Asymptotic notation is a shorthand used to give a quick measure of the behaivior of a function f.n/ as n grows large.
We can convert any sum into sum by taking logarithm.
f(x)=O.g(x)/ means f(x) is less than or equal to g(x)
Every common divisor of a and b divides gcd(a,b).
If gcd(a,b)=1 and gcd(a,c)=1, then gcd(a,bc)=1
gcd(ka,kb)=k.gcd(a,b) for all k positve.
sink
sourse
1 & 2 both
Markov theorem depends only on the mean of the random variable.
Chebyshev theorem makes use of the mean and variance.
Chernoff bounds says that certain random variables are very unlikely to significantly exceed their expectation.
is another way to solve recurrences.
also sometims called expansion or iteration.
Both of these.
Compliment of every element in a Boolean algebra B is unique.
A random variable that takes on each possible value with the same probability is said to be uniform.
Bernoulli distribution is a distribution for an indicator random variable.
(1/13)
(4/13)
(13/52)
P(E?F) / P(F), provided P(F) ? 0\n
P(E+F) / P(F), provided P(F) ? 0\n
P(E+F) / P(E), provided P(F) ? 0\n
Any connected subgraph is a tree.
There is not a unique simple path between every pair of vertices
Removing any age disconnects the graph.
Proper subgraph
Improper subgraph
Planer Subgraph
36
72
None of these.
Every non empty set of non negative integers has a smallest element.
Ordinary induction often works directly in proving that some staement about non negative integers holds for all of them.
A property that is preserved through a series of operations or steps is known as an invarient
nCr
(n+1)Cr
nC(r+1)
|A|>|B|
|A|=|B|
|A|<|B|
0
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Every graph with v vertices and e edges has atleast v-e connected components.
To vertices in a graph are said to be connected if there is a that begins at one and ends at the other.
A graph is said to be connected when every pair of vertices are connected.
The expected value of the indicator random variable for an event is just the probability of that event.
The expectation or expected value of a random variable is a single number.
The expected value also known as the average or mean.
(1/32)
(2/32)
(6/32)
Set of rational numbers Q is countable
Power set is always greater than the set itself.
Both 1 & 2
sure event
unsure event
impossible event
iAi
kAk
jAj
AUB is countable.
is countable.
There is a special case of the Akra Bazzi formula known as Master theorem.
The solution to virtally all divide and conquer solutions is given by the Akra Bazzi formula.
Master theorem handles some of the recurrences that commonly arise in computer science.
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\"b..\"
\"c..\"
(1/2)
(1/3)
(1/4)