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Posted on : June 13, 2025 By Tech World Times Development and Testing  Rate this post Sorting helps organize data in a specific order. It is used in search, reports, and efficient storage. Different sorting algorithms offer different performance. In this article, we will explain the Time Complexity of Sorting Algorithms in simple words. We will cover Python, Java, and C++ examples. 1. What Is Time Complexity? Time complexity tells how fast an algorithm runs. It measures the number of steps as input grows. It is written in Big-O notation. For example, O(n²) means steps grow with the square of inputs. 2. Types of Time Complexity Here are common types: O(1): Constant time O(n): Linear time O(n log n): Log-linear time O(n²): Quadratic time We will now apply these to sorting. 3. Bubble Sort Bubble Sort compares two numbers and swaps them if needed. It repeats until the list is sorted. Time Complexity: Best Case: O(n) (if already sorted) Average Case: O(n²) Worst Case: O(n²) Python Example: pythonCopyEditdef bubble_sort(arr): n = len(arr) for i in range(n): for j in range(n - i - 1): if arr[j] > arr[j+1]: arr[j], arr[j+1] = arr[j+1], arr[j] Java Example: javaCopyEditvoid bubbleSort(int arr[]) { int n = arr.length; for (int i = 0; i < n-1; i++) for (int j = 0; j < n-i-1; j++) if (arr[j] > arr[j+1]) { int temp = arr[j]; arr[j] = arr[j+1]; arr[j+1] = temp; } } C++ Example: cppCopyEditvoid bubbleSort(int arr[], int n) { for (int i = 0; i < n-1; i++) for (int j = 0; j < n-i-1; j++) if (arr[j] > arr[j+1]) swap(arr[j], arr[j+1]); } 4. Selection Sort This sort picks the smallest number and places it at the front. Time Complexity: Best Case: O(n²) Average Case: O(n²) Worst Case: O(n²) Python Example: pythonCopyEditdef selection_sort(arr): for i in range(len(arr)): min_idx = i for j in range(i+1, len(arr)): if arr[j] < arr[min_idx]: min_idx = j arr[i], arr[min_idx] = arr[min_idx], arr[i] 5. Insertion Sort This algorithm builds the final list one item at a time. Time Complexity: Best Case: O(n) Average Case: O(n²) Worst Case: O(n²) Java Example: javaCopyEditvoid insertionSort(int arr[]) { for (int i = 1; i < arr.length; i++) { int key = arr[i]; int j = i - 1; while (j >= 0 && arr[j] > key) { arr[j + 1] = arr[j]; j = j - 1; } arr[j + 1] = key; } } 6. Merge Sort Merge Sort splits the array into halves and merges them back in order. Time Complexity of Sorting Algorithms like Merge Sort is usually better. Best Case: O(n log n) Average Case: O(n log n) Worst Case: O(n log n) Python Example: pythonCopyEditdef merge_sort(arr): if len(arr) > 1: mid = len(arr) // 2 left = arr[:mid] right = arr[mid:] merge_sort(left) merge_sort(right) i = j = k = 0 while i < len(left) and j < len(right): if left[i] < right[j]: arr[k] = left[i] i += 1 else: arr[k] = right[j] j += 1 k += 1 arr[k:] = left[i:] + right[j:] 7. Quick Sort Quick Sort picks a pivot and places smaller numbers before it. Time Complexity: Best Case: O(n log n) Average Case: O(n log n) Worst Case: O(n²) C++ Example: cppCopyEditint partition(int arr[], int low, int high) { int pivot = arr[high]; int i = low - 1; for (int j = low; j < high; j++) { if (arr[j] < pivot) { i++; swap(arr[i], arr[j]); } } swap(arr[i+1], arr[high]); return i + 1; } void quickSort(int arr[], int low, int high) { if (low < high) { int pi = partition(arr, low, high); quickSort(arr, low, pi - 1); quickSort(arr, pi + 1, high); } } 8. Built-in Sort Methods Languages have built-in sort functions. These are well-optimized. Python: sorted() or list.sort() uses TimSort Time Complexity: O(n log n) Java: Arrays.sort() uses Dual-Pivot QuickSort Time Complexity: O(n log n) C++: std::sort() uses IntroSort Time Complexity: O(n log n) These are better for most real-world tasks. 9. Time Complexity Comparison Table AlgorithmBestAverageWorstStableBubble SortO(n)O(n²)O(n²)YesSelection SortO(n²)O(n²)O(n²)NoInsertion SortO(n)O(n²)O(n²)YesMerge SortO(n log n)O(n log n)O(n log n)YesQuick SortO(n log n)O(n log n)O(n²)NoTimSort (Python)O(n)O(n log n)O(n log n)YesIntroSort (C++)O(n log n)O(n log n)O(n log n)No 10. How to Choose the Right Algorithm? Use Merge Sort for large stable data. Use Quick Sort for faster average speed. Use Insertion Sort for small or nearly sorted lists. Use built-in sort functions unless you need control. Conclusion The Time Complexity of Sorting Algorithms helps us pick the right tool. Bubble, Selection, and Insertion Sort are simple but slow. Merge and Quick Sort are faster and used often. Built-in functions are highly optimized. Python, Java, and C++ each have their strengths. Understand your problem and input size. Then pick the sorting method. This ensures better speed and performance in your code. Tech World TimesTech World Times (TWT), a global collective focusing on the latest tech news and trends in blockchain, Fintech, Development & Testing, AI and Startups. If you are looking for the guest post then contact at techworldtimes@gmail.com

