Analyze project tasks, dependencies, durations, and identify the critical path to ensure timely completion. Understand potential delays and optimize resource allocation.
Project Trace Analysis
Enter a unique name for the task.
Estimated number of working days to complete the task.
Comma-separated names of tasks that must be completed before this one can start (e.g., Task A, Task B).
Analysis Results
Total Project Duration (Days)0
Critical Path TasksNone
Number of Tasks0
Formula Used: This calculator uses the Critical Path Method (CPM). It identifies the longest sequence of dependent tasks (the critical path) that determines the minimum project duration. Tasks on the critical path have zero float (slack), meaning any delay in these tasks will delay the entire project.
Project Timeline Visualization
Gantt-style representation of tasks and their durations.
Task Details Table
Task Name
Duration (Days)
Dependencies
Early Start
Early Finish
Late Start
Late Finish
Float (Slack)
Critical Path
No tasks added yet.
What is a Trace Calculator?
A Trace Calculator, often referred to as a Critical Path Method (CPM) calculator or project timeline analyzer, is a tool designed to help project managers and teams visualize, plan, and manage complex projects. It focuses on identifying the sequence of tasks that are essential for completing the project on time. By calculating the earliest and latest start and finish times for each task, and determining the 'float' or 'slack' (the amount of time a task can be delayed without delaying the project), it highlights the critical path – the longest path through the project network. Tasks on this path have zero float, meaning any delay directly impacts the project's overall completion date. This makes the trace calculator invaluable for resource allocation, risk management, and ensuring project deadlines are met.
Who should use it: Project managers, team leads, construction planners, software development teams, event organizers, and anyone managing projects with multiple interdependent tasks and strict deadlines. It's particularly useful for projects with a high degree of complexity or where timely delivery is paramount.
Common misconceptions: A common misconception is that a trace calculator only focuses on the longest task. In reality, it focuses on the longest *sequence* of dependent tasks. Another misconception is that it predicts the future perfectly; it's a planning tool based on estimated durations and dependencies, and actual project execution may vary. It's also sometimes confused with simple task lists, but its power lies in analyzing interdependencies and calculating float.
Trace Calculator Formula and Mathematical Explanation
The core of the trace calculator relies on the Critical Path Method (CPM). This involves several steps and calculations for each task within a project network:
1. Forward Pass: Calculating Early Start (ES) and Early Finish (EF)
The forward pass determines the earliest possible time each task can begin and end. It starts from the beginning of the project.
For the first task(s) with no dependencies: ES = 0.
For subsequent tasks: ES = Maximum (EF of all immediate predecessors).
The Early Finish (EF) for any task is calculated as:
EF = ES + Duration
The Total Project Duration is the maximum EF of all tasks that have no successors (i.e., the final tasks in the project).
2. Backward Pass: Calculating Late Finish (LF) and Late Start (LS)
The backward pass works from the end of the project back to the beginning, determining the latest possible time each task can finish and start without delaying the project completion date.
For the last task(s) with no successors: LF = Total Project Duration (calculated from the forward pass).
For preceding tasks: LF = Minimum (LS of all immediate successors).
The Late Start (LS) for any task is calculated as:
LS = LF - Duration
3. Calculating Float (Slack)
Float (or Slack) is the amount of time a task can be delayed without affecting the project's overall completion date. It's calculated as:
Float = LF - EF or Float = LS - ES
4. Identifying the Critical Path
The critical path consists of all tasks where the Float is zero (or very close to zero, accounting for potential rounding). These are the tasks that, if delayed, will directly delay the entire project.
Variables Table
Variable
Meaning
Unit
Typical Range
ES
Early Start Time
Days
0 to Project Duration
EF
Early Finish Time
Days
0 to Project Duration
LS
Late Start Time
Days
0 to Project Duration
LF
Late Finish Time
Days
0 to Project Duration
Duration
Time required to complete a task
Days
≥ 1
Float (Slack)
Time a task can be delayed without delaying the project
Days
≥ 0
Dependencies
Tasks that must be completed before the current task can start
Task Names
N/A
Practical Examples (Real-World Use Cases)
Example 1: Small Software Feature Development
A team is developing a new login feature. The tasks and estimated durations are:
Design UI (Task A): Duration 3 days, No dependencies.
Develop Backend API (Task B): Duration 5 days, Depends on Task A.
Develop Frontend (Task C): Duration 4 days, Depends on Task A.
