Leçons — Collège

A bright university whiteboard in a sunlit classroom displays a clean Venn diagram of nested complexity classes: a small blue circle labeled "P" sits inside a larger green circle labeled "NP," containing an orange ring labeled "NP-complete," all enclosed within a yellow rectangle labeled "PSPACE." A friendly professor points enthusiastically at the diagram while students at desks sketch notes, surrounded by warm natural light and colorful textbooks.

A bright, sunlit design studio with white walls and large windows. A cheerful designer sits at a clean desk with an open laptop displaying a friendly app interface. Colorful sticky notes arranged around a central user silhouette form a clean diagram labeled "USER NEEDS," "USABILITY," and "AFFORDANCE." A coffee mug, pencil sketches of interface wireframes, and a small plant complete the warm, organized workspace.

A bright, sunlit whiteboard in a clean university classroom displays a colorful weighted graph with labeled vertices (A–F) connected by edges marked with small numbers (1–9). Two side-by-side diagrams show Kruskal's algorithm sorting edges by weight in ascending order, and Prim's algorithm growing a highlighted green minimum spanning tree outward from vertex A, with bold red edges forming the MST and the label "O(E log E)" written neatly below.

A bright university seminar room with large windows letting in sunlight. A diverse group of students gathered around a glowing whiteboard displaying a balanced scale icon, with illustrated figures representing different people on each side. Colorful sticky notes label concepts: "Bias," "Privacy," "Accountability," "Fairness." A laptop shows a flowchart with checkpoints marked by green and red flags, symbolizing ethical decision nodes in algorithm design.

Bright university study room with large windows flooding natural daylight across a clean whiteboard. A focused student points to three labeled columns: "Linear Search O(n)" showing a row of numbered boxes searched one-by-one with a moving arrow, "Binary Search O(log n)" showing a sorted array with a midpoint bisection diagram, and "Hash Table O(1)" showing a key mapping directly to a highlighted bucket. Color-coded complexity curves arc above each column.

A bright, sunlit computer science classroom with a large whiteboard showing colorful vertical bars being sorted — tall and short pastel-colored columns arranging themselves in ascending order, labeled "Quick Sort" and "Merge Sort" with small "O(n log n)" annotations. A cheerful student points to a binary search diagram on a tablet, while sticky notes display recursive trees and a golden coin trail illustrates a greedy algorithm path across a clean white desk.

A bright, sunlit university study space with a large whiteboard displaying a clean flowchart: oval "START" connecting via arrows through rectangular process boxes labeled "INPUT," "CALCULATE," "OUTPUT," ending at oval "STOP." A cheerful student points to the diagram beside a portrait of Alan Turing. Open textbooks, a laptop showing pseudocode, and fresh coffee sit on a wooden desk. Warm afternoon light streams through tall windows.

Bright university whiteboard scene in a sunlit classroom. A large, cleanly drawn decision tree fills the board — nodes are white circles connected by bold colored branches. Some branches are marked with cheerful red "✗" dead-ends, while a highlighted green path winds successfully to a solution node labeled "✓". A friendly professor points to a backtracked branch. Small labels read "partial solution" and "prune" at key nodes. Warm golden light, clean blue-and-white aesthetic, optimistic and clear.

A bright, sunlit whiteboard in a modern university classroom shows a large colorful array bar splitting into two equal halves, each half splitting again into smaller segments, forming a clean tree diagram downward. A cheerful student points to the three labeled stages: "DIVIDE → SOLVE → COMBINE" in bold colors. Numbered blocks [5,2,8,1] progressively sort and merge back upward with arrows, rendered in coral, teal, and yellow on a crisp white background.

A bright university computer science classroom bathed in warm daylight. A large whiteboard displays three clean curves labeled **O(n²)**, **O(n log n)**, and **O(n)** plotted on a simple graph with axes labeled "Time" and "Input Size n." A focused student points at the curves with a marker, while a laptop nearby shows a running benchmark timer. Color-coded sticky notes reading **Big-O**, **Ω**, **Θ** accent the whiteboard's corners.

