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Consider the problem of computing N! = 1 2 3 N.(a) If N is an n-bit number, how many

Chapter 1, Problem 1.31

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QUESTION:

Consider the problem of computing \(N !=1 \cdot 2 \cdot 3 \cdots N\).

(a) If N is an n-bit number, how many bits long is N!, approximately (in \(\Theta(\cdot)\) form)?

(b) Give an algorithm to compute N! and analyze its running time.

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QUESTION:

Consider the problem of computing \(N !=1 \cdot 2 \cdot 3 \cdots N\).

(a) If N is an n-bit number, how many bits long is N!, approximately (in \(\Theta(\cdot)\) form)?

(b) Give an algorithm to compute N! and analyze its running time.

ANSWER:

Step 1 of 5

a)

Note that the result of the factorial   is

Since   is   bits long,

Also, if  , then   has   bits.

Finally, the product of two numbers that have   and   bits is a number that has   bits.

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