message stringlengths 2 59.7k | message_type stringclasses 2
values | message_id int64 0 1 | conversation_id int64 37 108k | cluster float64 20 20 | __index_level_0__ int64 74 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Xenia the beginner mathematician is a third year student at elementary school. She is now learning the addition operation.
The teacher has written down the sum of multiple numbers. Pupils should calculate the sum. To make the calculation easier, the sum only contains numbers 1, 2 and 3. Still, that isn't enough for Xenia. She is only beginning to count, so she can calculate a sum only if the summands follow in non-decreasing order. For example, she can't calculate sum 1+3+2+1 but she can calculate sums 1+1+2 and 3+3.
You've got the sum that was written on the board. Rearrange the summans and print the sum in such a way that Xenia can calculate the sum.
Input
The first line contains a non-empty string s — the sum Xenia needs to count. String s contains no spaces. It only contains digits and characters "+". Besides, string s is a correct sum of numbers 1, 2 and 3. String s is at most 100 characters long.
Output
Print the new sum that Xenia can count.
Examples
Input
3+2+1
Output
1+2+3
Input
1+1+3+1+3
Output
1+1+1+3+3
Input
2
Output
2
Submitted Solution:
```
#!/usr/bin/env python
# coding: utf-8
# In[26]:
s = list(map(str, input().split("+")))
s.sort()
result = ""
for i in s[:-1]:
result += i + "+"
result += s[-1]
print(result)
# In[5]:
# In[20]:
# In[ ]:
for i in s:
if i != s[len(s)-1]:
result += i + "+"
else:
result += i
print(result)
``` | instruction | 0 | 57,449 | 20 | 114,898 |
No | output | 1 | 57,449 | 20 | 114,899 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Xenia the beginner mathematician is a third year student at elementary school. She is now learning the addition operation.
The teacher has written down the sum of multiple numbers. Pupils should calculate the sum. To make the calculation easier, the sum only contains numbers 1, 2 and 3. Still, that isn't enough for Xenia. She is only beginning to count, so she can calculate a sum only if the summands follow in non-decreasing order. For example, she can't calculate sum 1+3+2+1 but she can calculate sums 1+1+2 and 3+3.
You've got the sum that was written on the board. Rearrange the summans and print the sum in such a way that Xenia can calculate the sum.
Input
The first line contains a non-empty string s — the sum Xenia needs to count. String s contains no spaces. It only contains digits and characters "+". Besides, string s is a correct sum of numbers 1, 2 and 3. String s is at most 100 characters long.
Output
Print the new sum that Xenia can count.
Examples
Input
3+2+1
Output
1+2+3
Input
1+1+3+1+3
Output
1+1+1+3+3
Input
2
Output
2
Submitted Solution:
```
s=input()
for i in range(0,len(s),2):
for j in range(0, i,2):
if (s[j]>s[i]):
temp=s[j]
s=s.replace(s[j],s[i])
s=s.replace(s[i],temp)
print(s)
``` | instruction | 0 | 57,450 | 20 | 114,900 |
No | output | 1 | 57,450 | 20 | 114,901 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z | instruction | 0 | 57,587 | 20 | 115,174 |
Tags: brute force, constructive algorithms, math
Correct Solution:
```
from math import log
from decimal import Decimal
asd=["x^y^z","x^z^y","(x^y)^z","(x^z)^y","y^x^z","y^z^x","(y^x)^z","(y^z)^x","z^x^y","z^y^x","(z^x)^y","(z^y)^x"]
ans=[]
x,y,z=map(Decimal,input().split())
def pow2(a,b):
return a**b
ans.append(x.ln()*pow2(y,z))
ans.append(x.ln()*pow2(z,y))
ans.append(x.ln()*y*z)
ans.append(x.ln()*y*z)
ans.append(y.ln()*pow2(x,z))
ans.append(y.ln()*pow2(z,x))
ans.append(y.ln()*x*z)
ans.append(y.ln()*x*z)
ans.append(z.ln()*pow2(x,y))
ans.append(z.ln()*pow2(y,x))
ans.append(z.ln()*y*x)
ans.append(z.ln()*y*x)
anss=-10000000000000000000000000000
for i in range(12):
if(ans[i]>anss):
anss=ans[i]
for i in range(12):
if(ans[i]==anss):
print(asd[i])
exit()
``` | output | 1 | 57,587 | 20 | 115,175 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z | instruction | 0 | 57,588 | 20 | 115,176 |
Tags: brute force, constructive algorithms, math
Correct Solution:
```
from math import log, inf
from itertools import product, permutations
def comp_key(p, A, mode):
a = log(A[p[0][1]])*A[p[0][2]] if p[1] else log(A[p[0][1]]) + log(A[p[0][2]])
k = A[p[0][0]] if mode else 1/A[p[0][0]]
return a + log(log(k)) if k > 1 else -inf
def solve(A):
mode = any((x > 1 for x in A))
c = (max if mode else min)(((x,y) for y in [True, False] for x in permutations(range(3))), key = lambda p: comp_key(p, A, mode))
k = 'xyz'
return ('{0}^{1}^{2}' if c[1] else '({0}^{1})^{2}').format(k[c[0][0]], k[c[0][1]], k[c[0][2]])
A = [float(s) for s in input().split()]
print(solve(A))
``` | output | 1 | 57,588 | 20 | 115,177 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z | instruction | 0 | 57,589 | 20 | 115,178 |
Tags: brute force, constructive algorithms, math
Correct Solution:
```
from math import log
from decimal import Decimal
x, y, z = [Decimal(x) for x in input().split()]
variants = sorted([
((y ** z) * Decimal(log(x)), -1),
((z ** y) * Decimal(log(x)), -2),
(y * z * Decimal(log(x)), -3),
((x ** z) * Decimal(log(y)), -5),