A bright, sunlit university study space with a large whiteboard showing a clean diagram: a complex network of colorful nodes connected by paths, with one highlighted route marked "Approx. Solution" and a dotted route labeled "Optimal." A cheerful student points to a bold ratio label "≤ 2× OPT" written nearby. Scattered papers show simple graphs and checkmarks. Warm daylight floods through tall windows, bookshelves visible in the background.

Bright university whiteboard scene in a sunny classroom. A cheerful weighted graph drawn in bold colors shows six labeled vertices (A–F) connected by edges with small weight numbers (1, 3, 4, 2, 5, 6). Highlighted edges in vivid green form the minimum spanning tree, visually distinct from grey unused edges. A small legend labels "MST Total = 15." Two color-coded boxes beside it read "Prim's" and "Kruskal's" with arrow pointers toward the graph.

A bright university lecture hall bathed in warm afternoon sunlight. A large whiteboard displays three clearly labeled columns: "Best," "Average," "Worst" with ascending bar graphs beneath each, with the middle "Average" column highlighted by a glowing yellow circle. A friendly professor points to a probability curve drawn above the bars. Scattered across a wooden desk: dice, probability trees sketched on notepad pages, and a labeled bell curve diagram. Clean, optimistic blue and gold color palette.

Bright whiteboard-style illustration showing a clean weighted graph with six labeled nodes (A through F) connected by edges bearing bold distance numbers. A highlighted golden path traces A→C→E→F as the shortest route, glowing with a warm yellow stroke. A small progress table beside it shows visited nodes and current shortest distances updating step by step. Surrounding icons suggest GPS maps and network diagrams, all set against a crisp light background with cheerful blue and orange accents.

A bright whiteboard-style illustration showing a colorful undirected graph with labeled circular nodes (A–G) connected by clean lines. On the left, a DFS path glows orange, diving deep along one branch with a bold arrow trail. On the right, a BFS path radiates teal in concentric rings from node A. A small stack icon labels DFS; a queue icon labels BFS. Sunny white background, crisp geometry, cheerful academic clarity.

A bright, sunlit study desk viewed from above, showing an open knapsack with a capacity bar labeled "15kg." Beside it, three neatly arranged items — gold coins, gemstones, and spices — each tagged with value-to-weight ratio labels (6, 4, 2). A student's hand scoops the highest-ratio item first, then portions a second item mid-scoop. A sorted arrow labeled "Sort by V/W ↓" points down the lineup, clean and clear on a warm cream background.

Bright university study space with clean white walls and warm afternoon sunlight. A large whiteboard displays a colorful DP table grid with labeled cells showing Fibonacci values: 0,1,1,2,3,5,8,13. Arrows connect overlapping subproblems in teal and orange. A cheerful student points to a highlighted "optimal substructure" label. A small illustrated knapsack sits nearby with numbered weight tags. Neat annotation reads "store → reuse" above the memoization table.

A bright, sunlit computer science classroom whiteboard shows a clean graph diagram with numbered nodes (1–8) connected by bold lines. A cheerful robot character demonstrates BFS by holding an orange queue tray with nodes lined up in order, while colored rings radiate outward level by level from node 1 — yellow, then teal, then coral. Arrows and small "Level 0, 1, 2" labels mark each ring clearly.

A bright university lab with white walls and large sunny windows. A glowing whiteboard displays a clean diagram: a classical bit labeled "0 or 1" beside a quantum sphere (Bloch sphere) labeled "qubit" showing superposition. A cheerful student points to a factor tree breaking down a large number "N = p × q," illustrating Shor's algorithm. Circuit diagrams with labeled quantum gates (H, CNOT) float as colorful sticky notes nearby. Sunlight streams across the clean desk.

