How To Make Cutting Of Chudidar Pajama

Project 4 Project 3: Fibonacci Series

What is recursion?
Programming is a tool that we use to call a function within a function.

What is iteration?
is when you have to repeat an action a number of times.

When using recursion?
When it comes to solving complex problems that can be subdivided into several steps and can not be solved by iteration.

is it used?
An example of this is to solve problems having to do with the factorial of a number or logic games.

Factorial: Http://ce.azc.uam.mx/profesores/franz/omi/recursion2.html



On this occasion we chose the Fibonacci series is a clear example of problems can be solved by iteration.

/ \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\

Teamwork.

How worked as a team?

We communicate via email, because we did not agree to see us somewhere specific, so in some ways it was easier for everyone, so we could find information separately.

What was your contribution to work?

I focused to get general information about the Fibonacci Series.

How to compare what you did with the work of others?

Each of us tried to provide as much information as he could, each one giving his own opinion, and through debate, we gather all the information necessary for the group presentation.

could be improved in the future? Tr

tie agree that we put us further in advance, as in this occasion we did not, because I believe that we are confident that the delivery date had changed.

My teammates: Klaudia

Lozano Gerardo Ossio

Gustavo Chavana

Presentation Group. Fibonacci series. Fibonacci Series

How To Make Cutting Of Chudidar Pajama

Project 4 Project 3: Fibonacci Series

What is recursion?
Programming is a tool that we use to call a function within a function.

What is iteration?
is when you have to repeat an action a number of times.

When using recursion?
When it comes to solving complex problems that can be subdivided into several steps and can not be solved by iteration.

is it used?
An example of this is to solve problems having to do with the factorial of a number or logic games.

Factorial: Http://ce.azc.uam.mx/profesores/franz/omi/recursion2.html



On this occasion we chose the Fibonacci series is a clear example of problems can be solved by iteration.

/ \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\

Teamwork.

How worked as a team?

We communicate via email, because we did not agree to see us somewhere specific, so in some ways it was easier for everyone, so we could find information separately.

What was your contribution to work?

I focused to get general information about the Fibonacci Series.

How to compare what you did with the work of others?

Each of us tried to provide as much information as he could, each one giving his own opinion, and through debate, we gather all the information necessary for the group presentation.

could be improved in the future? Tr

tie agree that we put us further in advance, as in this occasion we did not, because I believe that we are confident that the delivery date had changed.

My teammates: Klaudia

Lozano Gerardo Ossio

Gustavo Chavana

Presentation Group. Fibonacci series. Fibonacci Series

Remove Formaldehyde From Trailer

Problem Jeep (Exploration Problem)


Description
Maximize the distance of a Jeep can get into the wilderness with a given amount of fuel. The jeep is allowed to go ahead, download a little fuel, and then return to base with fuel left in the tank. At its base, refuel and be off again. When it reaches the fuel saved earlier, then it can be used to partially fill your tank.

Problem
There are n units fuel stored in a fixed base. The jeep can carry at most 1 unit of fuel at any time, and can travel 1 unit of distance in 1 unit of fuel (fuel consumption of the jeep is supposed to be constant.) At any point in a jeep tour can leave any amount of fuel being performed on a fuel dump, or you can catch any remaining fuel in a fuel dump on a previous trip, as long as his fuel load in no case exceed 1 unit.

There are two variants of the problem:
• Exploring the desert - The jeep should return to base after each trip.
• Crossing the desert - The jeep has to return to base after each trip, except for the final trip, when the jeep traveling as far as I can before running out of fuel.

In any case objective is to maximize the distance traveled by jeep on his final journey. Alternatively, the goal may be to find the least amount of fuel needed to produce a final travel a given distance.

In the classical problem of fuel in the jeep and fuel dumps is treated as a continuous quantity. More complex variations on the problem have been proposed in which the fuel can only be left or collected in discrete amounts.


Solution

A strategy that maximizes the distance covered on the final voyage of the "variant to explore the wilderness" is as follows:

• On each trip starts from the bottom with 1 unit of fuel.
• In the first jeep trip covers a distance of 1 / (2n) units and leaves (n-1) / n units of fuel in a fuel dump. The jeep still has 1 / (2n) units of fuel - just enough to return to base.
• In each of these n-1 lists the jeep trips 1 / (2n) units of fuel from the first unloading fuel at the outlet, so that leaves the fuel discharge of 1 unit of transportation fuel . It also collects 1 / (2n) Units of fuel from the first discharge of fuel on the way back, which is just enough fuel to return to base.
• On the second trip the jeep travels to the unloading and reloading of fuel cells first. It then travels a distance of 1 / (2n-2) units and leaves (n-2) / (n-1) units of fuel in a fuel dump second. The jeep still has 1 / (2n-2) units fuel, which is just enough to return to the discharge of fuel first. Here is collected 1 / (2n) units of fuel, which is just enough fuel to return to base.
• In each of these n-2 jeep tours collects 1 / (2n-2) units of fuel to the fuel dump to second exit, which exits the discharge of fuel of 1 unit of fuel transport . It also collects 1 / (2n-2) units of fuel from the second discharge of fuel on the way back, which is just enough fuel to return to the discharge of fuel first.
• The jeep is in this way, so the trip k k sets a new fuel or dump at a distance of 1 / (2n-2k + 2) units above the discharge of fuel and leaves (n - k) / (n - k + 1) units of fuel there. In each of these n - k trips collects 1 / (2n-2k + 2) units of fuel k download, or on their way out and another 1 / (2n-2k + 2) units of fuel in its path return.





Solution to "explore the desert" variant for n = 3, showing the jeep fuel content and fuel tanks at the beginning of each trip and at the point of turnround on each trip.






When the jeep started his last journey, there are n-1 fuel dumps. The furthest contains 1 / 2 of a unit of fuel, far below contain 1 / 3 of a unit of fuel, and so on, and the nearest trash fuel is barely 1 / n units of fuel left. Along with 1 unit of fuel that starts from the base, this means that the jeep can travel a total distance round of the units in its last trip (the maximum distance traveled in the desert is half this).
It collects half of the remaining fuel in each stream to the output, what fills your tank. After leaving the dump fuel farthest traveled to 1 / 2 of a unit in the desert and then back away further from the fuel. Remaining fuel accumulates each discharge of fuel into the way back, which is just enough to get to the next or the discharge of fuel in the final stage, returning to base.

The distance traveled on the last trip is not number of harmonics [1] , Hn. Since they are not bounded in harmonic numbers is possible to overcome any distance on the trip end, and along with enough fuel is available at the base. However, the amount of fuel required and the number of fuel tanks, both increase exponentially with the distance to be covered.

The "crossing the desert" variant can be solved with a similar strategy, except that there is no longer required to collect the fuel on the way back in the final journey. So the trip k jeep down a new k fuel or dump at a distance of 1 / (2n-2k + 1) units of the fuel discharge and previous sheets (2n-2k-1) / (2n- 2k + 1) units of fuel there. In each of the next n - k-1 trip that collects 1 / (2n-2k + 1) units of fuel k download, or on their way out and another 1 / (2n-2k + 1) units of fuel on their way back.

Now, when the jeep started his last journey, there are n-1 fuel dumps. The furthest contains 1 / 3 of a unit of fuel, the following further contain 1 / 5 of a fuel unit, and so on, and the nearest fuel dump just 1 / (2n-1) units of fuel left. Along with 1 unit of fuel that starts from the base, this means that the jeep can travel a total distance of the units in their final journey. Collect all the fuel remaining in each stream to the output, what fills your tank. After leaving the dump fuel farthest travels a distance of 1 unit.

Note that it is theoretically possible, cross a desert of any given size sufficient fuel in the base. As before, the amount of fuel required and the number of fuel tanks, both increase exponentially with the distance to be covered.

--------------------------

Maximum distance Ln Alcanzada, n combustible

Referencias

[1] http://en.wikipedia.org/wiki/Harmonic_number

http://mathworld.wolfram.com/JeepProblem.html

http://en.wikipedia.org/wiki/Jeep_problem

http://page.mi.fu-berlin.de/rote/Papers/pdf/Optimal+logistics+for+expeditions+-+the+jeep+problem+with+complete+refilling.pdf

Remove Formaldehyde From Trailer

Problem Jeep (Exploration Problem)


Description
Maximize the distance of a Jeep can get into the wilderness with a given amount of fuel. The jeep is allowed to go ahead, download a little fuel, and then return to base with fuel left in the tank. At its base, refuel and be off again. When it reaches the fuel saved earlier, then it can be used to partially fill your tank.

Problem
There are n units fuel stored in a fixed base. The jeep can carry at most 1 unit of fuel at any time, and can travel 1 unit of distance in 1 unit of fuel (fuel consumption of the jeep is supposed to be constant.) At any point in a jeep tour can leave any amount of fuel being performed on a fuel dump, or you can catch any remaining fuel in a fuel dump on a previous trip, as long as his fuel load in no case exceed 1 unit.

There are two variants of the problem:
• Exploring the desert - The jeep should return to base after each trip.
• Crossing the desert - The jeep has to return to base after each trip, except for the final trip, when the jeep traveling as far as I can before running out of fuel.

In any case objective is to maximize the distance traveled by jeep on his final journey. Alternatively, the goal may be to find the least amount of fuel needed to produce a final travel a given distance.