((z ** x) * Decimal(log(y)), -6),
(x * z * Decimal(log(y)), -7),
((x ** y) * Decimal(log(z)), -9),
((y ** x) * Decimal(log(z)), -10),
(x * y * Decimal(log(z)), -11)
])
expressions = [
"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y",
"y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x",
"z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"
]
print(expressions[abs(variants[-1][1]) - 1])
``` | output | 1 | 57,589 | 20 | 115,179 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z | instruction | 0 | 57,590 | 20 | 115,180 |
Tags: brute force, constructive algorithms, math
Correct Solution:
```
from decimal import *
getcontext().prec = 333
a,b,c = input().split()
x = Decimal(a)
y = Decimal(b)
z = Decimal(c)
l = [
(x).ln()*(y**z),
(x).ln()*(z**y),
(x**y).ln()*z,
(x**z).ln()*y,
(y).ln()*(x**z),
(y).ln()*(z**x),
(y**x).ln()*z,
(y**z).ln()*x,
(z).ln()*(x**y),
(z).ln()*(y**x),
(z**x).ln()*y,
(z**y).ln()*x
]
#getcontext().prec = 300
#l = [i.quantize(Decimal('.' + '0'*250 + '1'), rounding=ROUND_DOWN) for i in l]
#print(l)
m = max(l)
s = [
"x^y^z",
"x^z^y",
"(x^y)^z",
"(x^z)^y",
"y^x^z",
"y^z^x",
"(y^x)^z",
"(y^z)^x",
"z^x^y",
"z^y^x",
"(z^x)^y",
"(z^y)^x"
]
#for t in l:
# print(t)
i = 0
for j in range(12):
#print(abs(l[j]-m))
if abs(l[j]-m) < Decimal('.' + '0'*100 + '1'):
i = j
break
print(s[i])
``` | output | 1 | 57,590 | 20 | 115,181 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z | instruction | 0 | 57,591 | 20 | 115,182 |
Tags: brute force, constructive algorithms, math
Correct Solution:
```
from decimal import *
getcontext().prec = 500
x, y, z = map(float, input().split())
x = Decimal(x)
y = Decimal(y)
z = Decimal(z)
a = [Decimal(0) for i in range(12)]
a[0] = ((Decimal(x).log10()) * Decimal(Decimal(y) ** Decimal(z)))
a[1] = ((Decimal(x).log10()) * Decimal(Decimal(z) ** Decimal(y)))
a[2] = ((Decimal(x).log10()) * Decimal(Decimal(y) * Decimal(z)))
a[3] = ((Decimal(x).log10()) * Decimal(Decimal(y) * Decimal(z)))
a[4] = ((Decimal(y).log10()) * Decimal(Decimal(x) ** Decimal(z)))
a[5] = ((Decimal(y).log10()) * Decimal(Decimal(z) ** Decimal(x)))
a[6] = ((Decimal(y).log10()) * Decimal(Decimal(x) * Decimal(z)))
a[7] = ((Decimal(y).log10()) * Decimal(Decimal(x) * Decimal(z)))
a[8] = ((Decimal(z).log10()) * Decimal(Decimal(x) ** Decimal(y)))
a[9] = ((Decimal(z).log10()) * Decimal(Decimal(y) ** Decimal(x)))
a[10] = ((Decimal(z).log10()) * Decimal(Decimal(x) * Decimal(y)))
a[11] = ((Decimal(z).log10()) * Decimal(Decimal(x) * Decimal(y)))
maxx = a[0]
for i in range(12):
if a[i] > maxx:
maxx = a[i]
s = ["" for i in range(12)]
s[0] = "x^y^z"
s[1] = "x^z^y"
s[2] = "(x^y)^z"
s[3] = "(x^z)^y"
s[4] = "y^x^z"
s[5] = "y^z^x"
s[6] = "(y^x)^z"
s[7] = "(y^z)^x"
s[8] = "z^x^y"
s[9] = "z^y^x"
s[10] = "(z^x)^y"
s[11] = "(z^y)^x"
for i in range(12):
if a[i] == maxx:
print (s[i])
break
``` | output | 1 | 57,591 | 20 | 115,183 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z | instruction | 0 | 57,592 | 20 | 115,184 |
Tags: brute force, constructive algorithms, math
Correct Solution:
```
from math import log
def rk(x, y, z):
if x <= 1 and y <= 1 and z <= 1:
return rk1(x, y, z)
else:
return rk2(x, y, z)
def rk1(x, y, z):
if x == 1:
return 'x^y^z'
elif y == 1:
return 'y^x^z'
elif z == 1:
return 'z^x^y'
lx = log(x)
ly = log(y)
lz = log(z)
l2x = log(-lx)
l2y = log(-ly)
l2z = log(-lz)
a = [
(z*ly + l2x, 'x^y^z'),
(y*lz + l2x, 'x^z^y'),
(ly + lz + l2x, '(x^y)^z'),
(z*lx + l2y, 'y^x^z'),
(x*lz + l2y, 'y^z^x'),
(lz + lx + l2y, '(y^x)^z'),
(y*lx + l2z, 'z^x^y'),
(x*ly + l2z, 'z^y^x'),
(ly + lx + l2z, '(z^x)^y'),
]
return min(a, key=lambda t:t[0])[1]
def rk2(x, y, z):
lx = log(x)
ly = log(y)
lz = log(z)
a = []
if x > 1:
l2x = log(lx)
a += [
(z*ly + l2x, 'x^y^z'),
(y*lz + l2x, 'x^z^y'),
(ly + lz + l2x, '(x^y)^z'),
]
if y > 1:
l2y = log(ly)
a += [
(z*lx + l2y, 'y^x^z'),
(x*lz + l2y, 'y^z^x'),
(lz + lx + l2y, '(y^x)^z'),
]
if z > 1:
l2z = log(lz)
a += [
(y*lx + l2z, 'z^x^y'),
(x*ly + l2z, 'z^y^x'),
(ly + lx + l2z, '(z^x)^y'),
]
return max(a, key=lambda t:t[0])[1]
if __name__ == '__main__':
x, y, z = map(float, input().split())
print(rk(x, y, z))
``` | output | 1 | 57,592 | 20 | 115,185 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z | instruction | 0 | 57,593 | 20 | 115,186 |
Tags: brute force, constructive algorithms, math
Correct Solution:
```
from decimal import *
x, y, z = map(Decimal, input().split(' '))
getcontext().prec = 100
a = [0] * 9
a[0] = x.ln() * (y ** z)
a[1] = x.ln() * (z ** y)
a[2] = x.ln() * y * z
a[3] = y.ln() * (x ** z)
a[4] = y.ln() * (z ** x)
a[5] = y.ln() * x * z
a[6] = z.ln() * (x ** y)
a[7] = z.ln() * (y ** x)
a[8] = z.ln() * x * y
mx = 0
for i in range(9):
if abs(a[i] - a[mx]) > Decimal(10) ** (-50) and a[i] > a[mx]:
mx = i
s = [""] * 9
s[0] = "x^y^z"
s[1] = "x^z^y"
s[2] = "(x^y)^z"
s[3] = "y^x^z"
s[4] = "y^z^x"
s[5] = "(y^x)^z"
s[6] = "z^x^y"
s[7] = "z^y^x"
s[8] = "(z^x)^y"
print(s[mx])
``` | output | 1 | 57,593 | 20 | 115,187 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z | instruction | 0 | 57,594 | 20 | 115,188 |
Tags: brute force, constructive algorithms, math
Correct Solution:
```
from decimal import *
