ALGORITMIK MASALALARNI YECHISHDA MATEMATIK USULLARDAN FOYDALANISHNING NAZARIY VA AMALIY ASOSLARI
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Kalit so‘zlar: algoritm, matematik usul, matematik model, murakkablik, graf, optimallashtirish, sonli usul, hisoblash samaradorligi##common.commaListSeparator## Keywords: algorithm, mathematical method, mathematical model, complexity, graph, optimization, numerical methodAnnotatsiya
Annotatsiya. Mazkur maqolada algoritmik masalalarni yechish jarayonida matematik usullardan foydalanishning nazariy asoslari, ularning algoritm loyihalash, murakkablikni baholash, optimallashtirish va sonli hisoblashdagi o‘rni tahlil qilinadi. Diskret matematika, graflar nazariyasi, chiziqli algebra, ehtimollar nazariyasi hamda matematik optimallashtirish usullarining algoritmik modellar bilan integratsiyasi ko‘rib chiqiladi. Deykstra algoritmi, iteratsion sonli usullar va optimallashtirish masalalari misolida matematik modeldan hisoblash algoritmiga o‘tish bosqichlari yoritiladi. Shuningdek, algoritm samaradorligini vaqt va xotira murakkabligi, aniqlik, barqarorlik va yechimning optimaligi mezonlari asosida baholash taklif etiladi.
Abstract. The article examines theoretical foundations of applying mathematical methods to algorithmic problem solving and their role in algorithm design, complexity analysis, optimization and numerical computation. The integration of discrete mathematics, graph theory, linear algebra, probability and mathematical optimization with algorithmic models is discussed. The transition from a mathematical model to a computational procedure is illustrated through shortest-path, iterative numerical and optimization problems.
