This is a challenge from 10 Day statistics on Hackerrank.(https://www.hackerrank.com/challenges/s10-interquartile-range/problem?h_r=next-challenge&h_v=zen)
Task :
Task
The interquartile range of an array is the difference between its first (Q1) and third (Q3) quartiles (i.e., Q3 - Q1).
Given an array,X, of n integers and an array, F, representing the respective frequencies of X's elements, construct a data set, S, where each xi occurs at frequency fi. Then calculate and print S's interquartile range, rounded to a scale of 1 decimal place (i.e., 12.3 format).
Following is my code.
n = int(input())
x = list(map(int, input().split()))
f = list(map(int, input().split()))
s = []
for i in range(len(x)):
j = f[i]
for k in range(j):
s.append(x[i])
n = len(s)
s.sort()
if n%2 == 0:
Q21 = s[n//2]
Q22 = s[n//2 - 1]
Q2 = (Q21 + Q22) / 2
else:
Q2 = s[n//2]
LH = s[:n//2]
if n%2==0:
UH = s[n//2:]
else:
UH = s[n//2+1:]
Q1_len = len(LH)
Q3_len = len(UH)
if Q1_len%2 == 0:
Q11 = LH[Q1_len//2]
Q12 = LH[Q1_len//2 - 1]
Q1 = (Q11 + Q12) / 2
else:
Q1 = LH[Q1_len//2]
if Q3_len%2 == 0:
Q31 = UH[Q3_len//2]
Q32 = UH[Q3_len//2 - 1]
Q3 = (Q31 + Q32) / 2
else:
Q3 = UH[Q3_len//2]
print(round(Q3 - Q1,1))
# print(int(Q2))
# print(int(Q3))
Here is the test case: with std input.
5
10 40 30 50 20
1 2 3 4 5
Expected output:
30.0
My code output:
30.0 # I get this output on my code editor but not on Hackerrank
Can someone help me on this where I am wrong ?
I get the output what is expected but it shows as failed.
print(float(Q3 - Q1))
Basically is the answer.
Related
im trying to write a program that gives the integral approximation of e(x^2) between 0 and 1 based on this integral formula:
Formula
i've done this code so far but it keeps giving the wrong answer (Other methods gives 1.46 as an answer, this one gives 1.006).
I think that maybe there is a problem with the two for cycles that does the Riemman sum, or that there is a problem in the way i've wrote the formula. I also tried to re-write the formula in other ways but i had no success
Any kind of help is appreciated.
import math
import numpy as np
def f(x):
y = np.exp(x**2)
return y
a = float(input("¿Cual es el limite inferior? \n"))
b = float(input("¿Cual es el limite superior? \n"))
n = int(input("¿Cual es el numero de intervalos? "))
x = np.zeros([n+1])
y = np.zeros([n])
z = np.zeros([n])
h = (b-a)/n
print (h)
x[0] = a
x[n] = b
suma1 = 0
suma2 = 0
for i in np.arange(1,n):
x[i] = x[i-1] + h
suma1 = suma1 + f(x[i])
alfa = (x[i]-x[i-1])/3
for i in np.arange(0,n):
y[i] = (x[i-1]+ alfa)
suma2 = suma2 + f(y[i])
z[i] = y[i] + alfa
int3 = ((b-a)/(8*n)) * (f(x[0])+f(x[n]) + (3*(suma2+f(z[i]))) + (2*(suma1)))
print (int3)
I'm not a math major but I remember helping a friend with this rule for something about waterplane area for ships.
Here's an implementation based on Wikipedia's description of the Simpson's 3/8 rule:
# The input parameters
a, b, n = 0, 1, 10
# Divide the interval into 3*n sub-intervals
# and hence 3*n+1 endpoints
x = np.linspace(a,b,3*n+1)
y = f(x)
# The weight for each points
w = [1,3,3,1]
result = 0
for i in range(0, 3*n, 3):
# Calculate the area, 4 points at a time
result += (x[i+3] - x[i]) / 8 * (y[i:i+4] * w).sum()
# result = 1.4626525814387632
You can do it using numpy.vectorize (Based on this wikipedia post):
a, b, n = 0, 1, 10**6
h = (b-a) / n
x = np.linspace(0,n,n+1)*h + a
fv = np.vectorize(f)
(
3*h/8 * (
f(x[0]) +
3 * fv(x[np.mod(np.arange(len(x)), 3) != 0]).sum() + #skip every 3rd index
2 * fv(x[::3]).sum() + #get every 3rd index
f(x[-1])
)
)
#Output: 1.462654874404461
If you use numpy's built-in functions (which I think is always possible), performance will improve considerably:
a, b, n = 0, 1, 10**6
x = np.exp(np.square(np.linspace(0,n,n+1)*h + a))
(
3*h/8 * (
x[0] +
3 * x[np.mod(np.arange(len(x)), 3) != 0].sum()+
2 * x[::3].sum() +
x[-1]
)
)
#Output: 1.462654874404461
I have to arrange and/or fit 2d tiles into a 2d square or rectangular plane with AI algorithm using python program. Each tile has a length and width. For example if a plane is 4x3 and set of tiles is
S={(2,3),(1,2),(2,2)}
these tiles can be rotated 90 degrees in order to fit the matrix.