from math import log
def d_log(x):
return Decimal(log(x))
if __name__ == "__main__":
#getcontext().prec = 1024
x , y , z = map( Decimal , input().split() )
exps = [ ( (y**z)*d_log(x), 0),
( (z**y)*d_log(x), 1),
( z*y*d_log(x), 2),
#( y*d_log(x**z), 3),
( (x**z)*d_log(y), 4),
( (z**x)*d_log(y), 5),
( z*x*d_log(y), 6),
#( x*d_log(y**z), 7),
( (x**y)*d_log(z), 8),
( (y**x)*d_log(z), 9),
( y*x*d_log(z), 10),
#( x*d_log(z**y), 11),
]
exps.sort(key=lambda e:(-e[0],e[1]))
#for r,index in exps:
# print( "exp(", index, ") =" , r )
c = exps[0][1]
res = [ "x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y",
"y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x",
"z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"
]
print( res[c] )
``` | output | 1 | 57,594 | 20 | 115,189 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z
Submitted Solution:
```
import math
s = ['x^y^z',
'x^z^y',
'(x^y)^z',
'(x^z)^y',
'y^x^z',
'y^z^x',
'(y^x)^z',
'(y^z)^x',
'z^x^y',
'z^y^x',
'(z^x)^y',
'(z^y)^x']
x, y, z = map(float, input().split())
ma = float('-inf')
c = -1
if x > 1:
if ma < z * math.log(y) + math.log(math.log(x)):
ma = z * math.log(y) + math.log(math.log(x))
c = 0
if ma < y * math.log(z) + math.log(math.log(x)):
ma = y * math.log(z) + math.log(math.log(x))
c = 1
if ma < math.log(y) + math.log(z) + math.log(math.log(x)):
ma = math.log(y) + math.log(z) + math.log(math.log(x))
c = 2
if y > 1:
if ma < z * math.log(x) + math.log(math.log(y)):
ma = z * math.log(x) + math.log(math.log(y))
c = 4
if ma < x * math.log(z) + math.log(math.log(y)):
ma = x * math.log(z) + math.log(math.log(y))
c = 5
if ma < math.log(x) + math.log(z) + math.log(math.log(y)):
ma = math.log(x) + math.log(z) + math.log(math.log(y))
c = 6
if z > 1:
if ma < y * math.log(x) + math.log(math.log(z)):
ma = y * math.log(x) + math.log(math.log(z))
c = 8
if ma < x * math.log(y) + math.log(math.log(z)):
ma = x * math.log(y) + math.log(math.log(z))
c = 9
if ma < math.log(x) + math.log(y) + math.log(math.log(z)):
ma = math.log(x) + math.log(y) + math.log(math.log(z))
c = 10
# if max(x , y, z) <= 1
if c == -1:
if ma < x ** (y ** z):
ma = x ** (y ** z)
c = 0
if ma < x ** (z ** y):
ma = x ** (z ** y)
c = 1
if ma < (x ** y) ** z:
ma = (x ** y) ** z
c = 2
if ma < y ** (x ** z):
ma = y ** (x ** z)
c = 4
if ma < y ** (z ** x):
ma = y ** (z ** x)
c = 5
if ma < (y ** x) ** z:
ma = (y ** x) ** z
c = 6
if ma < z ** (x ** y):
ma = z ** (x ** y)
c = 8
if ma < z ** (y ** x):
ma = z ** (y ** x)
c = 9
if ma < (z ** x) ** y:
ma = (z ** x) ** y
c = 10
print(s[c])
``` | instruction | 0 | 57,595 | 20 | 115,190 |
Yes | output | 1 | 57,595 | 20 | 115,191 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z
Submitted Solution:
```
from decimal import *
x,y,z=map(Decimal,input().split())
print(max((y**z*x.ln(),9,'x^y^z'),(z**y*x.ln(),8,'x^z^y'),(y*z*x.ln(),7,'(x^y)^z'),
(x**z*y.ln(),6,'y^x^z'),(z**x*y.ln(),5,'y^z^x'),(z*x*y.ln(),4,'(y^x)^z'),(x**y*z.ln(),3,'z^x^y'),(y**x*z.ln(),2,'z^y^x'),(y*x*z.ln(),1,'(z^x)^y'))[2])
``` | instruction | 0 | 57,596 | 20 | 115,192 |
Yes | output | 1 | 57,596 | 20 | 115,193 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z
Submitted Solution:
```
from decimal import *
x, y, z = input().split()
x = Decimal(x)
y = Decimal(y)
z = Decimal(z)
cal1 = lambda x, y, z : y ** z * Decimal.log10(x)
cal2 = lambda x, y, z : y * z * Decimal.log10(x)
ans, v = "x^y^z", cal1(x, y, z)
if cal1(x, z, y) > v:
ans, v = "x^z^y", cal1(x, z, y)
if cal2(x, y, z) > v:
ans, v = "(x^y)^z", cal2(x, y, z)
if cal2(x, z, y) > v:
ans, v = "(x^z)^y", cal2(x, z, y)
if cal1(y, x, z) > v:
ans, v = "y^x^z", cal1(y, x, z)
if cal1(y, z, x) > v:
ans, v = "y^z^x", cal1(y, z, x)
if cal2(y, x, z) > v:
ans, v = "(y^x)^z", cal2(y, x, z)
if cal2(y, z, x) > v:
ans, v = "(y^z)^x", cal2(y, z, x)
if cal1(z, x, y) > v:
ans, v = "z^x^y", cal1(z, x, y)
if cal1(z, y, x) > v:
ans, v = "z^y^x", cal1(z, y, x)
if cal2(z, x, y) > v:
ans, v = "(z^x)^y", cal2(z, x, y)
if cal2(z, y, x) > v:
ans, v = "(z^y)^x", cal2(z, y, x)
print(ans)
``` | instruction | 0 | 57,597 | 20 | 115,194 |
Yes | output | 1 | 57,597 | 20 | 115,195 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z
Submitted Solution:
```
from math import *
from decimal import *
def p1(x, y, z):
return Decimal(log(x, 2)) * Decimal(Decimal(y) ** Decimal(z))
def p2(x, y, z):
return Decimal(log(x, 2)) * Decimal(Decimal(y) * Decimal(z))
x, y, z = map(float, input().split())
f = [p1(x, y, z), p1(x, z, y), p2(x, y, z), p2(x, z, y), p1(y, x, z), p1(y, z, x),
p2(y, x, z), p2(y, z, x), p1(z, x, y), p1(z, y, x), p2(z, x, y), p2(z, y, x)]
ans = ['x^y^z', 'x^z^y', '(x^y)^z', '(x^z)^y', 'y^x^z', 'y^z^x', '(y^x)^z', '(y^z)^x','z^x^y', 'z^y^x', '(z^x)^y', '(z^y)^x']
x = 0
eps = 1e-6
for i in range(0, 12):
if (f[i] > f[x] + Decimal(eps)):
x = i
print(ans[x])
``` | instruction | 0 | 57,598 | 20 | 115,196 |
Yes | output | 1 | 57,598 | 20 | 115,197 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z
Submitted Solution:
```
from decimal import *
from math import log
def d_log(x):
return Decimal(log(x))
if __name__ == "__main__":
#getcontext().prec = 1024
x , y , z = map( Decimal , input().split() )