Integrate API & Frontend (Task D): Duration 2 days, Depends on Task B, Task C.
Testing (Task E): Duration 3 days, Depends on Task D.
Inputs to Calculator:
Task A, 3,
Task B, 5, Task A
Task C, 4, Task A
Task D, 2, Task B, Task C
Task E, 3, Task D
Calculator Output:
Total Project Duration: 14 days
Critical Path Tasks: A, B, D, E
Float for Task C: 2 days (It can be delayed by 2 days without affecting the project end date).
Financial Interpretation: The team knows the project will take at least 14 days. They can allocate resources confidently. If Task B or Task D faces a delay, the project end date is immediately threatened. Task C has some flexibility, allowing for potential reprioritization if needed.
Example 2: Building a House Foundation
Planning the foundation for a house involves several sequential steps:
Site Preparation (Task P): Duration 2 days, No dependencies.
Excavation (Task Q): Duration 4 days, Depends on Task P.
Rebar Placement (Task S): Duration 2 days, Depends on Task R.
Concrete Pour (Task T): Duration 1 day, Depends on Task S.
Curing (Task U): Duration 7 days, Depends on Task T.
Inputs to Calculator:
Task P, 2,
Task Q, 4, Task P
Task R, 3, Task Q
Task S, 2, Task R
Task T, 1, Task S
Task U, 7, Task T
Calculator Output:
Total Project Duration: 19 days
Critical Path Tasks: P, Q, R, S, T, U
Float for all tasks: 0 days
Financial Interpretation: This foundation work is entirely on the critical path. Any delay in excavation, formwork, rebar, pouring, or curing will directly push back the entire construction schedule, potentially incurring significant costs due to extended labor, equipment rental, and delayed occupancy. Careful scheduling and resource management are crucial here.
How to Use This Trace Calculator
Using the Trace Calculator is straightforward and designed to provide quick insights into your project's timeline.
Input Task Details: In the "Project Trace Analysis" section, enter the details for each task in your project.
Task Name: Provide a unique and descriptive name (e.g., "Design Mockups", "Server Setup").
Duration (Days): Estimate the number of working days required to complete the task. Be realistic!
Dependencies (Task Names): List the names of tasks that must be finished *before* this current task can begin. Separate multiple dependencies with commas (e.g., "Task A, Task B"). If a task has no predecessors, leave this field blank.
Add Tasks: Click the "Add Task" button after entering the details for each task. The calculator will process the inputs and update the results in real-time.
Review Results: Below the input section, you'll find:
Total Project Duration: The minimum time required to complete the entire project.
Critical Path Tasks: A list of tasks that have zero float. Delays in these tasks directly impact the project end date.
Number of Tasks: The total count of tasks entered.
Task Details Table: A comprehensive breakdown including Early Start (ES), Early Finish (EF), Late Start (LS), Late Finish (LF), Float (Slack), and whether each task is on the critical path.
Project Timeline Visualization: A chart offering a visual representation of your project's schedule.
Interpret the Data:
Focus your attention on the Critical Path Tasks. These require the most rigorous monitoring.
Use the Float values to identify tasks that offer flexibility in scheduling.
The Total Project Duration provides a baseline completion estimate.
Make Decisions: Use the insights to allocate resources effectively, identify potential bottlenecks early, and communicate realistic timelines to stakeholders.
Reset: If you need to start over or clear the current project analysis, click the "Reset" button.
Copy Results: Use the "Copy Results" button to easily transfer the key findings to reports or other documents.
Key Factors That Affect Trace Calculator Results
While the trace calculator provides a structured analysis, several real-world factors can influence the accuracy and interpretation of its results:
Accuracy of Duration Estimates: The most significant factor. Overly optimistic or pessimistic duration estimates will skew the entire project timeline, critical path, and float calculations. This requires experienced judgment and historical data.
Completeness of Dependencies: Missing or incorrect dependencies can fundamentally alter the project network. If Task X truly depends on Task Y but isn't listed, the calculator won't reflect the real sequence, potentially misidentifying the critical path.
Resource Availability: The calculator assumes resources are available when needed for each task. Shortages of skilled labor, equipment, or materials can cause delays not reflected in the initial calculation, impacting float and potentially shifting the critical path.
Task Parallelism vs. Sequential Execution: While the calculator handles dependencies, the *degree* to which tasks can be performed in parallel versus strictly sequentially impacts efficiency. Overlapping tasks where possible can shorten the overall duration.