input
first line contains length and width of the plane
second line number of tiles
and then the length,width of the subsequent tiles
but the inputs should be tab seperated
for eg
4 3
3
2 3
1 2
2 2
output
for eg
1 1 2 2
1 1 3 3
1 1 3 3
I have trouble solving this as i have to use only standard libraries in python no NumPy and no CSP library
~Edit 2`
my code so far I cant figure out how to add algorithm without csp library or to generate grid
from sys import stdin
a = stdin.readline()
x = a.split()
rectangular_plane = [[0] * int(x[0]) for i in range(int(x[1]))]
num_of_rectangles = stdin.readline()
r_widths = []
r_lengths= []
for l in range(int(num_of_rectangles)):
b = stdin.readline()
y = b.split()
r_lengths.insert(l,y[0])
r_widths.insert(l,y[1])
I've solved task with backtracking approach and without any non-standard modules.
Try it online!
import sys
nums = list(map(int, sys.stdin.read().split()))
pw, ph = nums[0:2]
ts = list(zip(nums[3::2], nums[4::2]))
assert len(ts) == nums[2]
if sum([e[0] * e[1] for e in ts]) != pw * ph:
print('Not possible!')
else:
def Solve(*, it = 0, p = None):
if p is None:
p = [[0] * pw for i in range(ph)]
if it >= len(ts):
for e0 in p:
for e1 in e0:
print(e1, end = ' ')
print()
return True
for tw, th in [(ts[it][0], ts[it][1]), (ts[it][1], ts[it][0])]:
zw = [0] * tw
ow = [it + 1] * tw
for i in range(ph - th + 1):
for j in range(pw - tw + 1):
if all(p[k][j : j + tw] == zw for k in range(i, i + th)):
for k in range(i, i + th):
p[k][j : j + tw] = ow
if Solve(it = it + 1, p = p):
return True
for k in range(i, i + th):
p[k][j : j + tw] = zw
return False
if not Solve():
print('Not possible!')
Example input:
4 3
3
2 3
1 2
2 2
Output:
1 1 2 2
1 1 3 3
1 1 3 3
algorithm question:
Given n points on a 2D plane, find the maximum number of points that lie on the same straight line.
Example 1:
Input: [[1,1],[2,2],[3,3]]
Output: 3
Explanation:
^
|
| o
| o
| o
+------------->
0 1 2 3 4
Example 2:
Input: [[1,1],[3,2],[5,3],[4,1],[2,3],[1,4]]
Output: 4
the working python 3 code is below:
wondering
snippet 1 d[slope] = d.get(slope, 1) + 1 is working
but why this snippet 2 is not working correctly for example 2 even though snippet 1 and 2 are the same
if slope in d:
d[slope] += 1
else:
d[slope] = 1
def gcd(self, a, b):
if b == 0:
return a
return self.gcd(b, a%b)
def get_slope(self, p1, p2):
dx = p1[0] - p2[0]
dy = p1[1] - p2[1]
c = self.gcd(dx, dy)
dx /= c
dy /= c
return str(dy) + "/" + str(dx)
def is_same_points(self, p1:List[int], p2:List[int]):
return p1[0] == p2[0] and p1[1] == p2[1]
def maxPoints(self, points: List[List[int]]) -> int:
if not points:
return 0
n = len(points)
count = 1
for i in range(0, n):
d = {}
duped = 0
localmax = 1
p1 = points[i]
for j in range(i+1, n):
p2 = points[j]
if self.is_same_points(p1, p2):
duped += 1
else:
slope = self.get_slope(p1, p2)
# 1) not work: output is 3 in example 2
# if slope in d:
# d[slope] += 1
# else:
# d[slope] = 1
# 2) works: correct output 4 for example 2
d[slope] = d.get(slope, 1) + 1
localmax = max(localmax, d[slope]);
count = max(count, localmax + duped)
return count
Interesting problem and nice solution.
The reason why the commented out code doesn't work is because of that:
else:
d[slope] = 1 ## correct would be d[slope] = 2
Every 2 points are on the same line, you are counting only one point for the first two p1 p2, thus you get one less in the final answer.