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Enterprise artificial intelligence investment is unprecedented, with IDC projecting global spending on AI and GenAI to double to $631 billion by 2028. Yet beneath the impressive budget allocations and boardroom enthusiasm lies a troubling reality: most organisations struggle to translate their AI ambitions into operational success.The sobering statistics behind AI’s promiseModelOp’s 2025 AI Governance Benchmark Report, based on input from 100 senior AI and data leaders at Fortune 500 enterprises, reveals a disconnect between aspiration and execution.While more than 80% of enterprises have 51 or more generative AI projects in proposal phases, only 18% have successfully deployed more than 20 models into production.The execution gap represents one of the most significant challenges facing enterprise AI today. Most generative AI projects still require 6 to 18 months to go live – if they reach production at all.The result is delayed returns on investment, frustrated stakeholders, and diminished confidence in AI initiatives in the enterprise.The cause: Structural, not technical barriersThe biggest obstacles preventing AI scalability aren’t technical limitations – they’re structural inefficiencies plaguing enterprise operations. The ModelOp benchmark report identifies several problems that create what experts call a “time-to-market quagmire.”Fragmented systems plague implementation. 58% of organisations cite fragmented systems as the top obstacle to adopting governance platforms. Fragmentation creates silos where different departments use incompatible tools and processes, making it nearly impossible to maintain consistent oversight in AI initiatives.Manual processes dominate despite digital transformation. 55% of enterprises still rely on manual processes – including spreadsheets and email – to manage AI use case intake. The reliance on antiquated methods creates bottlenecks, increases the likelihood of errors, and makes it difficult to scale AI operations.Lack of standardisation hampers progress. Only 23% of organisations implement standardised intake, development, and model management processes. Without these elements, each AI project becomes a unique challenge requiring custom solutions and extensive coordination by multiple teams.Enterprise-level oversight remains rare Just 14% of companies perform AI assurance at the enterprise level, increasing the risk of duplicated efforts and inconsistent oversight. The lack of centralised governance means organisations often discover they’re solving the same problems multiple times in different departments.The governance revolution: From obstacle to acceleratorA change is taking place in how enterprises view AI governance. Rather than seeing it as a compliance burden that slows innovation, forward-thinking organisations recognise governance as an important enabler of scale and speed.Leadership alignment signals strategic shift. The ModelOp benchmark data reveals a change in organisational structure: 46% of companies now assign accountability for AI governance to a Chief Innovation Officer – more than four times the number who place accountability under Legal or Compliance. This strategic repositioning reflects a new understanding that governance isn’t solely about risk management, but can enable innovation.Investment follows strategic priority. A financial commitment to AI governance underscores its importance. According to the report, 36% of enterprises have budgeted at least $1 million annually for AI governance software, while 54% have allocated resources specifically for AI Portfolio Intelligence to track value and ROI.What high-performing organisations do differentlyThe enterprises that successfully bridge the ‘execution gap’ share several characteristics in their approach to AI implementation:Standardised processes from day one. Leading organisations implement standardised intake, development, and model review processes in AI initiatives. Consistency eliminates the need to reinvent workflows for each project and ensures that all stakeholders understand their responsibilities.Centralised documentation and inventory. Rather than allowing AI assets to proliferate in disconnected systems, successful enterprises maintain centralised inventories that provide visibility into every model’s status, performance, and compliance posture.Automated governance checkpoints. High-performing organisations embed automated governance checkpoints throughout the AI lifecycle, helping ensure compliance requirements and risk assessments are addressed systematically rather than as afterthoughts.End-to-end traceability. Leading enterprises maintain complete traceability of their AI models, including data sources, training methods, validation results, and performance metrics.Measurable impact of structured governanceThe benefits of implementing comprehensive AI governance extend beyond compliance. Organisations that adopt lifecycle automation platforms reportedly see dramatic improvements in operational efficiency and business outcomes.A financial services firm profiled in the ModelOp report experienced a halving of time to production and an 80% reduction in issue resolution time after implementing automated governance processes. Such improvements translate directly into faster time-to-value and increased confidence among business stakeholders.Enterprises with robust governance frameworks