Scope Creep: Uncontrolled changes or additions to the project scope (new features, changed requirements) will necessitate adding new tasks or extending existing ones, invalidating the original trace analysis. A robust change management process is essential.
External Factors & Risks: Weather delays (construction), supplier lead times, regulatory approvals, or unforeseen technical issues are external risks. While not directly input, they can cause delays on critical path tasks, reducing float to zero and impacting the schedule. Risk management planning is key.
Communication & Coordination: Poor communication between teams or individuals responsible for dependent tasks can lead to delays, even if dependencies are correctly mapped. Handoffs need to be smooth.
Quality Control & Rework: If a task fails quality checks, rework is required, extending its duration. This adds unplanned time, potentially impacting float and the critical path. Building in time for quality assurance is crucial.
Frequently Asked Questions (FAQ)
What is the difference between Float and Slack?
There is no difference. Float and Slack are synonymous terms in project management, referring to the amount of time a task can be delayed without delaying the project's final completion date.
Can a project have multiple critical paths?
Yes, a project can have multiple critical paths if there are several sequences of tasks that result in the same longest total duration.
What happens if a non-critical task is delayed?
If a non-critical task is delayed by an amount less than or equal to its float, the project's overall completion date will not be affected. However, if it's delayed beyond its float, it can become a critical task and delay the project.
How accurate are the results?
The accuracy of the trace calculator's results is entirely dependent on the accuracy of the input data, specifically the task durations and dependencies. It's a planning tool based on estimates.
Can I use this for very large projects?
For extremely large projects with thousands of tasks, specialized project management software (like Microsoft Project or Primavera) might offer more robust features and better performance. However, this calculator is excellent for understanding the core principles and managing moderately sized projects.
What if a task duration is uncertain?
If a task duration is uncertain, consider using techniques like PERT (Program Evaluation and Review Technique) which uses three-point estimates (optimistic, most likely, pessimistic) to calculate an expected duration. You could run the calculator multiple times with different duration scenarios (best-case, worst-case) to understand the range of possible project completion dates.
Does the calculator account for holidays or weekends?
This basic calculator assumes durations are in 'working days' and does not automatically factor in specific holidays or weekends. You need to ensure your duration estimates reflect this, or adjust the final dates manually based on a calendar.
How can I improve my project's critical path?
You can shorten the critical path by: 1) Reducing the duration of critical tasks (e.g., by adding resources, using more efficient methods). 2) Performing critical tasks in parallel if dependencies allow (crashing the schedule). 3) Re-evaluating dependencies to see if any can be altered.
var tasks = [];
var taskMap = {}; // To quickly look up task objects by name
function validateInput(id, errorId, min, max, allowEmpty) {
var input = document.getElementById(id);
var errorSpan = document.getElementById(errorId);
var value = input.value.trim();
errorSpan.textContent = "; // Clear previous error
if (value === " && !allowEmpty) {
errorSpan.textContent = 'This field cannot be empty.';
return false;
}
if (value !== " && isNaN(value)) {
errorSpan.textContent = 'Please enter a valid number.';
return false;
}
if (value !== " && !isNaN(value)) {
var numValue = parseFloat(value);
if (min !== undefined && numValue max) {
errorSpan.textContent = 'Value cannot exceed ' + max + '.';
return false;
}
}
return true;
}
function addTask() {
var taskName = document.getElementById('taskName').value.trim();
var durationStr = document.getElementById('duration').value.trim();
var dependenciesStr = document.getElementById('dependencies').value.trim();
var isValid = true;
