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Why recursion? Binary search can be expressed as iteration, or, since you actually have a constant bound on the number of iterations here, an unrolled iteration. That would IMO still count as the same algorithm, just a different realization of it.
left + (right - left) / 2
This trick is to avoid overflow. There cannot be any overflow here anyway, since both left and right will be well below MAXINT (at most they'll be the square root of MAXINT). So you can write it the simple/shorter/faster way.
middle == 0 && middle <= x / (middle + 1)
Is this even correct? Note that the right operand of the && effectively checks whether 0 <= x which is not useful since x is known to be non-negative (pre-condition).
The whole zero business can be avoided by checking whether middle * middle > x (this multiplication cannot overflow unless incorrect bounds were passed), which by avoiding division is both "zero-safe" and more efficient.
I am interested on how to convert a point in 3D space (x,y,z) to 2D Space (x,y) using perspective accurate projection. I have found lots of things online showing how to do this, but they all use a bunch of stuff I don't understand like matrixes. I am only a grade 9 student so I don't know a lot of advanced math. If you guys could explain it to me in a simple way like:
x' = (something with x and z)
y' = (something with y and z)
That would be awesome
Thanks in advance everyone.
Sidenote, if you want to send me some example code please do it in python its the only language I'm any good at
I'm sorry ... but if you want to create a pseudo-3D-Point inside a 2D-View you need to know "a little bit" about Matrixes and vector-calculation.
Normally your pseudo-3d-Axises are something like this :
.... but as a real 3D-Point the Y-vector is not to be seen because it's in direction "into the screen".
So now, depending on your view-point (or camera-point) you have to calculate it's new position inside the 2D-View.
I looked at this problem and assuming most node are behind a firewall that blocks port forwarding and the nodes are small machines then I just cannot come up with a plan that scales to millions of users that won't end up flooding the network with internal chatter.
My current thoughts are of specialized DNS type nodes working as a replicated cluster to provide the service and then dealing with sub-domaining the address at a later date if needs be but this is not the way I like working and is made worse because the lookup's will be 100-200 bytes in size.
As if things could not get any worse the data needs to be encrypted before being written to files but the values are 32 byte public keys that can be broken down and map 35 X 35 X 35 files which seems like the starting point.
1. In the group of people we define the relationship: A does not like B. This relation is not symmetrical.
If there is a series of relationships A1 does not like A2, A2 does not like A3 ... Ak does not like A1,
all people in this cycle belong to one group of "disliking".
For the given pair specifying the relations, determine the maximum division
groups of "disliking". Provide complexity and justify the correctness of your solution.
2. There are some animosities in the group of naughty children. The preschool teacher decided to
set the children in a row. If A does not like B, he can not stand in a row in front of B (not to throw papers in it).
a) Specify if a group of children can be set in one row.
b) If not, enter the minimum number of rows to set children in above configuration.
Provide complexity and justify the correctness of your solution.
c) Enter the minimum number of rows necessary to set the children, if:
Child A does not like child B, it must stand in a row with a lower number.
I know that in the first task I have to find strongly connected components. Actually I did it using Tarjan's algorithm in PHP implementations. I wonder that is it correct approach and how to provide complexity of my solution. Unfortunately I don't have any information how to solve second task. Maybe someone has an idea and could give a clue.
there is no straightforward way to solve this problem. Instead, you should try different schemes and calculate how many boxes you can store in each of them, then pick the optimum.
Assuming box dimension d3 * d2 * d1 with d3>=d2>=d1, boxes are allowed to be rotated in any way and can be stacked all the way to the top, and assuming the cargo room is much longer than its diameter, this is what I would do in a first attempt, and I expect it to get really close to the absolute optimum:
- work one layer at a time, i.e. the problem gets reduced from a 3D problem to a number of much easier 2D problems;
- the first layer would have thickness d1;
- now fit as many boxes as possible in that one layer; obvious choices would be: all in long direction, or all in cross direction (the former normally being better than the latter);
- first refinement: if length of cargo room isn't a multiple of d3, you might be slightly better of splitting it (per layer!) in two parts, a big part using long direction, the remainder using cross direction;
- once the maximum is found for that layer proceed to the next layer again using thickness d1; note that the second layer has the same length but a larger width than the first layer, hence the result could be a larger number of boxes;
- continue designing your layers with thickness d1 until you reach the 45 degree angle, then the layer height should equal d2 (instead of d1), everything else remains the same;
- and once you reach the 135 degree angle, switch back to the original scheme (thickness d1).
Second refinement, somewhat more difficult: as you will probably not reach exactly 45 degrees, you might consider one less layer with thickness d1; similarly you might consider one less layer with thickness d2. This yields four cases to consider, there is a possibility one of them gives you one more layer in total, and a better solution.
Final remark: it is not sure that orthogonal filling yields the optimum, the optimum could consist of arches and other schemes that might not be practical at all, I would guess you won't care for those...
i am not able to figure out why linspace not able to create equal intervals till the value of machine epsilon
here is the code....
from numpy import *
import numpy as np
# machine epsilon
h = np.linspace(1,epsilon,1000)
e1= (((sin(x)- sin(x-h))/h-cos(x))/cos(x)) #realtive error in first order
e2= (((sin(x-2*h)-4*sin(x-h)+3*sin(x))/(2*h)-cos(x))/cos(x)) #realtive error in second order
e3= (((2*sin(x+h)+3*sin(x)-6*sin(x-h)+sin(x-2*h))/(6*h)-cos(x))/cos(x))#realtive error in third order
e4 = (((-sin(x-3*h)+6*sin(x-2*h)-18*sin(x-h)+10*sin(x)+3*sin(x+h))/(12*h)-cos(x))/cos(x))#realtive error in fourth order
import matplotlib.pyplot as plt
plt.legend(['first order','second order','third order','fourth order'])
plt.title('Effect of order of accuracy on the numerical differentiation')
NOAA's National Centers for Environmental Information collects global climate data and aggregates this data to provide information on climate trends and variability. One product they offer is a monthly regional analysis. The following table gives "anomaly" data by continent for January 2017. "Anomaly" means the value is the temperature difference from the average temperature from years 1910–2000.
Continent Anomaly (C)
North America 3.18
South America 1.36
Your task is to develop an algorithm that would sort data such as these from least to greatest. Specifically, given an unsorted set of N decimal values, your algorithm should sort them to give an answer of the sorted data. For this set of N = 6, your algorithm should produce:
Execute your algorithm for a different set of data, such as a subset of the given data, data you make up, or another month's climate data, such as February 2017: https://www.ncdc.noaa.gov/sotc/global-regions/201702
Does your algorithm work for any N? Have you thought of corner cases it might need to handle, such as N = 0 or N = 1?