report the ability to many times more models simultaneously while maintaining oversight and control. This scalability lets organisations pursue AI initiatives in multiple business units without overwhelming their operational capabilities.The path forward: From stuck to scaledThe message from industry leaders that the gap between AI ambition and execution is solvable, but it requires a shift in approach. Rather than treating governance as a necessary evil, enterprises should realise it enables AI innovation at scale.Immediate action items for AI leadersOrganisations looking to escape the ‘time-to-market quagmire’ should prioritise the following:Audit current state: Conduct an assessment of existing AI initiatives, identifying fragmented processes and manual bottlenecksStandardise workflows: Implement consistent processes for AI use case intake, development, and deployment in all business unitsInvest in integration: Deploy platforms to unify disparate tools and systems under a single governance frameworkEstablish enterprise oversight: Create centralised visibility into all AI initiatives with real-time monitoring and reporting abilitiesThe competitive advantage of getting it rightOrganisations that can solve the execution challenge will be able to bring AI solutions to market faster, scale more efficiently, and maintain the trust of stakeholders and regulators.Enterprises that continue with fragmented processes and manual workflows will find themselves disadvantaged compared to their more organised competitors. Operational excellence isn’t about efficiency but survival.The data shows enterprise AI investment will continue to grow. Therefore, the question isn’t whether organisations will invest in AI, but whether they’ll develop the operational abilities necessary to realise return on investment. The opportunity to lead in the AI-driven economy has never been greater for those willing to embrace governance as an enabler not an obstacle.(Image source: Unsplash)

A coiled giant anaconda. They are the largest snake species in Brazil and play a major role in legends including the ‘Boiuna’ and the ‘Cobra Grande.’ CREDIT: Beatriz Cosendey. Get the Popular Science daily newsletter💡 Breakthroughs, discoveries, and DIY tips sent every weekday. South America’s lush Amazon region is a biodiversity hotspot, which means that every living thing must find a way to co-exist. Even some of the most feared snakes on the planet–anacondas. In a paper published June 16 in the journal Frontiers in Amphibian and Reptile Science, conservation biologists Beatriz Cosendey and Juarez Carlos Brito Pezzuti from the Federal University of Pará’s Center for Amazonian Studies in Brazil, analyze the key points behind the interactions between humans and the local anaconda populations. Ahead of the paper’s publication, the team at Frontiers conducted this wide-ranging Q&A with Conesday. It has not been altered. Frontiers: What inspired you to become a researcher? Beatriz Cosendey: As a child, I was fascinated by reports and documentaries about field research and often wondered what it took to be there and what kind of knowledge was being produced. Later, as an ecologist, I felt the need for approaches that better connected scientific research with real-world contexts. I became especially interested in perspectives that viewed humans not as separate from nature, but as part of ecological systems. This led me to explore integrative methods that incorporate local and traditional knowledge, aiming to make research more relevant and accessible to the communities involved. F: Can you tell us about the research you’re currently working on? BC: My research focuses on ethnobiology, an interdisciplinary field intersecting ecology, conservation, and traditional knowledge. We investigate not only the biodiversity of an area but also the relationship local communities have with surrounding species, providing a better understanding of local dynamics and areas needing special attention for conservation. After all, no one knows a place better than those who have lived there for generations. This deep familiarity allows for early detection of changes or environmental shifts. Additionally, developing a collaborative project with residents generates greater engagement, as they recognize themselves as active contributors; and collective participation is essential for effective conservation. Local boating the Amazon River. CREDIT: Beatriz Cosendey. F: Could you tell us about one of the legends surrounding anacondas? BC: One of the greatest myths is about the Great Snake—a huge snake that is said to inhabit the Amazon River and sleep beneath the town. According to the dwellers, the Great Snake is an anaconda that has grown too large; its movements can shake the river’s waters, and its eyes look like fire in the darkness of night. People say anacondas can grow so big that they can swallow large animals—including humans or cattle—without difficulty. F: What could be the reasons why the traditional role of anacondas as a spiritual and mythological entity has changed? Do you think the fact that fewer anacondas have been seen in recent years contributes to their diminished importance as an