isValid = validateInput('taskName', 'taskNameError', 0, undefined, false) && isValid;
isValid = validateInput('duration', 'durationError', 1, undefined, false) && isValid; // Duration must be at least 1 day
if (!isValid) {
return;
}
var duration = parseInt(durationStr, 10);
var dependencies = dependenciesStr === " ? [] : dependenciesStr.split(',').map(function(dep) { return dep.trim(); });
// Check if task name already exists
if (taskMap[taskName]) {
document.getElementById('taskNameError').textContent = 'Task name already exists.';
return;
}
// Validate dependencies exist
for (var i = 0; i < dependencies.length; i++) {
if (dependencies[i] !== '' && !taskMap[dependencies[i]]) {
document.getElementById('dependenciesError').textContent = 'Dependency "' + dependencies[i] + '" not found.';
return;
}
}
var newTask = {
name: taskName,
duration: duration,
dependencies: dependencies,
es: 0, ef: 0, ls: 0, lf: 0, float: 0, critical: false
};
tasks.push(newTask);
taskMap[taskName] = newTask; // Add to map for quick lookup
// Clear input fields for next entry
document.getElementById('taskName').value = 'Task ' + (tasks.length + 1);
document.getElementById('duration').value = '5';
document.getElementById('dependencies').value = '';
document.getElementById('taskNameError').textContent = '';
document.getElementById('durationError').textContent = '';
document.getElementById('dependenciesError').textContent = '';
calculateProjectTrace();
updateTable();
updateChart();
}
function calculateProjectTrace() {
if (tasks.length === 0) {
document.getElementById('totalDuration').textContent = '0';
document.getElementById('criticalPathTasks').textContent = 'None';
document.getElementById('numberOfTasks').textContent = '0';
return;
}
// Reset calculations for all tasks
for (var i = 0; i 0) {
var currentTask = queue.shift();
if (processedTasks.has(currentTask.name)) continue;
// Calculate ES based on predecessors' EF
var maxPredEF = 0;
for (var i = 0; i < currentTask.dependencies.length; i++) {
var predTaskName = currentTask.dependencies[i];
if (taskMap[predTaskName]) {
maxPredEF = Math.max(maxPredEF, taskMap[predTaskName].ef);
}
}
currentTask.es = maxPredEF;
currentTask.ef = currentTask.es + currentTask.duration;
processedTasks.add(currentTask.name);
// Find tasks that depend on the current task
for (var i = 0; i < tasks.length; i++) {
var task = tasks[i];
if (task.dependencies.includes(currentTask.name)) {
// Check if all dependencies of 'task' are processed before adding to queue
var allDepsProcessed = true;
for(var j=0; j<task.dependencies.length; j++) {
if (!processedTasks.has(task.dependencies[j])) {
allDepsProcessed = false;
break;
}
}
if (allDepsProcessed && !processedTasks.has(task.name)) {
queue.push(task);
}
}
}
}
// Check for circular dependencies or unprocessed tasks
if (processedTasks.size !== tasks.length) {
console.error("Circular dependency detected or tasks not reachable.");
// Handle error appropriately, maybe clear results or show a message
document.getElementById('totalDuration').textContent = 'Error';
document.getElementById('criticalPathTasks').textContent = 'Error';
return;
}
// Determine overall project duration
projectDuration = 0;
for (var i = 0; i < tasks.length; i++) {
projectDuration = Math.max(projectDuration, tasks[i].ef);
}
document.getElementById('totalDuration').textContent = projectDuration;
// — Backward Pass —
var finalTasks = tasks.filter(function(task) {
var isFinal = true;
for (var i = 0; i < tasks.length; i++) {
if (tasks[i].dependencies.includes(task.name)) {
isFinal = false;
break;
}
}
return isFinal;
});
for (var i = 0; i 0) {
var currentTask = backwardQueue.shift();
if (backwardProcessed.has(currentTask.name)) continue;
backwardProcessed.add(currentTask.name);
// Find tasks that are predecessors to the current task
for (var i = 0; i < tasks.length; i++) {
var potentialPred = tasks[i];
if (potentialPred.dependencies.includes(currentTask.name)) {
potentialPred.lf = Math.min(potentialPred.lf === Infinity ? projectDuration : potentialPred.lf, currentTask.ls);
potentialPred.ls = potentialPred.lf – potentialPred.duration;
backwardQueue.push(potentialPred); // Add predecessor to queue for further backward calculation
}
}
}
// — Calculate Float and Identify Critical Path —
var criticalPath = [];
for (var i = 0; i < tasks.length; i++) {
tasks[i].float = tasks[i].lf – tasks[i].ef;
if (tasks[i].float === 0) {
