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Finding the Shortest Path - Directions, Aptitude Video Lecture - Quant
FAQs on Finding the Shortest Path - Directions, Aptitude Video Lecture - Quant
| 1. What is the shortest path algorithm used for? |  |
| 2. How does the shortest path algorithm work? | |
Ans. The shortest path algorithm works by exploring all possible paths between two points and calculating the length or cost of each path. It then selects the path with the lowest length or cost as the shortest path.
| 3. What are the common applications of the shortest path algorithm? | |
Ans. The shortest path algorithm has various applications, including route planning in transportation networks, finding the quickest route for delivery services, optimizing network routing, and determining the shortest path for data transmission in computer networks.
| 4. Are there different variations of the shortest path algorithm? | |
Ans. Yes, there are different variations of the shortest path algorithm, such as Dijkstra's algorithm, Bellman-Ford algorithm, and Floyd-Warshall algorithm. Each variation has its own advantages and is suitable for different types of networks or graphs.
| 5. Can the shortest path algorithm handle networks with negative edge weights? | |
Ans. It depends on the variation of the algorithm being used. Dijkstra's algorithm and Bellman-Ford algorithm can handle networks with negative edge weights, while the Floyd-Warshall algorithm cannot. However, negative edge weights may affect the optimality of the shortest path.
Text Transcript from Video
- [voiceover] In the figure
above, the solid lines
show the path of a traveler
who began at town A
went North five miles
then East three miles,
North again two miles, and then
East three miles to town B.
If instead, the traveler had
taken the most direct route
from town A to town B
along the dashed line,
how many miles would she have traveled?
We need to figure out this dashed line
distance right over here.
One way to do it is if we could figure out
the total amount going from,
or the total difference
between town A and town B
along the horizontal direction
and then if we were to
figure out the total distance
in the vertical direction, just like that,
this is a right angle here,
then we could the Pythagorean
Theorem to figure out
this straight distance
between town A and town B,
the length of this dotted line.
What is the length of this
green line right over here?
It's going to be three plus three.
It's going to be six miles.
Then what is the length
of this magenta line?
It's going to be five plus two.
It's going to be seven.
Now we can use the Pythagorean
Theorem to figure out
this dashed line right over here.
Let's just call the dashed line,
let's just call that distance C.
Pythagorean Theorem,
the sum of the squares
of the two shorter sides
is going to be equal to
the square of the hypotenuse.
This is the hypotenuse.
It's the longest side
of this right triangle.
It's the side opposite the right angle.
We get six squared.
It's one of the shorter sides.
Length six is one of the shorter sides.
I'm going to square
it, plus seven squared,
plus seven squared is going
to be equal to C squared,
is going to be equal to C squared.
We get 36 plus 49, plus
49, is equal to C squared.
Let's see, what is this
going to be equal to?
Let's see, if I have six
plus 49, that gets me to 55
plus another 30 is 85.
85 is equal to C squared,
C squared, or we could say
that C is going to be the
principal route of 85,
is going to be the principal route of 85.
Let's see, are there any
perfect squares in here?
Can I do anything interesting here?
Let's see, 85 is, 85,
if I tried to factor it,
that is five times, is it five times 17?
Yeah, that's right.
This is 50 plus 35.
That's five times 17.
There's no perfect squares
that I can factor this into.
I would just leave this as
the square root of 85 miles.
above, the solid lines
show the path of a traveler
who began at town A
went North five miles
then East three miles,
North again two miles, and then
East three miles to town B.
If instead, the traveler had
taken the most direct route
from town A to town B
along the dashed line,
how many miles would she have traveled?
We need to figure out this dashed line
distance right over here.
One way to do it is if we could figure out
the total amount going from,
or the total difference
between town A and town B
along the horizontal direction
and then if we were to
figure out the total distance
in the vertical direction, just like that,
this is a right angle here,
then we could the Pythagorean
Theorem to figure out
this straight distance
between town A and town B,
the length of this dotted line.
What is the length of this
green line right over here?
It's going to be three plus three.
It's going to be six miles.
Then what is the length
of this magenta line?
It's going to be five plus two.
It's going to be seven.
Now we can use the Pythagorean
Theorem to figure out
this dashed line right over here.
Let's just call the dashed line,
let's just call that distance C.
Pythagorean Theorem,
the sum of the squares
of the two shorter sides
is going to be equal to
the square of the hypotenuse.
This is the hypotenuse.
It's the longest side
of this right triangle.
It's the side opposite the right angle.
We get six squared.
It's one of the shorter sides.
Length six is one of the shorter sides.
I'm going to square
it, plus seven squared,
plus seven squared is going
to be equal to C squared,
is going to be equal to C squared.
We get 36 plus 49, plus
49, is equal to C squared.
Let's see, what is this
going to be equal to?
Let's see, if I have six
plus 49, that gets me to 55
plus another 30 is 85.
85 is equal to C squared,
C squared, or we could say
that C is going to be the
principal route of 85,
is going to be the principal route of 85.
Let's see, are there any
perfect squares in here?
Can I do anything interesting here?
Let's see, 85 is, 85,
if I tried to factor it,
that is five times, is it five times 17?
Yeah, that's right.
This is 50 plus 35.
That's five times 17.
There's no perfect squares
that I can factor this into.
I would just leave this as
the square root of 85 miles.
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Mar 08, 2025
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