In the classical problem of fuel in the jeep and fuel dumps is treated as a continuous quantity. More complex variations on the problem have been proposed in which the fuel can only be left or collected in discrete amounts.


Solution

A strategy that maximizes the distance covered on the final voyage of the "variant to explore the wilderness" is as follows:

• On each trip starts from the bottom with 1 unit of fuel.
• In the first jeep trip covers a distance of 1 / (2n) units and leaves (n-1) / n units of fuel in a fuel dump. The jeep still has 1 / (2n) units of fuel - just enough to return to base.
• In each of these n-1 lists the jeep trips 1 / (2n) units of fuel from the first unloading fuel at the outlet, so that leaves the fuel discharge of 1 unit of transportation fuel . It also collects 1 / (2n) Units of fuel from the first discharge of fuel on the way back, which is just enough fuel to return to base.
• On the second trip the jeep travels to the unloading and reloading of fuel cells first. It then travels a distance of 1 / (2n-2) units and leaves (n-2) / (n-1) units of fuel in a fuel dump second. The jeep still has 1 / (2n-2) units fuel, which is just enough to return to the discharge of fuel first. Here is collected 1 / (2n) units of fuel, which is just enough fuel to return to base.
• In each of these n-2 jeep tours collects 1 / (2n-2) units of fuel to the fuel dump to second exit, which exits the discharge of fuel of 1 unit of fuel transport . It also collects 1 / (2n-2) units of fuel from the second discharge of fuel on the way back, which is just enough fuel to return to the discharge of fuel first.
• The jeep is in this way, so the trip k k sets a new fuel or dump at a distance of 1 / (2n-2k + 2) units above the discharge of fuel and leaves (n - k) / (n - k + 1) units of fuel there. In each of these n - k trips collects 1 / (2n-2k + 2) units of fuel k download, or on their way out and another 1 / (2n-2k + 2) units of fuel in its path return.





Solution to "explore the desert" variant for n = 3, showing the jeep fuel content and fuel tanks at the beginning of each trip and at the point of turnround on each trip.






When the jeep started his last journey, there are n-1 fuel dumps. The furthest contains 1 / 2 of a unit of fuel, far below contain 1 / 3 of a unit of fuel, and so on, and the nearest trash fuel is barely 1 / n units of fuel left. Along with 1 unit of fuel that starts from the base, this means that the jeep can travel a total distance round of the units in its last trip (the maximum distance traveled in the desert is half this).
It collects half of the remaining fuel in each stream to the output, what fills your tank. After leaving the dump fuel farthest traveled to 1 / 2 of a unit in the desert and then back away further from the fuel. Remaining fuel accumulates each discharge of fuel into the way back, which is just enough to get to the next or the discharge of fuel in the final stage, returning to base.

The distance traveled on the last trip is not number of harmonics [1] , Hn. Since they are not bounded in harmonic numbers is possible to overcome any distance on the trip end, and along with enough fuel is available at the base. However, the amount of fuel required and the number of fuel tanks, both increase exponentially with the distance to be covered.

The "crossing the desert" variant can be solved with a similar strategy, except that there is no longer required to collect the fuel on the way back in the final journey. So the trip k jeep down a new k fuel or dump at a distance of 1 / (2n-2k + 1) units of the fuel discharge and previous sheets (2n-2k-1) / (2n- 2k + 1) units of fuel there. In each of the next n - k-1 trip that collects 1 / (2n-2k + 1) units of fuel k download, or on their way out and another 1 / (2n-2k + 1) units of fuel on their way back.

Now, when the jeep started his last journey, there are n-1 fuel dumps. The furthest contains 1 / 3 of a unit of fuel, the following further contain 1 / 5 of a fuel unit, and so on, and the nearest fuel dump just 1 / (2n-1) units of fuel left. Along with 1 unit of fuel that starts from the base, this means that the jeep can travel a total distance of the units in their final journey. Collect all the fuel remaining in each stream to the output, what fills your tank. After leaving the dump fuel farthest travels a distance of 1 unit.

Note that it is theoretically possible, cross a desert of any given size sufficient fuel in the base. As before, the amount of fuel required and the number of fuel tanks, both increase exponentially with the distance to be covered.

--------------------------

Maximum distance Ln Alcanzada, n combustible

Referencias

[1] http://en.wikipedia.org/wiki/Harmonic_number

http://mathworld.wolfram.com/JeepProblem.html

http://en.wikipedia.org/wiki/Jeep_problem

http://page.mi.fu-berlin.de/rote/Papers/pdf/Optimal+logistics+for+expeditions+-+the+jeep+problem+with+complete+refilling.pdf