implemented the whole stack myself with a linked list (and also got rid of the boxing/unboxing of Char to Character) but surprisingly, this code was even way more inefficient than the one I first put here! It was only 29% faster than other solutions! I guess the only thing left is properly implement your solution and check how much faster my code gets. – enigma6174 Nov 6 '17 at 11:06

All right, so after a lot of discussions and experiments, I finally came up with the code that gave me the best performance. But before I dwell on that, here are some things I would like to sum up (from all the answers and comments above) :

• Avoid wrapper class for primitive data types as the boxing/unboxing affects performance.
• The java.util.Stack library is old and uses synchronisation which again affects performance.
• If we can implement a stack with dynamic array, then it would lead to much better performance.
• Using a linked list for stack implementation may again affect performance.
• Keeping checks in between the code for early return always make the code more efficient and optimised (provided the checks are valid).
• Queue is a better choice than stack.
• LeetCode submissions give different runtimes for the same code.
• For each loop and indexed for loop give the same performance.
• For each loop is just better and easier to use.
• Keep the variables as close to their usage block as possible.
• Placement of braces doesn't affect performance but may lead to more/less bugs depending on their usage and/or placement.

So, below is the link to the final code I wrote. It gave me 98% performance at best and 40% at worst.

github.com/parentheses

Finally, thank you everyone for the in depth answers and the wealth of knowledge shared. I learned a lot.

P.S. Please point out the mistakes (if any) in my summarisation.