mythological entity? BC: Not exactly. I believe the two are related, but not in a direct way. The mythology still exists, but among Aritapera dwellers, there’s a more practical, everyday concern—mainly the fear of losing their chickens. As a result, anacondas have come to be seen as stealthy thieves. These traits are mostly associated with smaller individuals (up to around 2–2.5 meters), while the larger ones—which may still carry the symbolic weight of the ‘Great Snake’—tend to retreat to more sheltered areas; because of the presence of houses, motorized boats, and general noise, they are now seen much less frequently. A giant anaconda is being measured. Credit: Pedro Calazans. F: Can you share some of the quotes you’ve collected in interviews that show the attitude of community members towards anacondas? How do chickens come into play? BC: When talking about anacondas, one thing always comes up: chickens. “Chicken is her [the anaconda’s] favorite dish. If one clucks, she comes,” said one dweller. This kind of remark helps explain why the conflict is often framed in economic terms. During the interviews and conversations with local dwellers, many emphasized the financial impact of losing their animals: “The biggest loss is that they keep taking chicks and chickens…” or “You raise the chicken—you can’t just let it be eaten for free, right?” For them, it’s a loss of investment, especially since corn, which is used as chicken feed, is expensive. As one person put it: “We spend time feeding and raising the birds, and then the snake comes and takes them.” One dweller shared that, in an attempt to prevent another loss, he killed the anaconda and removed the last chicken it had swallowed from its belly—”it was still fresh,” he said—and used it for his meal, cooking the chicken for lunch so it wouldn’t go to waste. One of the Amazonas communities where the researchers conducted their research. CREDIT: Beatriz Cosendey. Some interviewees reported that they had to rebuild their chicken coops and pigsties because too many anacondas were getting in. Participants would point out where the anaconda had entered and explained that they came in through gaps or cracks but couldn’t get out afterwards because they ‘tufavam’ — a local term referring to the snake’s body swelling after ingesting prey. We saw chicken coops made with mesh, with nylon, some that worked and some that didn’t. Guided by the locals’ insights, we concluded that the best solution to compensate for the gaps between the wooden slats is to line the coop with a fine nylon mesh (to block smaller animals), and on the outside, a layer of wire mesh, which protects the inner mesh and prevents the entry of larger animals. F: Are there any common misconceptions about this area of research? How would you address them? BC: Yes, very much. Although ethnobiology is an old science, it’s still underexplored and often misunderstood. In some fields, there are ongoing debates about the robustness and scientific validity of the field and related areas. This is largely because the findings don’t always rely only on hard statistical data. However, like any other scientific field, it follows standardized methodologies, and no result is accepted without proper grounding. What happens is that ethnobiology leans more toward the human sciences, placing human beings and traditional knowledge as key variables within its framework. To address these misconceptions, I believe it’s important to emphasize that ethnobiology produces solid and relevant knowledge—especially in the context of conservation and sustainable development. It offers insights that purely biological approaches might overlook and helps build bridges between science and society. The study focused on the várzea regions of the Lower Amazon River. CREDIT: Beatriz Cosendey. F: What are some of the areas of research you’d like to see tackled in the years ahead? BC: I’d like to see more conservation projects that include local communities as active participants rather than as passive observers. Incorporating their voices, perspectives, and needs not only makes initiatives more effective, but also more just. There is also great potential in recognizing and valuing traditional knowledge. Beyond its cultural significance, certain practices—such as the use of natural compounds—could become practical assets for other vulnerable regions. Once properly documented and understood, many of these approaches offer adaptable forms of environmental management and could help inform broader conservation strategies elsewhere. F: How has open science benefited the reach and impact of your research? BC: Open science is crucial for making research more accessible. By eliminating access barriers, it facilitates a broader exchange of knowledge—important especially for interdisciplinary research like mine which draws on multiple knowledge systems and gains value when shared widely. For scientific work, it ensures that knowledge reaches a wider audience, including practitioners and policymakers. This openness fosters dialogue across different sectors, making research more inclusive and encouraging greater collaboration among diverse groups. The Q&A can also be read here.