exps = [ ( (y**z)*d_log(x), 0),
( (z**y)*d_log(x), 1),
( z*d_log(x**y), 2),
#( y*d_log(x**z), 3),
( (x**z)*d_log(y), 4),
( (z**x)*d_log(y), 5),
( z*d_log(y**x), 6),
#( x*d_log(y**z), 7),
( (x**y)*d_log(z), 8),
( (y**x)*d_log(z), 9),
( y*d_log(z**x), 10),
#( x*d_log(z**y), 11),
]
exps.sort(key=lambda e:(-e[0],e[1]))
#for r,index in exps:
# print( "exp(", index, ") =" , r )
c = exps[0][1]
res = [ "x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y",
"y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x",
"z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"
]
print( res[c] )
``` | instruction | 0 | 57,599 | 20 | 115,198 |
No | output | 1 | 57,599 | 20 | 115,199 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z
Submitted Solution:
```
from math import log
line = input()
line = line.split()
line = [float(x) for x in line]
nums = []
x,y,z = line
if(x<5 and y<5 and z<5):
strs = [
"x^y^z",
"x^z^y",
"(x^y)^z",
"(x^z)^y",
"y^x^z",
"y^z^x",
"(y^x)^z",
"(y^z)^x",
"z^x^y",
"z^y^x",
"(z^x)^y",
"(z^y)^x"
]
nums.append(y**z*log(x))
nums.append(z**y*log(x))
nums.append(y*z*log(x))
nums.append(z*y*log(x))
nums.append(x**z*log(y))
nums.append(z**x*log(y))
nums.append(x*z*log(y))
nums.append(z*x*log(y))
nums.append(x**y*log(z))
nums.append(y**x*log(z))
nums.append(x*y*log(z))
nums.append(y*x*log(z))
cur = 0
for i in range(0,12):
if(nums[i]>nums[cur]):
cur = i
print(strs[cur])
else:
strs = [
"x^y^z",
"x^z^y",
"(x^y)^z",
"y^x^z",
"y^z^x",
"(y^x)^z",
"z^x^y",
"z^y^x",
"(z^x)^y",
]
nums.append(z*log(y)+log(log(x)))
nums.append(y*log(z)+log(log(x)))
nums.append(log(y)+log(z)+log(log(x)))
nums.append(x*log(z)+log(log(y)))
nums.append(z*log(x)+log(log(y)))
nums.append(log(x)+log(z)+log(log(y)))
nums.append(x*log(y)+log(log(z)))
nums.append(y*log(x)+log(log(z)))
nums.append(log(x)+log(y)+log(log(z)))
cur = 0
for i in range(0,9):
print(nums[i])
if(nums[i]>nums[cur]):
cur = i
print(strs[cur])
``` | instruction | 0 | 57,600 | 20 | 115,200 |
No | output | 1 | 57,600 | 20 | 115,201 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z
Submitted Solution:
```
def solve():
m = 0
c = ''
s = list(map(float, input().split()))
f = ['x', 'y', 'z']
if max(s) <= 4:
return print(solve2(s))
s2 = sorted(s)
flag = False
if s2[0] < 2:
s2 = s2[1:] + s2[:1]
if s2[0] < 2:
s2[0], s2[1] = s2[1], s2[0]
if s2[1] * s2[2] > s2[1] ** s2[2]:
flag = True
ans = []
used = [0] * 3
for i in range(3):
j = s.index(s2[i])
while used[j]:
j = s.index(s2[i], j + 1, 3)
ans.append(f[j])
used[j] = 1
if flag:
if f.index(ans[2]) < f.index(ans[1]):
ans[1], ans[2] = ans[2], ans[1]
print(f'({ans[0]}^{ans[1]})^{ans[2]}')
else:
print(f'{ans[0]}^{ans[1]}^{ans[2]}')
def solve2(s):
m = 0
c = ''
f = ['x', 'y', 'z']
for i in range(3):
for j in range(2):
for e in range(3):
if e == i:
continue
cur = 0
if j == 0:
cur = (s[i]) ** ((s[e]) ** s[(3 ^ e) ^ i])
if cur > m:
m = cur
c = f'{f[i]}^{f[e]}^{f[(3 ^ e) ^ i]}'
else:
cur = (s[i]) ** (s[e] * s[(3 ^ e) ^ i])
if cur > m:
m = cur
c = f'({f[i]}^{f[e]})^{f[(3 ^ e) ^ i]}'
return c
solve()
``` | instruction | 0 | 57,601 | 20 | 115,202 |
No | output | 1 | 57,601 | 20 | 115,203 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.
Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:
1. a1 = xyz;
2. a2 = xzy;
3. a3 = (xy)z;
4. a4 = (xz)y;
5. a5 = yxz;
6. a6 = yzx;
7. a7 = (yx)z;
8. a8 = (yz)x;
9. a9 = zxy;
10. a10 = zyx;
11. a11 = (zx)y;
12. a12 = (zy)x.
Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.
Input
The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.
Output
Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.
xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).
Examples
Input
1.1 3.4 2.5
Output
z^y^x
Input
2.0 2.0 2.0
Output
x^y^z
Input
1.9 1.8 1.7
Output
(x^y)^z
Submitted Solution:
```
def POW(x, y):
return pow(x, y)
x, y, z = map(float, input().split())
while x > 4:
x /= 2
while y > 4:
y /= 2
while z > 4:
z /= 2
mn = POW(x, POW(y, z))
mn = max(mn, POW(x, POW(z, y)))
mn = max(mn, POW(POW(x, y), z))
mn = max(mn, POW(POW(x, z), y))
mn = max(mn, POW(y, POW(x, z)))
mn = max(mn, POW(y, POW(z, x)))
mn = max(mn, POW(POW(y, x), z))
mn = max(mn, POW(POW(y, z), x))
mn = max(mn, POW(z, POW(x, y)))
mn = max(mn, POW(z, POW(y, x)))
mn = max(mn, POW(POW(z, x), y))
mn = max(mn, POW(POW(z, y), x))
mn -= 0.00000000000000001
if POW(x, POW(y, z)) >= mn:
print("x^y^z")
elif POW(x, POW(z, y)) >= mn:
print("x^z^y")
elif POW(POW(x, y), z) >= mn:
print("(x^y)^z")
elif POW(POW(x, z), y) >= mn:
print("(x^z)^y")
elif POW(y, POW(x, z)) >= mn:
print("y^x^z")
elif POW(y, POW(z, x)) >= mn:
print("y^z^x")
elif POW(POW(y, x), z) >= mn:
print("(y^x)^z")
elif POW(POW(y, z), x) >= mn:
print("(x^z)^x")
elif POW(z, POW(x, y)) >= mn:
print("z^x^y")
elif POW(z, POW(y, x)) >= mn:
print("z^y^x")
elif POW(POW(z, x), y) >= mn:
print("(z^x)^y")
elif POW(POW(z, y), x) >= mn:
print("(z^y)^x")
``` | instruction | 0 | 57,602 | 20 | 115,204 |
No | output | 1 | 57,602 | 20 | 115,205 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In late autumn evening n robots gathered in the cheerful company of friends. Each robot has a unique identifier — an integer from 1 to 109.
