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Update appendix-b.md
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discrete-maths/appendix-b.md

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@@ -64,8 +64,9 @@ $$Since, f(N) = C(N) * \sum_{n=1}^N N_c$$
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- Back-substitution yields: $$N_c = N^2 * (N_{c_b} + N_{\phi}) = N^2 * (N_c + N_{\phi}) = N^2 * (N * (N_{c_c} + N''\_{\phi}) + N'\_{\phi})$$
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$$= N^3 * (N_{c_c} + N''\_{\phi}) + N^2 * N'\_{\phi}$$
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- The following formulas are derivable:
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$$ N_{c_c} = [(N_c - N^2 * N'\_{\phi}) / N^3] - N''\_{\phi} $$
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$$ N''\_{\phi} = [(N_c - N^2 * N'\_{\phi}) / N^3] - N_{c_c} $$
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$$1)\ N_{c_c} = [(N_c - N^2 * N'\_{\phi}) / N^3] - N''\_{\phi}$$
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$$2)\ N''\_{\phi} = [(N_c - N^2 * N'\_{\phi}) / N^3] - N_{c_c}$$
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$$3)\ N'\_{\phi}= [N_c - N^3 * (N_{c_c} + N''\_{\phi})] / N^2$$
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- Now, if `command()` has a clock-complexity of (1):
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$$N_c = N^3 * (N_{c_c} + N''\_{\phi}) + N^2 * N'\_{\phi} = N^3 * (1 + 0) + N^2 * 0 = N^3$$

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