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ProblemsClear skill: Correctness Complexity Build a practice set

ProblemCourse & topicStatus

ALG:9920001Let all logarithms have base 2, and let all functions have domain the positive integers.

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

—

ALG:9920002Arrange the following functions into asymptotic equivalence classes, ordering the classes from smallest to largest…

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920003Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920004Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920005In the unit-cost RAM model, each execution of `count = count + 1` costs one unit.

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920006Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920007Let `popcount(n)` denote the number of 1-bits in the ordinary base-2 representation of a positive integer n.

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920008For a positive integer n, consider: ```text count = 0 for i = 1 to n: j = 1 while j <= n: count = count + 1 if j…

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920009Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920010Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920011Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920012Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920013Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920014Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920015Consider: ```text Split(n): if n == 1: perform one unit of local work return Split(floor(n/2)) Split(ceil(n/2))…

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920016Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920017Consider insertion sort: ```text for j = 2 to n: key = A[j] i = j - 1 while i >= 1 and A[i] > key: A[i + 1] = A[i]…

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920018Let A[1..n] be sorted in nondecreasing order, let x be a key, and consider: ```text lo = 1 hi = n + 1 while lo…

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920019Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920020For a real number x and a nonnegative integer n, consider: ```text Pow(x, n): if n == 0: return 1 y = Pow(x…

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920021Let A[1..p] and B[1..q] be nondecreasing arrays.

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920022Let A[1..n] be an array and P a constant-time predicate.

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920023Mathematical problem title

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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ALG:9920024Consider: ```text for i = 1 to n - 1: if A[i] > A[i + 1]: swap A[i] and A[i + 1] return A` `` Determine whether…

Correctness ComplexityAlgorithms Problem Solving

Correctness proofs and asymptotic complexityAlgorithms · Calculation

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Showing 24 of 50 matching problems.

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Let f,g:\mathbb

N\to(0,\infty)

.

For each positive integer

n

, define…

Consider the following code, where

n\ge2

is an integer and every arithmetic operation has unit cost: ```text count…

In the following code,

`ceil_sqrt(i)`

returns \lceil\sqrt

i\rceil

in unit time.

Given an integer

n\ge4

, design nonrecursive pseudocode containing a designated unit-cost statement that executes…

Let

T(1)=1

, and for every integer

n\ge2

, let

T(n)=T(\lfloor n/2\rfloor)+T(\lceil n/2\rceil)+n

.

Let

T(n)=1

for integers

1\le n\le2

, and for

n\ge3

, let

T(n)=4T(\lceil n/2\rceil)+\frac{n^2}{\log_2n}

.

Let

T(n)=1

for integers

0\le n\le1

, and for

n\ge2

, let

T(n)=T(\lfloor n/3\rfloor)+T(\lfloor2n/3\rfloor)+n

.

Let

T(n)=1

for integers

0\le n\le1

, and for

n\ge2

, let

T(n)=T(\lfloor n/2\rfloor)+T(\lfloor n/3\rfloor)+n

.

Two algorithms have running times defined on powers of

2

by

A(1)=1,\qquad A(n)=8A(n/2)+n^3

, and…

For integers

a\ge

b\ge0

,

(a,b)\ne(0,0)

, consider Euclid's algorithm: ```text while b != 0: r = a mod b a = b b = r…

An array A[1..n],

n\ge2

, contains distinct comparable keys.