At some moment, robots decided to play the game "Snowball". Below there are the rules of this game. First, all robots stand in a row. Then the first robot says his identifier. After that the second robot says the identifier of the first robot and then says his own identifier. Then the third robot says the identifier of the first robot, then says the identifier of the second robot and after that says his own. This process continues from left to right until the n-th robot says his identifier.
Your task is to determine the k-th identifier to be pronounced.
Input
The first line contains two positive integers n and k (1 ≤ n ≤ 100 000, 1 ≤ k ≤ min(2·109, n·(n + 1) / 2).
The second line contains the sequence id1, id2, ..., idn (1 ≤ idi ≤ 109) — identifiers of roborts. It is guaranteed that all identifiers are different.
Output
Print the k-th pronounced identifier (assume that the numeration starts from 1).
Examples
Input
2 2
1 2
Output
1
Input
4 5
10 4 18 3
Output
4
Note
In the first sample identifiers of robots will be pronounced in the following order: 1, 1, 2. As k = 2, the answer equals to 1.
In the second test case identifiers of robots will be pronounced in the following order: 10, 10, 4, 10, 4, 18, 10, 4, 18, 3. As k = 5, the answer equals to 4.
Submitted Solution:
```
'''input
3 4
4 5 6
'''
from math import floor
n, k = map(int, input().split())
i = list(map(int, input().split()))
x = floor((2*k)**0.5)
print(i[k - x*(x+1)//2 - 1])
``` | instruction | 0 | 57,631 | 20 | 115,262 |
No | output | 1 | 57,631 | 20 | 115,263 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers' kids solve this riddle in 5-10 minutes. How fast can you do it?
Input
The input contains a single integer n (0 ≤ n ≤ 2000000000).
Output
Output a single integer.
Examples
Input
11
Output
2
Input
14
Output
0
Input
61441
Output
2
Input
571576
Output
10
Input
2128506
Output
3 | instruction | 0 | 57,661 | 20 | 115,322 |
Tags: *special
Correct Solution:
```
n = int(input())
summa = 0
first = True
while n>0 or first:
first = False
x = n%16
n //= 16
if x==4 or x==0 or x==6 or x==9 or x==10 or x==13:
summa += 1
if x==8 or x==11:
summa += 2
print(summa)
``` | output | 1 | 57,661 | 20 | 115,323 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers' kids solve this riddle in 5-10 minutes. How fast can you do it?
Input
The input contains a single integer n (0 ≤ n ≤ 2000000000).
Output
Output a single integer.
Examples
Input
11
Output
2
Input
14
Output
0
Input
61441
Output
2
Input
571576
Output
10
Input
2128506
Output
3 | instruction | 0 | 57,662 | 20 | 115,324 |
Tags: *special
Correct Solution:
```
cur = int(input())
hex = ""
shit = ['A', 'B', 'C', 'D', 'E', 'F']
if cur == 0:
print(1)
exit(0)
while cur != 0:
temp = cur % 16
cur = cur // 16
if temp >= 10:
hex += shit[temp - 10]
else:
hex += str(temp)
answ = 0
for a in hex:
if a == 'A' or a == '6' or a == '0' or a == 'D' or a == '4' or a == '9':
answ = answ + 1
elif a == '8' or a == 'B':
answ += 2
print(answ)
``` | output | 1 | 57,662 | 20 | 115,325 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers' kids solve this riddle in 5-10 minutes. How fast can you do it?
Input
The input contains a single integer n (0 ≤ n ≤ 2000000000).
Output
Output a single integer.
Examples
Input
11
Output
2
Input
14
Output
0
Input
61441
Output
2
Input
571576
Output
10
Input
2128506
Output
3 | instruction | 0 | 57,663 | 20 | 115,326 |
Tags: *special
Correct Solution:
```
def count(x):
if x == 0:
return 1
ans = 0
holes = [1, 0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 2, 0, 1, 0, 0]
while x:
ans += holes[x % 16]
x //= 16
return ans
print(count(int(input())))
``` | output | 1 | 57,663 | 20 | 115,327 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers' kids solve this riddle in 5-10 minutes. How fast can you do it?
Input
The input contains a single integer n (0 ≤ n ≤ 2000000000).
Output
Output a single integer.
Examples
Input
11
Output
2
Input
14
Output
0
Input
61441
Output
2
Input
571576
Output
10
Input
2128506
Output
3 | instruction | 0 | 57,664 | 20 | 115,328 |
Tags: *special
Correct Solution:
```
a = int(input())
h = hex(a)
s = str(h)[2:]
oneHole = ['0', '4', '6', '9', 'a', 'd']
twoHoles = ['8', 'b']
count = 0
for i in range(len(s)):
if s[i] in oneHole:
count += 1
elif s[i] in twoHoles:
count += 2
print(count)
``` | output | 1 | 57,664 | 20 | 115,329 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers' kids solve this riddle in 5-10 minutes. How fast can you do it?
Input
The input contains a single integer n (0 ≤ n ≤ 2000000000).
Output
Output a single integer.
Examples
Input
11
Output
2
Input
14
Output
0
Input
61441
Output
2
Input
571576
Output
10
Input
2128506
Output
3 | instruction | 0 | 57,665 | 20 | 115,330 |
Tags: *special
Correct Solution:
```
"""
Codeforces April Fools Contest 2017 Problem B
Author : chaotic_iak
Language: Python 3.5.2
"""
################################################### SOLUTION
def main():
n, = read()
n = hex(n).upper()[2:]
dc = [1,0,0,0,1,0,1,0,2,1,1,2,0,1,0,0]
sm = 0
for c in n:
if ord(c) < 58:
sm += dc[ord(c)-48]
else:
sm += dc[ord(c)-65+10]
print(sm)
#################################################### HELPERS
def read(callback=int):
return list(map(callback, input().strip().split()))
def write(value, end="\n"):
if value is None: return
try:
if not isinstance(value, str):
value = " ".join(map(str, value))
except:
pass
print(value, end=end)
write(main())
``` | output | 1 | 57,665 | 20 | 115,331 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers' kids solve this riddle in 5-10 minutes. How fast can you do it?