Bright university classroom setting with a large whiteboard displaying a clean complexity growth chart. Colorful curves plotted on clearly labeled axes (x = "n", y = "time") show six distinct lines: a flat horizontal line labeled O(1), a gentle curve O(log n), a diagonal O(n), a slightly steeper O(n log n), a pronounced upward curve O(n²), and a dramatically steep O(2^n). Small cartoon gears and arrows emphasize each curve's growth rate in warm daylight.

A bright, sunlit classroom whiteboard displays five colorful vertical bar charts side by side, each labeled with a sorting algorithm name: Bubble Sort, Selection Sort, Insertion Sort, Merge Sort, Quick Sort. Animated arrows show elements swapping between pastel-colored blocks. Complexity labels O(n²) and O(n log n) appear in clean bold text. A friendly professor points enthusiastically at the organized bars, while students take notes at clean desks under warm daylight streaming through tall windows.

A bright, airy university lab with large sunny windows. A confident student stands at a glowing whiteboard divided into three labeled columns: "Supervised," "Unsupervised," and "Reinforcement Learning." Each column shows a clean diagram — labeled data points feeding a decision tree, scattered clusters grouping organically, and a small robot earning star rewards. Color-coded arrows connect data icons to a central "Model" brain graphic, illustrating the full learning pipeline.

A bright university computer lab with large sunny windows. A whiteboard displays a Huffman coding tree with labeled nodes showing letters A, B, C and binary codes "0", "10", "11" branching clearly downward. On a clean desk, a large colorful bar diagram compares original file size versus compressed size, dramatically smaller. Nearby, stacked labeled blocks shrink progressively left to right, illustrating lossless versus lossy compression with cheerful blue, orange, and green color coding.

A bright university whiteboard scene bathed in warm daylight. Three clean overlapping circles form a Venn diagram labeled "P," "NP," and "NP-Hard," with "NP-Complete" marked at their intersection in bold color. A cheerful illustrated professor points to the diagram with a laser pointer. Small labeled puzzle pieces and padlocks represent classic problems like "SAT" and "TSP," scattered across a clean white surface with soft blue and yellow accents.

A bright, sunlit classroom whiteboard displays three clean overlapping circles forming a Venn diagram: a small circle labeled **P** (sky blue, filled with tiny sorted lists and search trees), a larger circle labeled **NP** (sunny yellow, containing puzzle pieces snapping together with a checkmark), and a ring labeled **NP-Complete** (coral orange) at the intersection boundary. A friendly professor gestures toward a bold question mark labeled **"P = NP?"** above the diagram. Clean, optimistic daylight fills the room.

A bright, airy overhead view of an interconnected city scene on a white background, divided into colorful sectors: a glowing search engine results panel with small ranked webpage icons, a financial district with upward-trending stock graphs, and delivery trucks following highlighted optimal route paths through city streets. Clean labeled arrows connect each sector reading "PageRank," "Trading Algorithm," "Route Optimizer" — all rendered in crisp, modern flat illustration style with bold blues, greens, and oranges.

A bright, sunlit university study space where a confident student stands at a large whiteboard. On the board, a colorful path diagram shows a traveler figure choosing the steepest uphill step at each fork, with arrows labeled "local best" converging toward a flag marked "Global Optimum" at the summit. Numbered decision nodes glow in cheerful yellow and teal. Coins of descending size on a clean desk nearby illustrate the classic coin-change greedy example.

A bright, sunlit university computer lab with white walls and large windows. A cheerful desk displays a glowing monitor showing a clean diagram: plaintext "HELLO" transforming through a colorful gear-and-lock icon into ciphertext "KHOOR" (Caesar cipher +3). Nearby, a open textbook shows a simple AES block diagram with labeled arrows. A coffee cup, keyboard, and sticky notes with "public key / private key" labels complete the warm, inviting workspace.

