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START Get the value of a number n Set the value of i to 2 Set the value of f to 1 While i is less than or equal to n (i ≤n) Set the value off to f * i Set the value of i to i + 1 Output f STOP

START Get the value of a number n Set the value of i to 2 Set the value of f to 1 While i is less than or equal to n (i ≤n) Set the value off to f * i Set the value of i to i + 1 Output f STOP

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Understanding the Algorithm:** **Purpose:** This algorithm is designed to compute the factorial of a given number `n`, but it starts the iterative process from 2 instead of 1. **Detailed Explanation:** 1. **Initialization:** - The algorithm begins by retrieving the value of an integer `n`. - It initializes an index variable `i` to 2. - Another variable `f` is initialized to 1, which will be used to store the factorial product. 2. **Iteration:** - The process enters a loop that continues as long as `i` is less than or equal to `n`. - Within each iteration: - `f` is updated to be the product of its current value and `i`. - `i` is then incremented by 1. 3. **Termination:** - Once `i` exceeds `n`, the loop terminates. - The algorithm outputs the final value of `f`, which holds the result of the factorial computation. **Conclusion:** The algorithm effectively calculates the factorial of a given number `n` (`n!`). However, noting that the iteration starts at 2, it assumes the initial product of 1 (`f = 1`) and multiplies this by all integers from 2 up to `n`. The final output is the factorial of `n`, i.e., `n! = 1 × 2 × 3 × ... × n`. **Example:** For `n = 5`, the steps will be: - Initialize `f = 1` and `i = 2`. - Iteration: - `f = 1 * 2` → `f = 2`, increment `i`. - `f = 2 * 3` → `f = 6`, increment `i`. - `f = 6 * 4` → `f = 24`, increment `i`. - `f = 24 * 5` → `f = 120`, increment `i`. - Output `f = 120`. Thus, `5! = 120`.
Transcribed Image Text:**Understanding the Algorithm:** **Purpose:** This algorithm is designed to compute the factorial of a given number `n`, but it starts the iterative process from 2 instead of 1. **Detailed Explanation:** 1. **Initialization:** - The algorithm begins by retrieving the value of an integer `n`. - It initializes an index variable `i` to 2. - Another variable `f` is initialized to 1, which will be used to store the factorial product. 2. **Iteration:** - The process enters a loop that continues as long as `i` is less than or equal to `n`. - Within each iteration: - `f` is updated to be the product of its current value and `i`. - `i` is then incremented by 1. 3. **Termination:** - Once `i` exceeds `n`, the loop terminates. - The algorithm outputs the final value of `f`, which holds the result of the factorial computation. **Conclusion:** The algorithm effectively calculates the factorial of a given number `n` (`n!`). However, noting that the iteration starts at 2, it assumes the initial product of 1 (`f = 1`) and multiplies this by all integers from 2 up to `n`. The final output is the factorial of `n`, i.e., `n! = 1 × 2 × 3 × ... × n`. **Example:** For `n = 5`, the steps will be: - Initialize `f = 1` and `i = 2`. - Iteration: - `f = 1 * 2` → `f = 2`, increment `i`. - `f = 2 * 3` → `f = 6`, increment `i`. - `f = 6 * 4` → `f = 24`, increment `i`. - `f = 24 * 5` → `f = 120`, increment `i`. - Output `f = 120`. Thus, `5! = 120`.
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