tasks[i].critical = true;
criticalPath.push(tasks[i].name);
}
}
document.getElementById('criticalPathTasks').textContent = criticalPath.join(', ');
document.getElementById('numberOfTasks').textContent = tasks.length;
}
function updateTable() {
var tableBody = document.getElementById('taskTableBody');
tableBody.innerHTML = ''; // Clear existing rows
if (tasks.length === 0) {
var row = tableBody.insertRow();
var cell = row.insertCell(0);
cell.colSpan = 9;
cell.textContent = 'No tasks added yet.';
return;
}
tasks.sort(function(a, b) { // Sort for better readability, e.g., by ES
return a.es – b.es;
});
for (var i = 0; i < tasks.length; i++) {
var task = tasks[i];
var row = tableBody.insertRow();
var cellName = row.insertCell(0);
cellName.textContent = task.name;
var cellDuration = row.insertCell(1);
cellDuration.textContent = task.duration;
var cellDependencies = row.insertCell(2);
cellDependencies.textContent = task.dependencies.join(', ');
var cellES = row.insertCell(3);
cellES.textContent = task.es;
var cellEF = row.insertCell(4);
cellEF.textContent = task.ef;
var cellLS = row.insertCell(5);
cellLS.textContent = task.ls === Infinity ? '-' : task.ls; // Handle initial Infinity value
var cellLF = row.insertCell(6);
cellLF.textContent = task.lf === Infinity ? '-' : task.lf; // Handle initial Infinity value
var cellFloat = row.insertCell(7);
cellFloat.textContent = task.float;
cellFloat.style.color = task.critical ? '#dc3545' : '#28a745'; // Red for critical, Green for float
var cellCritical = row.insertCell(8);
cellCritical.textContent = task.critical ? 'Yes' : 'No';
cellCritical.style.fontWeight = 'bold';
cellCritical.style.color = task.critical ? '#dc3545' : '#28a745';
}
}
function updateChart() {
var ctx = document.getElementById('projectChart').getContext('2d');
// Destroy previous chart instance if it exists
if (window.projectChartInstance) {
window.projectChartInstance.destroy();
}
var taskNames = tasks.map(function(task) { return task.name; });
var durations = tasks.map(function(task) { return task.duration; });
var earlyStarts = tasks.map(function(task) { return task.es; });
var lateFinishes = tasks.map(function(task) { return task.lf; }); // Use LF for the upper bound of the bar
// Determine max EF for chart scaling
var maxEF = 0;
tasks.forEach(function(task) {
maxEF = Math.max(maxEF, task.ef);
});
// Prepare data for chart
var chartData = {
labels: taskNames,
datasets: [
{
label: 'Early Start (ES)',
data: earlyStarts,
backgroundColor: 'rgba(0, 74, 153, 0.5)', // Primary color, semi-transparent
borderColor: 'rgba(0, 74, 153, 1)',
borderWidth: 1,
order: 2 // Render ES markers below bars
},
{
label: 'Task Duration',
data: durations,
backgroundColor: 'rgba(40, 167, 69, 0.7)', // Success color, slightly transparent
borderColor: 'rgba(40, 167, 69, 1)',
borderWidth: 1,
order: 1 // Render bars on top
},
{
label: 'Late Finish (LF)',
data: lateFinishes,
backgroundColor: 'rgba(220, 53, 69, 0.3)', // Danger color, very transparent
borderColor: 'rgba(220, 53, 69, 0.7)',
borderWidth: 1,
order: 3 // Render LF markers below bars
}
]
};
// Create the chart
window.projectChartInstance = new Chart(ctx, {
type: 'bar', // Using bar chart to simulate Gantt
data: chartData,
options: {
responsive: true,
maintainAspectRatio: false,
scales: {
x: {
stacked: false, // Keep X axis tasks separate
title: {
display: true,
text: 'Tasks'
}
},
y: {
stacked: false, // Keep Y axis values separate
beginAtZero: true,
max: maxEF + 5, // Add some padding to the top
title: {
display: true,
text: 'Time (Working Days)'
}
}
},
plugins: {
tooltip: {
callbacks: {
label: function(context) {
var label = context.dataset.label || '';
if (label) {
label += ': ';
}
if (context.parsed.y !== undefined) {
label += context.parsed.y;
}
// Add specific info for duration bars
if (context.dataset.label === 'Task Duration') {
var taskIndex = context.dataIndex;
var task = tasks[taskIndex];
label += ' (ES: ' + task.es + ', EF: ' + task.ef + ', Float: ' + task.float + ')';
}
return label;
}
}
},
legend: {
position: 'top',
}
},
// Custom drawing to simulate Gantt bars
// This requires more complex chart configuration or a different chart type.
// For simplicity, we'll use bars and rely on tooltips for details.
// A true Gantt chart often uses stacked bars or custom drawing.
// Here, we'll use the 'Task Duration' dataset as the primary bar.