A bright, sunlit university study space with a young woman at a whiteboard drawing a cascading tower of colorful nested boxes, each slightly smaller than the last, labeled **5!**, **4!**, **3!**, **2!**, **1!**, **0!=1** in bold clean markers. Arrows loop downward showing each call, then bounce back upward with results multiplying back. Warm natural light streams through large windows, bookshelves visible behind, cheerful and energetic atmosphere.

Bright university whiteboard scene flooded with daylight. Left side shows a clean 4×4 grid labeled "Adjacency Matrix" with rows and columns marked 0–3; cells contain 0s and 1s in bold teal and coral. Right side shows "Adjacency List" with four labeled nodes (0–3) each pointing to small linked boxes listing neighbors in warm orange. A simple four-node graph with connecting edges sits centered between both representations, visually linking the two methods.

A bright, sunlit university lab with white walls and large windows. A cheerful robot student sits at a clean desk sorting colorful labeled cards (marked "cat," "dog," "apple") into matching bins — illustrating supervised learning. A glowing decision tree diagram on a whiteboard behind shows branching paths with simple yes/no labels. Scattered data points in blue and orange cluster visibly on a nearby graph, clean and optimistic.

A bright, clean network diagram on a white background showing six circular nodes connected by directional arrows, labeled **S** (source, left, green) to **T** (sink, right, blue). Each edge displays capacity and flow values like **3/5**, **2/4**. A bold highlighted augmenting path glows yellow through the network. Small numerical annotations show updated flow values. Crisp, modern flat-design style with cheerful sky-blue, coral, and mint accents.

A bright, sunlit computer lab with a large interactive whiteboard displaying a clean network diagram. A padlock icon sits at the center, with labeled arrows showing TCP, IP, SSL, and TLS flowing between illustrated computers. Color-coded layered boxes represent the TCP/IP model stack. Shields and checkmarks decorate secure connection paths. Cables and nodes glow softly in daylight blue and green tones on a crisp white background.

A bright, sunlit university study space with a large whiteboard showing a clean, colorful graph diagram — labeled nodes marked **V1, V2, V3, V4, V5** connected by bold edges, with arrows indicating directed connections. One highlighted cycle glows in orange, a weighted edge labeled **"W=5"** in blue. Scattered nearby: a coffee cup, open laptop, and small portrait sketch of Euler. Cheerful teal, coral, and yellow color palette throughout.

A bright university computer science classroom with large windows letting in afternoon sunlight. A clean whiteboard displays two labeled diagrams side by side: "Total Space" showing stacked memory blocks labeled Input + Auxiliary, and "Auxiliary Space" showing only the working blocks. A confident student points to the formula **S(n) = O(1) + O(n)** written in blue marker. Color-coded memory towers in yellow and teal illustrate constant versus growing space consumption clearly.

A bright, sunlit computer science classroom with a large whiteboard displaying a clean graph: x-axis labeled "Input Size (n)", y-axis labeled "Time." Two smooth curves arc upward — an upper curve labeled "O(n²)" in blue and a lower curve labeled "Ω(n log n)" in orange, with a shaded region between them. A friendly illustrated robot character stands beside the graph pointing to both curves, surrounded by cheerful geometric shapes and soft warm lighting.

A bright university study space with large windows and afternoon sunlight. A clean whiteboard displays a crisp graph with labeled curves: O(1), O(log n), O(n), O(n²), with the x-axis marked "Input Size" and y-axis "Time." A focused student points to the curves with a marker, comparing their slopes. Color-coded sticky notes highlight each complexity class against a white background.

A bright university whiteboard scene bathed in warm daylight. A cheerful diagram shows a flowchart where a large colorful dice sits at a decision diamond, with arrows branching into multiple colorful paths labeled "Path A," "Path B," "Path C." Surrounding the board: a shuffled deck of cards, coin-flip symbols, and a simple graph showing randomized quicksort performance curve dipping efficiently below a deterministic curve. Clean, optimistic, academic energy.

