| {"id": "tutorial-binary-search", "title": "Binary search, step by step", "text": "Binary search finds a value in a sorted list by halving the part of the list that can still contain it.\n\n1. Start with two markers: low at the first position and high at the last.\n2. Look at the middle element, at position (low + high) // 2.\n3. If it equals the target, you are done. If it is smaller, the target can only be to its right, so move low to the middle plus one. If it is larger, move high to the middle minus one.\n4. Repeat until low passes high; then the value is not in the list.\n\nWhy does this work? Because the list is sorted, one comparison with the middle element rules out half of the remaining candidates. A list of 1,000 items therefore needs at most 10 comparisons, since 2^10 = 1,024. A linear scan may need all 1,000.\n\nExample: search for 23 in [2, 5, 8, 12, 16, 23, 38, 56, 72, 91]. The middle element is 16, which is smaller, so we keep [23, 38, 56, 72, 91]. Its middle is 56, which is larger, so we keep [23, 38]. The middle of that is 23: found after three comparisons.\n\nA common bug is computing the middle as (low + high) / 2 in languages with fixed-size integers, where low + high can overflow; low + (high - low) // 2 avoids it."} | |
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| {"id": "python-code", "code_language": "Python", "text": "def moving_average(values, window):\n \"\"\"Return the simple moving averages of `values` over `window` consecutive items.\n\n >>> moving_average([1, 2, 3, 4, 5], 2)\n [1.5, 2.5, 3.5, 4.5]\n \"\"\"\n if window <= 0:\n raise ValueError(\"window must be positive\")\n if window > len(values):\n return []\n total = sum(values[:window])\n out = [total / window]\n for i in range(window, len(values)):\n # slide the window: add the new item, drop the oldest one\n total += values[i] - values[i - window]\n out.append(total / window)\n return out\n"} | |
| {"id": "math-worked-example", "title": "Solving a quadratic equation", "text": "Solve x^2 - 5x + 6 = 0.\n\nWe look for two numbers whose product is 6 and whose sum is 5: these are 2 and 3. Hence x^2 - 5x + 6 = (x - 2)(x - 3).\nA product is zero exactly when one of its factors is zero, so x - 2 = 0 or x - 3 = 0, which gives x = 2 or x = 3.\n\nCheck with the quadratic formula: x = (5 ± sqrt(25 - 24)) / 2 = (5 ± 1) / 2, so x = 3 or x = 2. Substituting x = 2 gives 4 - 10 + 6 = 0, and x = 3 gives 9 - 15 + 6 = 0, as required."} | |
| {"id": "spanish-water-cycle", "title": "El ciclo del agua", "text": "El ciclo del agua describe cómo el agua se mueve entre los océanos, la atmósfera y la tierra. El calor del sol evapora el agua de los mares y lagos; el vapor sube, se enfría y se condensa en pequeñas gotas que forman las nubes. Cuando las gotas crecen lo suficiente, caen como lluvia o nieve. Parte de esa agua corre por los ríos de vuelta al mar, otra parte se infiltra en el suelo y alimenta los acuíferos, y las plantas devuelven una fracción a la atmósfera por transpiración. Así, la misma agua puede recorrer el ciclo muchas veces a lo largo de los siglos."} | |
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