Input
The input contains a single integer n (0 ≤ n ≤ 2000000000).
Output
Output a single integer.
Examples
Input
11
Output
2
Input
14
Output
0
Input
61441
Output
2
Input
571576
Output
10
Input
2128506
Output
3 | instruction | 0 | 57,666 | 20 | 115,332 |
Tags: *special
Correct Solution:
```
x = int(input(""))
x = hex(x)[2:]
one = ['0', '4', '6', '9', 'a', 'd']
two = ['8', 'b']
count = 0
for i in x:
if(i in one):
count += 1
elif(i in two):
count += 2
print(count)
``` | output | 1 | 57,666 | 20 | 115,333 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers' kids solve this riddle in 5-10 minutes. How fast can you do it?
Input
The input contains a single integer n (0 ≤ n ≤ 2000000000).
Output
Output a single integer.
Examples
Input
11
Output
2
Input
14
Output
0
Input
61441
Output
2
Input
571576
Output
10
Input
2128506
Output
3 | instruction | 0 | 57,667 | 20 | 115,334 |
Tags: *special
Correct Solution:
```
n = int(input())
r = (
(1, 0), (2, 0), (3, 0), (4, 1),
(5, 0), (6, 1), (7, 0), (8, 2),
(9, 1), (10, 1), (11, 2), (12, 0),
(13, 1), (14, 0), (15, 0), (0, 1), )
d = dict(r)
if n == 0 :
print(1)
else :
ans = 0
while n > 0 :
p = n - (n // 16) * 16;
n //= 16;
ans += d[p]
print(ans)
``` | output | 1 | 57,667 | 20 | 115,335 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers' kids solve this riddle in 5-10 minutes. How fast can you do it?
Input
The input contains a single integer n (0 ≤ n ≤ 2000000000).
Output
Output a single integer.
Examples
Input
11
Output
2
Input
14
Output
0
Input
61441
Output
2
Input
571576
Output
10
Input
2128506
Output
3 | instruction | 0 | 57,668 | 20 | 115,336 |
Tags: *special
Correct Solution:
```
s = hex(int(input()))[2:].upper()
x = 0
x += s.count('0')
x += s.count('4')
x += s.count('6')
x += s.count('8') << 1
x += s.count('9')
x += s.count('A')
x += s.count('B') << 1
x += s.count('D')
print(x)
``` | output | 1 | 57,668 | 20 | 115,337 |
Provide a correct Python 3 solution for this coding contest problem.
Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.
Constraints
* 1 \leq N < 10^{100}
* 1 \leq K \leq 3
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the count.
Examples
Input
100
1
Output
19
Input
25
2
Output
14
Input
314159
2
Output
937
Input
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3
Output
117879300 | instruction | 0 | 57,784 | 20 | 115,568 |
"Correct Solution:
```
from functools import lru_cache
@lru_cache(None)
def f(n,k):
if n<10:
if k<1: return 1
if k<2: return n
return 0
d,m=divmod(n,10)
c=0
if k:
c+=f(d,k-1)*m
c+=f(d-1,k-1)*(9-m)
c+=f(d,k)
return c
print(f(int(input()),int(input())))
``` | output | 1 | 57,784 | 20 | 115,569 |
Provide a correct Python 3 solution for this coding contest problem.
Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.
Constraints
* 1 \leq N < 10^{100}
* 1 \leq K \leq 3
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the count.
Examples
Input
100
1
Output
19
Input
25
2
Output
14
Input
314159
2
Output
937
Input
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3
Output
117879300 | instruction | 0 | 57,785 | 20 | 115,570 |
"Correct Solution:
```
digits = [int(c) for c in input()]
n = len(digits)
m = int(input())
dp = [[[0 for _ in range(2)] for _ in range(m + 1)] for _ in range(n + 1)]
dp[0][0][0] = 1
for i, digit in enumerate(digits):
for j in range(m + 1):
for k in range(2):
for d in range(10 if k else digit + 1):
if j + (d > 0) <= m:
dp[i + 1][j + (d > 0)][k or (d < digit)] += dp[i][j][k]
print(sum(dp[n][m]))
``` | output | 1 | 57,785 | 20 | 115,571 |
Provide a correct Python 3 solution for this coding contest problem.
Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.
Constraints
* 1 \leq N < 10^{100}
* 1 \leq K \leq 3
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the count.
Examples
Input
100
1
Output
19
Input
25
2
Output
14
Input
314159
2
Output
937
Input
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3
Output
117879300 | instruction | 0 | 57,787 | 20 | 115,574 |
"Correct Solution:
```
def calc(a,D,K):
if K==1:
return a+(D-1)*9
elif K==2:
return (a-1)*(D-1)*9 + (D-1)*(D-2)//2*81
else:
return (a-1)*(D-1)*(D-2)//2*81 + (D-1)*(D-2)*(D-3)//6*729
N=input()
K=int(input())
D = len(N)
score=0
for i,a in enumerate(N):
if a!="0":
score+=calc(int(a),D-i,K)
K-=1
if K==0:
break
print(score)
``` | output | 1 | 57,787 | 20 | 115,575 |
Provide a correct Python 3 solution for this coding contest problem.
Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.
Constraints
* 1 \leq N < 10^{100}
* 1 \leq K \leq 3
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the count.
Examples
Input
100
1
Output
19
Input
25
2
Output
14
Input
314159
2
Output
937
Input
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3
Output
117879300 | instruction | 0 | 57,790 | 20 | 115,580 |
"Correct Solution:
```
N = int(input())
K = int(input())
def func(num,counter):
remain = num%10
quotient = num//10
if counter == 0:
return 1
if num<10:
if counter ==1:
return num
else:
return 0
return func(quotient,counter-1)*remain + func(quotient-1,counter-1)*(9-remain) + func(quotient,counter)
print(func(N,K))
``` | output | 1 | 57,790 | 20 | 115,581 |
Provide a correct Python 3 solution for this coding contest problem.
Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.
Constraints
* 1 \leq N < 10^{100}
* 1 \leq K \leq 3
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the count.
Examples
Input
100
1
Output
19
Input
25
2
Output
14
Input
314159
2
Output
937
Input
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3
Output
117879300 | instruction | 0 | 57,791 | 20 | 115,582 |
"Correct Solution:
```
s=input();n=len(s)
def f(i,t,k):
if k>n-i:return 0
a=max(t,int(s[i]));i+=1;
return(f(i,9,k)+(a-1)*f(i,9,k-1)+f(i,t,k-1)if k-1 else a+(n-i)*9)if a else f(i,t,k)
print(f(0,0,int(input())))
``` | output | 1 | 57,791 | 20 | 115,583 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.
