TAOCP 1.1: Algorithms

Section 1.1 exercises: 9/9 solved.

9 items

Section 1.1. Algorithms

Exercises from TAOCP Volume 1 Section 1.1: 9/9 solved.

#	Rating	Category	Status	Time
1	[10]	simple	verified	2m24s
2	[15]	simple	verified	1m05s
3	[20]	medium	verified	3m53s
4	[16]	medium	verified	1m11s
5	▶ [12]	simple	verified	3m12s
6	[20]	medium	verified	47s
7	▶ [M21]	math-medium	verified	48s
8	[M25]	math-medium	verified	4m45s
9	▶ [M30]	math-hard	verified	1m55s

Practice › Mathematics › TAOCP › TAOCP Vol 1: Fundamental Algorithms › TAOCP 1.1: Algorithms ›

TAOCP 1.1 Exercise 1

We give a fully rigorous solution to Exercise 1.

Practice › Mathematics › TAOCP › TAOCP Vol 1: Fundamental Algorithms › TAOCP 1.1: Algorithms ›

TAOCP 1.1 Exercise 2

We prove by examining the structure of Algorithm E that $m \ge n$ holds at the beginning of step E1, except possibly at the first execution of that step.

Practice › Mathematics › TAOCP › TAOCP Vol 1: Fundamental Algorithms › TAOCP 1.1: Algorithms ›

TAOCP 1.1 Exercise 3

The trivial replacement in Algorithm E occurs at step E3: m \leftarrow n,\qquad n \leftarrow r.

Practice › Mathematics › TAOCP › TAOCP Vol 1: Fundamental Algorithms › TAOCP 1.1: Algorithms ›

TAOCP 1.1 Exercise 4

Apply Algorithm E to $m = 6099$ and $n = 2166$.

Practice › Mathematics › TAOCP › TAOCP Vol 1: Fundamental Algorithms › TAOCP 1.1: Algorithms ›

TAOCP 1.1 Exercise 5

The exercise asks about the specific "Procedure for Reading This Set of Books" printed after the preface.

Practice › Mathematics › TAOCP › TAOCP Vol 1: Fundamental Algorithms › TAOCP 1.1: Algorithms ›

TAOCP 1.1 Exercise 6

By definition, $T_5$ is the average number of times step E1 is performed, taken over all positive integers $m$ when $n=5$.

Practice › Mathematics › TAOCP › TAOCP Vol 1: Fundamental Algorithms › TAOCP 1.1: Algorithms ›

TAOCP 1.1 Exercise 7

For a fixed positive integer $m$, define $U_m$ to be the average number of executions of step E1 in Algorithm E when the second argument $n$ ranges over all positive integers.

Practice › Mathematics › TAOCP › TAOCP Vol 1: Fundamental Algorithms › TAOCP 1.1: Algorithms ›

TAOCP 1.1 Exercise 8

We will now present a fully corrected solution to **Exercise 1.

Practice › Mathematics › TAOCP › TAOCP Vol 1: Fundamental Algorithms › TAOCP 1.1: Algorithms ›

TAOCP 1.1 Exercise 9

Let C_1=(Q_1,I_1,\Omega_1,f_1), \qquad C_2=(Q_2,I_2,\Omega_2,f_2) be computational methods in the sense of Eqs.