recursion - Recursive Runtime of T(n-k) -


मैं समीकरण के क्रम को खोजने की कोशिश कर रहा हूं;

T (n) = T (n-2) + n³।

जब मैं इसे हल करता हूं, तो मैं समीकरण टी (एन) = टी (एनके) + एसएआर k = 0 पर पहुंचता हूं। ।, N / 2 (n-2k) ³।
उस राशि को हल करने से मुझे 1/8 (एन 2) (n + 2) ² मिलता है। इसे सुलझाने के लिए मुझे क्रम के लिए Θ (एन.ई.) बनना होगा। हालांकि, मुझे लगता है कि मैंने कुछ गलत किया, क्या किसी के पास कोई विचार है?

आपको ऐसा क्यों लगता है कि यह गलत है? यह समीकरण स्पष्ट रूप से थीटा (एन ^ 4)

अधिक विस्तृत समाधान Wolframalpha से प्राप्त किया जा सकता है (क्या आपने इसे पुनरावृत्ति समीकरणों को हल किया है?)

आप कुछ सीमा के मामलों को भी जोड़ सकते हैं, जैसे टी (0) = टी (1) = 1

सीमा के मामले के साथ

और अंत में: असीमपटाटिक भूखंड, दिखा रहा है कि यह वास्तव में N ^ 4 फ़ंक्शन की तरह व्यवहार करता है

plot


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