Constraints
* 1 \leq N < 10^{100}
* 1 \leq K \leq 3
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the count.
Examples
Input
100
1
Output
19
Input
25
2
Output
14
Input
314159
2
Output
937
Input
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3
Output
117879300
Submitted Solution:
```
from math import factorial as f
from functools import reduce
def C(n,k):
a,b=sorted((k,n-k))
return reduce(int.__mul__, range(b+1,n+1),1) // f(a)
def almost_everywhere_zero(v, k):
if not v or not k: return 0
s = str(v)
n,d = len(s), int(s[0])
if k>n: return 0
below = 9**k * C(n-1,k) if n>k else 0
return below + ( d if k==1 else (d-1) * 9**(k-1) * C(n-1,k-1) + almost_everywhere_zero(int(s[1:]), k-1) )
N = input()
K = int(input())
print(almost_everywhere_zero(N,K))
``` | instruction | 0 | 57,793 | 20 | 115,586 |
Yes | output | 1 | 57,793 | 20 | 115,587 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.
Constraints
* 1 \leq N < 10^{100}
* 1 \leq K \leq 3
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the count.
Examples
Input
100
1
Output
19
Input
25
2
Output
14
Input
314159
2
Output
937
Input
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3
Output
117879300
Submitted Solution:
```
def calc(n,k):
while n[0] == '0' and len(n)>1:
n=n[1:]
digit = len(n)
if digit < k:
return 0
comb = [1]*(k+1)
for i in range(1,k+1):
comb[i] = comb[i-1] * (digit-i) //i
if k==1:
return 9*comb[1] + int(n[0])
elif k==2:
return (9**2)*comb[2] + (int(n[0])-1) * 9*comb[1] + calc(n[1:],1)
elif k==3:
return (9**3)*comb[3] + (int(n[0])-1) * (9**2) * comb[2] + calc(n[1:],2)
n=input()
k=int(input())
print(calc(n,k))
``` | instruction | 0 | 57,795 | 20 | 115,590 |
Yes | output | 1 | 57,795 | 20 | 115,591 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.
Constraints
* 1 \leq N < 10^{100}
* 1 \leq K \leq 3
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the count.
Examples
Input
100
1
Output
19
Input
25
2
Output
14
Input
314159
2
Output
937
Input
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3
Output
117879300
Submitted Solution:
```
from scipy.misc import comb
def f(n_str, k):
while n_str[0] == '0':
n_str = n_str[1:]
if n_str == "":
return 0
if k == 1:
return int(n_str[0]) + 9 * (len(n_str) - 1)
else:
return (int(n_str[0]) - 1) * f('9' * (len(n_str) - 1), k - 1) + f(n_str[1:], k - 1) + 9 ** k * comb(len(n_str) - 1, k, exact=True)
n = input()
k = int(input())
print(f(n, k))
``` | instruction | 0 | 57,797 | 20 | 115,594 |
No | output | 1 | 57,797 | 20 | 115,595 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.
Constraints
* 1 \leq N < 10^{100}
* 1 \leq K \leq 3
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the count.
Examples
Input
100
1
Output
19
Input
25
2
Output
14
Input
314159
2
Output
937
Input
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3
Output
117879300
Submitted Solution:
```
N = int(input())
K = int(input())
keta = len(str(N))
suu = []
for i in range(keta):
suu += [int(str(N)[i])]
ans = 0
if K == 1:
for i in range(len(str(N))):
if i > 0:
ans += 9
else :
ans += int(str(N)[i])
print(ans)
elif K == 2:
# top桁を0にする
if keta -1 >= 2:
ans += (keta-1)*(keta-2)//2 * 9*9
# top桁に数字が入る
if keta >= 2:
# top桁はNより小さい
ans += (int(str(N)[0])-1) * (keta-1) * 9
# top桁がNに一致
ans += suu[1] + 9 * (keta-2)
print(ans)
else:
# top桁を0にする
if keta - 1 >= 3:
ans += (keta-1)*(keta-2)*(keta-3)//6 * 9*9*9
if keta >= 3:
#top桁はNより小さい
ans += (int(str(N)[0])-1) * (keta-1)*(keta-2)//2 * 9 * 9
#top桁はNに一致し、かつ次の桁が0
ans += (keta-2)*(keta-3)//2 * 9 * 9
#top桁はNに一致し、かつ次の桁がNより小さい
ans += (int(str(N)[1])-1) * (keta-2) * 9
#top桁はNに一致し、かつ次の桁もNに一致
ans += suu[2] + 9 * (keta-3)
print(ans)
``` | instruction | 0 | 57,799 | 20 | 115,598 |
No | output | 1 | 57,799 | 20 | 115,599 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
One day Petya dreamt of a lexicographically k-th permutation of integers from 1 to n. Determine how many lucky numbers in the permutation are located on the positions whose indexes are also lucky numbers.
Input
The first line contains two integers n and k (1 ≤ n, k ≤ 109) — the number of elements in the permutation and the lexicographical number of the permutation.
Output
If the k-th permutation of numbers from 1 to n does not exist, print the single number "-1" (without the quotes). Otherwise, print the answer to the problem: the number of such indexes i, that i and ai are both lucky numbers.
Examples
Input
7 4
Output
1
Input
4 7
Output
1
Note
A permutation is an ordered set of n elements, where each integer from 1 to n occurs exactly once. The element of permutation in position with index i is denoted as ai (1 ≤ i ≤ n). Permutation a is lexicographically smaller that permutation b if there is such a i (1 ≤ i ≤ n), that ai < bi, and for any j (1 ≤ j < i) aj = bj. Let's make a list of all possible permutations of n elements and sort it in the order of lexicographical increasing. Then the lexicographically k-th permutation is the k-th element of this list of permutations.
In the first sample the permutation looks like that:
1 2 3 4 6 7 5
The only suitable position is 4.