A bright, sunlit whiteboard-style illustration split into two halves. On the left, a cheerful maze diagram shows a small explorer figure navigating branching paths — some marked with red "✗" dead ends and arrows looping back, others with green checkmarks, illustrating backtracking. On the right, a large colorful problem-block divides recursively into smaller equal sub-blocks like a clean tree diagram, labeled "Divide & Conquer." Both sides share warm yellows, blues, and greens on a crisp white background.

A bright, sunlit university computer lab with white walls and large windows. A cheerful student sits at a clean desk with an open laptop showing a glowing function tree diagram. Beside the laptop, a colorful physical "memo board" displays sticky notes labeled with input-output pairs like "f(5)=120", with bold arrows showing cached results being reused. A second identical branch of the tree is crossed out with a friendly checkmark, illustrating redundant work eliminated through memoization.

A bright, sunlit university whiteboard filled with clean colorful diagrams showing nested complexity class bubbles: P inside NP inside PSPACE inside a large cheerful orange-outlined bubble labeled EXPTIME. A friendly illustrated Turing machine tape runs along the bottom. The formula O(2^p(n)) is written clearly in blue marker. Colored arrows point to example problems. Warm afternoon light streams through tall windows onto the neat, organized illustration.

A bright, sunlit university workspace with large windows showing a clear blue sky. A student sits at a clean white desk covered with colorful sticky notes, flowchart diagrams, and pseudocode sketches. A whiteboard shows a clean graph labeled "O(n log n)" with a smooth ascending curve. Open books, a laptop displaying a flowchart, and coffee cup surround organized project notes. The scene feels energetic, focused, and accomplished.

A bright, sunlit university commons where a diverse group of students stands around a large circular table topped with a glowing white display. Icons float above it in cheerful colors: a shield labeled "PRIVACY," a balanced scale for "FAIRNESS," and a small robot with a question mark for "AI ETHICS." Clean bookshelves and tall windows with blue sky fill the background. Students gesture thoughtfully, collaborating with open laptops and sticky notes.

A bright university computer science lab with large windows letting in warm daylight. A clean whiteboard displays a neatly drawn Binary Search Tree with labeled nodes (50 at root, 30 and 70 as children, 20/40/60/80 as leaves), arrows showing search path highlighted in yellow. Nearby desk shows open laptop with hash table grid and a small heap diagram. Cheerful, crisp, academic atmosphere with blue and white color palette.

A bright, sunlit university classroom scene where three friendly robot figures sit around a clean white circular table, each holding colored cards labeled "STRATEGY A," "STRATEGY B," and "STRATEGY C." A large whiteboard behind them displays a clean payoff matrix grid with cheerful blue and orange numbers. Arrows connect the robots showing mutual decision influences, with a glowing star labeled "NASH EQ" marking the optimal intersection point. Books labeled "CS," "ECONOMICS," and "GAME THEORY" stack neatly nearby.

A bright, sunlit computer lab with large windows. A clean whiteboard shows an array splitting into halves, then quarters, labeled with small numbered boxes — a parallel Merge Sort tree diagram. Four glowing monitors on white desks each display a colorful subarray being sorted simultaneously, connected by arrows converging back upward. Students gesture enthusiastically at screens. Bold labels read "Divide," "Conquer," and "Merge" at each diagram level. Warm daylight fills the cheerful scene.

A bright university whiteboard scene bathed in warm daylight. A hand-drawn map of six cities connected by colored route lines shows two paths: a red "Exact Optimal" route labeled "100 miles" and a blue "Approximation" route labeled "150 miles," with a bold ratio box showing "1.5× OPT." Surrounding icons include a tiny calendar for scheduling and a small globe, all on a clean white background with cheerful teal and yellow accents.

A bright university whiteboard in a sunny classroom displays a clean context-free grammar with labeled production rules: S → (S) | SS | ε. Beside it, a cheerful diagram of a pushdown automaton shows labeled states connected by arrows, with a tall illustrated stack holding parentheses symbols. A stack pointer highlights the top element. Color-coded arrows connect the grammar rules to corresponding stack operations, making the relationship clear and inviting.

