Valid Coordinate Pairs — Problem Statement & Solution Guide

StackMediummatching parentheses

TimeO(n)

SpaceO(1)

Quick Answer & Algorithm Key Takeaway

The optimized approach uses a single integer counter to track the balance of parentheses. It iterates through the string, incrementing the counter for '(' and decrementing for ')'. If the counter ever becomes negative or is not zero at the end, the string is invalid. This ensures correct ordering and nesting with O(n) time and O(1) space complexity.

TopicStack

Patternmatching parentheses

TimeO(n)

SpaceO(1)

Problem Description

Given a string that may contain zero or more coordinate literals formatted as (x, y) where x and y are signed integers, determine whether every parenthesis participates in a correctly nested and ordered pair. While scanning from left to right, a closing parenthesis must never appear before a matching opening one, and the total count of '(' must equal the count of ')'. Return true if the entire string satisfies these rules, otherwise false.

DSA Pattern Breakdown

"Valid Coordinate Pairs"

medium

WHY DOES IT MATTER?

The stack-based validation pattern is essential for parsing any structured data, from code syntax to configuration files. It ensures that hierarchical structures are well-formed, which is a prerequisite for any further processing or interpretation of the data.

OPTIMIZATION CHALLENGE

The key insight is recognizing that for simple parenthesis validation, we do not need to store the actual characters in the stack. A single integer counter is sufficient to track the balance, reducing space complexity from O(n) to O(1). This is a common optimization that interviewers look for to demonstrate understanding of memory constraints.

REAL-WORLD CONNECTION

This is analogous to how a web browser parses HTML. The browser uses a stack to keep track of open tags. If a closing tag does not match the most recent open tag, or if the document ends with unclosed tags, the browser must handle the error gracefully. Similarly, in distributed systems, message queues often use similar logic to ensure that transactions are properly committed or rolled back in the correct order.

During the interview, start by explaining the naive counting approach and why it fails. Then, introduce the stack-based solution. Finally, propose the counter optimization as a follow-up improvement. This shows a progression from basic understanding to optimized implementation, which is highly valued in technical interviews.

COMPLEXITY AT A GLANCE

⏱ Time:O(n)

💾 Space:O(1)

Core Theory — Why This Approach?

The problem of validating coordinate pairs is fundamentally a variation of the classic 'Valid Parentheses' problem, which relies on the properties of a stack data structure to enforce correct nesting and ordering. In a valid sequence, every closing parenthesis must correspond to a previously seen and unmatched opening parenthesis. A naive approach might simply count the total number of '(' and ')' characters; however, this fails to verify the structural integrity of the sequence. For instance, the string ')(' has equal counts but is structurally invalid because the closing parenthesis appears before its matching opener. Therefore, a simple count is insufficient for ensuring correct nesting.

Interview Questions on This Problem

Q1At a fintech platform, you are building a parser for financial transaction logs where coordinates represent (timestamp, amount). How would you handle malformed entries that might contain nested structures or extra whitespace?

I would use a stack-based approach to validate the parenthesis structure first. I would also implement a state machine or regex to ensure that between valid parentheses, the content strictly matches the expected integer format. If the stack becomes empty before the end of the string or if a closing parenthesis is encountered when the stack is empty, the entry is rejected. This ensures both structural validity and content correctness.

Q2In a high-growth startup's configuration system, users can define complex nested rules. If the input string is extremely large (e.g., 10^6 characters), how would you optimize the memory usage of your validation algorithm?

Since we only need to validate the balance and order of parentheses, we don't actually need to store the characters in the stack. We can use a single integer counter instead. Increment the counter for '(' and decrement for ')'. If the counter ever drops below zero, the string is invalid. At the end, the counter must be zero. This reduces space complexity from O(n) to O(1) while maintaining O(n) time complexity.

Q3At a global product company, you are designing a system to validate JSON-like structures. How does the logic for validating simple parentheses differ from validating JSON objects with keys and values?

For simple parentheses, we only care about the balance and order of open/close tokens. For JSON, we need to track the context (e.g., expecting a key, a colon, a value, or a closing brace). This requires a more complex state machine or a stack that stores the expected next token type. The parenthesis validation is a subset of this, focusing solely on the structural delimiters rather than the semantic content between them.

Examples

Example 1

Input

(1,2) (3,4)

Output

true

Explanation: The first '(' matches the first ')', and the second '(' matches the second ')'. No extra or misplaced parentheses exist, so the sequence is valid.

Example 2

Input

(5,6)) (7,8)

Output

false

Explanation: After the first coordinate the parser encounters an extra ')' with no preceding unmatched '('. This unmatched closing parenthesis invalidates the whole string.

Example 3

Input

((9,10),(11,12))

Output

true

Explanation: The outer '(' pairs with the final ')', and each inner '(' of the two coordinates pairs with its corresponding ')'. All parentheses are properly nested, making the string valid.

Constraints

1<=s.length<=10^5
s contains only digits, '+', '-', '(', ')', ',', and whitespace characters
If a coordinate appears it strictly follows the pattern '(' optional sign digits ',' optional sign digits ')'

Optimal Approach & Strategy

Brute Force Approach

The brute force approach involves counting the total number of '(' and ')' characters in the string. If the counts are equal, it returns true; otherwise, it returns false. This approach fails to check the correct ordering and nesting of the parentheses.

Code Solutions

Language:

JavaScript Solution

Time: O(n)

function isValidCoordinatePairs(s){
    let balance=0;
    for(let ch of s){
        if(ch==='(') balance++;
        else if(ch===')'){
            if(balance===0) return false;
            balance--;
        }
    }
    return balance===0;
}
const fs=require('fs');
const input=fs.readFileSync(0,'utf8').trimEnd();
console.log(isValidCoordinatePairs(input)?'true':'false');

#include <bits/stdc++.h>
using namespace std;
bool isValidCoordinatePairs(const string& s){
    int balance=0;
    for(char c: s){
        if(c=='(') balance++;
        else if(c==')'){
            if(balance==0) return false;
            balance--;
        }
    }
    return balance==0;
}
int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    string s;
    getline(cin,s);
    cout<<(isValidCoordinatePairs(s)?"true":"false");
    return 0;
}

import java.io.*;
public class Main{
    public static boolean isValidCoordinatePairs(String s){
        int balance=0;
        for(int i=0;i<s.length();i++){
            char c=s.charAt(i);
            if(c=='(') balance++;
            else if(c==')'){
                if(balance==0) return false;
                balance--;
            }
        }
        return balance==0;
    }
    public static void main(String[] args) throws Exception{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String s=br.readLine();
        System.out.println(isValidCoordinatePairs(s));
    }
}

def is_valid_coordinate_pairs(s):
    balance=0
    for ch in s:
        if ch=='(':
            balance+=1
        elif ch==')':
            if balance==0:
                return False
            balance-=1
    return balance==0

if __name__=="__main__":
    import sys
    s=sys.stdin.read().rstrip('\n')
    print(str(is_valid_coordinate_pairs(s)).lower())

function isValidCoordinatePairs(s){
    let balance=0;
    for(let ch of s){
        if(ch==='(') balance++;
        else if(ch===')'){
            if(balance===0) return false;
            balance--;
        }
    }
    return balance===0;
}
const fs=require('fs');
const input=fs.readFileSync(0,'utf8').trimEnd();
console.log(isValidCoordinatePairs(input)?'true':'false');

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