// ES and LF will be represented by points or lines if possible, or just tooltips.
// Let's adjust the chart type or options for better Gantt feel.
// A common approach is using stacked bars where the first segment is ES,
// the second is Duration, and the third is remaining float.
// However, the current setup with separate datasets and tooltips is simpler.
// Let's refine the bar chart to better represent Gantt.
// We can use the 'Task Duration' dataset as the main bar.
// ES can be represented by a point at the start of the bar.
// LF can be represented by a point at the end of the bar.
// This requires custom plugins or more advanced configuration.
// For this example, we'll stick to the simpler representation and rely on tooltips.
}
});
}
function resetCalculator() {
tasks = [];
taskMap = {};
document.getElementById('taskName').value = 'Task 1';
document.getElementById('duration').value = '5';
document.getElementById('dependencies').value = '';
document.getElementById('taskNameError').textContent = '';
document.getElementById('durationError').textContent = '';
document.getElementById('dependenciesError').textContent = '';
calculateProjectTrace();
updateTable();
updateChart();
}
function copyResults() {
var totalDuration = document.getElementById('totalDuration').textContent;
var criticalPathTasks = document.getElementById('criticalPathTasks').textContent;
var numberOfTasks = document.getElementById('numberOfTasks').textContent;
var tableHtml = document.getElementById('taskTableBody').innerHTML;
var tableHeaders = "
Task Name
Duration (Days)
Dependencies
Early Start
Early Finish
Late Start
Late Finish
Float (Slack)
Critical Path
";
var fullTable = "
" + tableHeaders + "" + tableHtml + "
";
var chartImageUrl = document.getElementById('projectChart').toDataURL(); // Get chart as image data URL
var assumptions = "Key Assumptions:\n";
tasks.forEach(function(task) {
assumptions += `- Task: ${task.name}, Duration: ${task.duration} days, Dependencies: ${task.dependencies.join(', ')}\n`;
});
var resultsText = `— Trace Calculator Results —\n\n`;
resultsText += `Primary Results:\n`;
resultsText += `Total Project Duration: ${totalDuration} days\n`;
resultsText += `Critical Path Tasks: ${criticalPathTasks}\n`;
resultsText += `Total Number of Tasks: ${numberOfTasks}\n\n`;
resultsText += `Key Assumptions:\n${assumptions}\n`;
resultsText += `\nTask Details:\n${fullTable}\n`;
resultsText += `\nChart: (Image data URL below – may not paste well in plain text)\n${chartImageUrl}`;
// Use navigator.clipboard for modern browsers
if (navigator.clipboard && navigator.clipboard.writeText) {
navigator.clipboard.writeText(resultsText).then(function() {
alert('Results copied to clipboard!');
}).catch(function(err) {
console.error('Failed to copy text: ', err);
fallbackCopyTextToClipboard(resultsText); // Fallback for older browsers
});
} else {
fallbackCopyTextToClipboard(resultsText); // Fallback for older browsers
}
}
// Fallback function for older browsers
function fallbackCopyTextToClipboard(text) {
var textArea = document.createElement("textarea");
textArea.value = text;
textArea.style.position = "fixed"; // Avoid scrolling to bottom
textArea.style.left = "-9999px";
textArea.style.top = "-9999px";
document.body.appendChild(textArea);
textArea.focus();
textArea.select();
try {
var successful = document.execCommand('copy');
var msg = successful ? 'successful' : 'unsuccessful';
console.log('Fallback: Copying text command was ' + msg);
alert('Results copied to clipboard!');
} catch (err) {
console.error('Fallback: Oops, unable to copy', err);
alert('Failed to copy results. Please copy manually.');
}
document.body.removeChild(textArea);
}
function toggleFaq(element) {
var faqItem = element.closest('.faq-item');
faqItem.classList.toggle('open');
var answer = faqItem.querySelector('.answer');
if (faqItem.classList.contains('open')) {
answer.style.display = 'block';
} else {
answer.style.display = 'none';
}
}
// Initial calculation and rendering on page load
document.addEventListener('DOMContentLoaded', function() {
// Add a default task to start with
addTask();
// Remove the default task added by addTask() if we want a truly blank slate initially
// Or keep it as a starting point. Let's keep it for now.
// If you want it blank, uncomment the next two lines:
// tasks = [];
// taskMap = {};
// calculateProjectTrace();
// updateTable();
// updateChart();
});