I am trying to understand the recursion function. I would like to know how that answer is coming with steps
def tri_recursion(k):
if(k>0):
result = k+tri_recursion(k-1)
print(result)
else:
result = 0
return result
print("\n\nRecursion Example Results")
tri_recursion(6)
results are this just want to know how its coming
1
3
6
10
15
21
The function computes the sum of all numbers between 0 and n, and prints intermediate results. The first 1 is 0+1, the 3 = 0+1+2, 6 = 0+1+2+3, 10 = 0+1+2+3+4, ...
To understand a recursive function, you need 2 points : how is the recursive call done, and when does the recursion stop.
The recursive call is given by result = k+tri_recursion(k-1)and the recursion stops when k <= 0and returns 0. So if we assume only positive numbers, we could describe tri_recursion so:
tri_recursion(k) = k + tri_recursion(k-1) if k > 0
tri_recursion(0) = 0
So tri_recursion(k) = k + tri_recursion(k-1) = k + (k-1) + tri_recursion(k-2) = k + (k-1) + (k-2) + tri_recursion(k-3) ... = k + (k-1) + (k-2) + ... + 0
So tri_recursion(k) is the sum of all numbers between 0 and k.
Note that the sum on all numbers between 0 and k equals k*(k+1) / 2 so tri_recursion(6) = 6 * 7 / 2 = 21
I need to find a way to write cos(1) in python using a while loop. But i cant use any math functions. Can someone help me out?
for example I also had to write the value of exp(1) and I was able to do it by writing:
count = 1
term = 1
expTotal = 0
xx = 1
while abs(term) > 1e-20:
print("%1d %22.17e" % (count, term))
expTotal = expTotal + term
term=term * xx/(count)
count+=1
I amm completely lost as for how to do this with the cos and sin values though.
Just change your expression to compute the term to:
term = term * (-1 * x * x)/( (2*count) * ((2*count)-1) )
Multiplying the count by 2 could be changed to increment the count by 2, so here is your copypasta:
import math
def cos(x):
cosTotal = 1
count = 2
term = 1
x=float(x)
while abs(term) > 1e-20:
term *= (-x * x)/( count * (count-1) )
cosTotal += term
count += 2
print("%1d %22.17e" % (count, term))
return cosTotal
print( cos(1) )
print( math.cos(1) )
You can calculate cos(1) by using the Taylor expansion of this function:
You can find more details on Wikipedia, see an implementation below:
import math
def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n-1)
def cos(order):
a = 0
for i in range(0, order):
a += ((-1)**i)/(factorial(2*i)*1.0)
return a
print cos(10)
print math.cos(1)
This gives as output:
0.540302305868
0.540302305868
EDIT: Apparently the cosine is implemented in hardware using the CORDIC algorithm that uses a lookup table to calculate atan. See below a Python implementation of the CORDIS algorithm based on this Google group question:
#atans = [math.atan(2.0**(-i)) for i in range(0,40)]
atans =[0.7853981633974483, 0.4636476090008061, 0.24497866312686414, 0.12435499454676144, 0.06241880999595735, 0.031239833430268277, 0.015623728620476831, 0.007812341060101111, 0.0039062301319669718, 0.0019531225164788188, 0.0009765621895593195, 0.0004882812111948983, 0.00024414062014936177, 0.00012207031189367021, 6.103515617420877e-05, 3.0517578115526096e-05, 1.5258789061315762e-05, 7.62939453110197e-06, 3.814697265606496e-06, 1.907348632810187e-06, 9.536743164059608e-07, 4.7683715820308884e-07, 2.3841857910155797e-07, 1.1920928955078068e-07, 5.960464477539055e-08, 2.9802322387695303e-08, 1.4901161193847655e-08, 7.450580596923828e-09, 3.725290298461914e-09, 1.862645149230957e-09, 9.313225746154785e-10, 4.656612873077393e-10, 2.3283064365386963e-10, 1.1641532182693481e-10, 5.820766091346741e-11, 2.9103830456733704e-11, 1.4551915228366852e-11, 7.275957614183426e-12, 3.637978807091713e-12, 1.8189894035458565e-12]
def cosine_sine_cordic(beta,N=40):
# in hardware, put this in a table.
def K_vals(n):
K = []
acc = 1.0
for i in range(0, n):
acc = acc * (1.0/(1 + 2.0**(-2*i))**0.5)
K.append(acc)
return K
#K = K_vals(N)
K = 0.6072529350088812561694
x = 1
y = 0
for i in range(0,N):
d = 1.0
if beta < 0:
d = -1.0
(x,y) = (x - (d*(2.0**(-i))*y), (d*(2.0**(-i))*x) + y)
# in hardware put the atan values in a table
beta = beta - (d*atans[i])
return (K*x, K*y)
if __name__ == '__main__':
beta = 1
cos_val, sin_val = cosine_sine_cordic(beta)
print "Actual cos: " + str(math.cos(beta))
print "Cordic cos: " + str(cos_val)
This gives as output:
Actual cos: 0.540302305868
Cordic cos: 0.540302305869