A bright, sunlit computer science classroom with a large whiteboard displaying colorful diagrams of six data structures side by side: a neat row of numbered boxes labeled "Array," chain-linked circles labeled "Linked List," a vertical stack of plates labeled "Stack," a horizontal queue of people labeled "Queue," a branching tree diagram, and a grid labeled "Hash Table." Clean marker-drawn arrows connect elements, rendered in vivid blue, orange, green, and yellow on white background.

A bright university workspace with a large whiteboard displaying interconnected geometric diagrams in vivid colors. A confident student plots scattered blue dots on a clean white coordinate plane, with a bold orange convex hull polygon connecting the outermost points. Nearby, a colorful Voronoi diagram partitions the plane into distinct pastel regions, each labeled with coordinate points. Delaunay triangulation lines connect vertices in crisp teal. Warm sunlight streams through tall windows.

Bright university whiteboard scene flooded with warm daylight. A confident student maps a clean complexity diagram: a large circle labeled "NP" contains a smaller circle labeled "P," with "SAT" marked boldly at the boundary as an NP-complete star. Arrows show polynomial-time reductions flowing from colorful problem nodes (CLIQUE, VERTEX COVER, 3-SAT) back to SAT. A Boolean formula "¬A ∨ B ∧ C" sits neatly beside truth-table rows marked ✓ or ✗. Cheerful, crisp, academic atmosphere.

A bright, sunlit computer science classroom with a large whiteboard displaying a clean binary tree diagram — a root node labeled "A" branching into clearly labeled child nodes "B" and "C," continuing two levels down with colored circular nodes in teal, coral, and yellow. Beside it, a min-heap triangle structure shows numbers 1, 3, 5, 7, 9 arranged hierarchically. A student points enthusiastically at the root node with a marker.

A bright, sunlit classroom whiteboard split into two halves. On the left, a clean blue "Waterfall" diagram shows six labeled boxes — Requirements → Design → Implementation → Testing → Deployment → Maintenance — connected by straight downward arrows like a flowing cascade. On the right, a vibrant orange "Agile" spiral with labeled segments: Plan, Build, Test, Review, cycling inward. A friendly professor points between both diagrams.

A bright, sunlit university study space where a cheerful student stands before a large whiteboard divided into four colorful labeled sections: "Dynamic Programming," "Backtracking," "Greedy," and "Divide & Conquer." Each section shows a clean mini-diagram — a grid with arrows, a branching decision tree, a path with checkmarks, and a splitting rectangle. Fresh markers, open laptops, and coffee cups sit on nearby white desks.

A bright, sunlit university workspace with a large central whiteboard displaying a clean flowchart connecting four color-coded domains: a red cross for healthcare, green leaf for environment, blue dollar sign for finance, and yellow network icon for social sciences. A cheerful student points to interconnecting algorithmic pathways linking all four. Data charts, ECG lines, and small labeled code snippets surround the diagram on a warm cream background.

Bright university study space with large windows letting in daylight. A clean whiteboard displays a colorful decision tree diagram with labeled nodes: "Feature A > 5?" branching into "Yes" and "No" paths, leading to leaf nodes marked "Class 1" and "Class 2." Scattered data points in teal and coral cluster nearby. A laptop shows a training accuracy graph curving upward. Books, coffee, and a O(n log n) notation complete the optimistic academic scene.

Bright university study room with large sunny windows and white walls. A clean whiteboard displays three labeled diagrams side by side: a circular TSP route connecting numbered city dots with arrows, a backpack with weighted items floating nearby labeled with values and weights, and a horizontal job-scheduling timeline bar chart. A focused student points confidently at the whiteboard, books and a laptop open on a light wooden desk nearby. Warm afternoon daylight fills the scene.