Finding Unique Character Bigrams
A character bigram is a pair of two adjacent characters in a string. We need to find the number of distinct bigrams in the string $thoughtsoftheghosts$.
String Analysis
The input string is: $thoughtsoftheghosts$.
Generating Bigrams
We can list all possible adjacent pairs (bigrams) from the string:
- th
- ho
- ou
- ug
- gh
- ht
- ts
- so
- of
- ft
- th
- he
- eg
- gh
- ho
- os
- st
- ts
Identifying Unique Bigrams
Now, let's identify the unique bigrams from the list above. We only count each distinct pair once:
- th
- ho
- ou
- ug
- gh
- ht
- ts
- so
- of
- ft
- he
- eg
- os
- st
Counting Unique Bigrams
By counting the unique bigrams listed above, we find there are 14 distinct bigrams.
Therefore, the total number of unique character bigrams in the string $thoughtsoftheghosts$ is 14.
Important Questions from Numerical Computation
$A$ is an ($n \times n$) matrix. Consider the following two statements
Statement 1: Columns of matrix $A$ are linearly independent
Statement 2: Inverse of matrix $A$ exists
Which one of the following statements is TRUE?
- Consider the function $G(x, y, z) = 0$. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial derivatives of the function $G(x, y, z)$ exist everywhere. Then, the value of $\left(\frac{\partial z}{\partial x} \times \frac{\partial x}{\partial y} \times \frac{\partial y}{\partial z}\right)$ is _________ (in integer)
- Levenshtein distance is used to measure the minimum edit distance between two strings by counting the minimum number of editing operations (such as, insertions, deletions, substitutions) required to transform one string to another. Consider an alternative version of the Levenshtein distance in which each insertion and each deletion has a cost of 1 and substitutions are not allowed.
Based on this alternative version, the Levenshtein distance between the strings, word and work is ______ (Answer in integer). - In a given collection of documents, let $N$ be the total number of documents and let $d$ be the number of documents in which the term $t$ occurs.
Which ONE of the following fractions is used to define the inverse document frequency (idf) of the term $t$? A bacterium can be approximated as a cylinder with a hemisphere at each end, as shown in the figure. The cylinder has a height of $1 \mu\text{m}$ and diameter of $1 \mu\text{m}$. Assuming that the density of the bacterium is equal to that of water, what is the approximate mass of this bacterium?
Given: density of water = $10^3 \text{ kg/m}^3$; $1 \mu\text{m} = 10^{-6}\text{ m}$
Volume of a cylinder = $\pi r^2 h$, where $r$ is the radius and $h$ is the height of the cylinder
Volume of a sphere = $\frac{4}{3} \pi r^3$, where $r$ is the radius of the sphere