In the second sample the permutation looks like that:
2 1 3 4
The only suitable position is 4. | instruction | 0 | 58,136 | 20 | 116,272 |
Tags: brute force, combinatorics, number theory
Correct Solution:
```
def lucky(x):
s=str(x)
return s.count('4')+s.count('7')==len(s)
def Gen_lucky(n):
if(len(n)==1):
if(n<"4"):
return 0
if(n<"7"):
return 1
return 2
s=str(n)
if(s[0]<'4'):
return 0
if(s[0]=='4'):
return Gen_lucky(s[1:])
if(s[0]<'7'):
return 2**(len(s)-1)
if(s[0]=='7'):
return 2**(len(s)-1)+Gen_lucky(s[1:])
else:
return 2**len(s)
def Form(X,k):
if(k==0):
return X
for i in range(len(X)):
if(k>=F[len(X)-i-1]):
h=k//F[len(X)-i-1]
r=k%F[len(X)-i-1]
G=list(X[i+1:])
G.remove(X[i+h])
G=[X[i]]+G
return Form(X[:i]+[X[i+h]]+G,r)
p=1
F=[1]
i=1
while(p<=10**15):
p*=i
F.append(p)
i+=1
n,k=map(int,input().split())
if(n<=14):
if(k>F[n]):
print(-1)
else:
L=Form(list(range(1,n+1)),k-1)
x=0
for i in range(n):
if(lucky(i+1) and lucky(L[i])):
x+=1
print(x)
else:
L=Form(list(range(n-14,n+1)),k-1)
ss=str(n-15)
x=0
for i in range(1,len(ss)):
x+=2**i
x+=Gen_lucky(ss)
for i in range(n-14,n+1):
if(lucky(L[i-n+14]) and lucky(i)):
x+=1
print(x)
``` | output | 1 | 58,136 | 20 | 116,273 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
One day Petya dreamt of a lexicographically k-th permutation of integers from 1 to n. Determine how many lucky numbers in the permutation are located on the positions whose indexes are also lucky numbers.
Input
The first line contains two integers n and k (1 ≤ n, k ≤ 109) — the number of elements in the permutation and the lexicographical number of the permutation.
Output
If the k-th permutation of numbers from 1 to n does not exist, print the single number "-1" (without the quotes). Otherwise, print the answer to the problem: the number of such indexes i, that i and ai are both lucky numbers.
Examples
Input
7 4
Output
1
Input
4 7
Output
1
Note
A permutation is an ordered set of n elements, where each integer from 1 to n occurs exactly once. The element of permutation in position with index i is denoted as ai (1 ≤ i ≤ n). Permutation a is lexicographically smaller that permutation b if there is such a i (1 ≤ i ≤ n), that ai < bi, and for any j (1 ≤ j < i) aj = bj. Let's make a list of all possible permutations of n elements and sort it in the order of lexicographical increasing. Then the lexicographically k-th permutation is the k-th element of this list of permutations.
In the first sample the permutation looks like that:
1 2 3 4 6 7 5
The only suitable position is 4.
In the second sample the permutation looks like that:
2 1 3 4
The only suitable position is 4.
Submitted Solution:
```
def lucky(x):
s=str(x)
return s.count('4')+s.count('7')==len(s)
def Gen_lucky(n):
s=str(n)
if(len(s)==1):
if(s[0]=='4' or s[0]=='7'):
return 1
return 0
x=0
for i in range(1,len(s)):
x+=2**i
if(s[0]<'4'):
return x
if(s[0]>'7'):
return x+2**len(s)
if(s[0]=='5' or s[0]=='6'):
return x+(2**(len(s)-1))
if(s[0]=='7'):
x+=2**(len(s)-1)
x+=Getlucky(s[1:])
return x
def Form(X,k):
if(k==0):
return X
for i in range(len(X)):
if(k>=F[len(X)-i-1]):
h=k//F[len(X)-i-1]
r=k%F[len(X)-i-1]
X[i],X[i+h]=X[i+h],X[i]
return [X[0]]+Form(X[1:],r)
p=1
F=[1]
i=1
while(p<=10**10):
p*=i
F.append(p)
i+=1
n,k=map(int,input().split())
if(n<=15):
L=Form(list(range(1,n+1)),k-1)
x=0
for i in range(n):
if(lucky(i+1) and lucky(L[i])):
x+=1
print(x)
else:
L=Form(list(range(n-13,n+1)),k-1)
x=Gen_lucky(n-14)
for i in range(n-13,n+1):
if(lucky(L[i-n+13]) and lucky(i)):
x+=1
print(x)
``` | instruction | 0 | 58,137 | 20 | 116,274 |
No | output | 1 | 58,137 | 20 | 116,275 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0 | instruction | 0 | 58,185 | 20 | 116,370 |
Tags: implementation, math
Correct Solution:
```
def maxreg(n):
c=0
while n>=3**c:
c+=1
return c
def totri(k,n):
tr=1
v=k*[0]
for c in range(k-1,-1,-1):
v[c]=n//3**c
n%=3**c
return v
def fromtri(v):
sm=0
for c,t in enumerate(v):
sm+=t*3**c
return sm
def getminnum(av,cv):
rv=[]
for c in range(len(av)):
rv.append((cv[c]+3-av[c])%3)
return fromtri(rv)
a,c=map(int,input().split(' '))
mr=max(maxreg(a),maxreg(c))
print(getminnum(totri(mr,a),totri(mr,c)))
``` | output | 1 | 58,185 | 20 | 116,371 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0 | instruction | 0 | 58,186 | 20 | 116,372 |
Tags: implementation, math
Correct Solution:
```
a, c = map(int, input().split())
b, i = 0, 1
while a > 0 or c > 0:
b += i * (((c % 3) - (a % 3)) % 3)
i *= 3
a //= 3
c //= 3
print(b)
``` | output | 1 | 58,186 | 20 | 116,373 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0 | instruction | 0 | 58,187 | 20 | 116,374 |
Tags: implementation, math
Correct Solution:
```
"""
Author - Satwik Tiwari .
4th Oct , 2020 - Sunday
"""
#===============================================================================================
#importing some useful libraries.
from __future__ import division, print_function
from fractions import Fraction
import sys
import os
from io import BytesIO, IOBase
# from itertools import *
from heapq import *
from math import gcd, factorial,floor,ceil
from copy import deepcopy
from collections import deque
# from collections import Counter as counter # Counter(list) return a dict with {key: count}
# from itertools import combinations as comb # if a = [1,2,3] then print(list(comb(a,2))) -----> [(1, 2), (1, 3), (2, 3)]
# from itertools import permutations as permutate
from bisect import bisect_left as bl
from bisect import bisect_right as br
from bisect import bisect
#==============================================================================================
#fast I/O region
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
def print(*args, **kwargs):
"""Prints the values to a stream, or to sys.stdout by default."""
sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
at_start = True
for x in args:
if not at_start:
file.write(sep)
file.write(str(x))
at_start = False
file.write(kwargs.pop("end", "\n"))
if kwargs.pop("flush", False):
file.flush()
if sys.version_info[0] < 3:
sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
# inp = lambda: sys.stdin.readline().rstrip("\r\n")
#===============================================================================================
### START ITERATE RECURSION ###
from types import GeneratorType
def iterative(f, stack=[]):
def wrapped_func(*args, **kwargs):
if stack: return f(*args, **kwargs)
to = f(*args, **kwargs)
while True:
if type(to) is GeneratorType:
stack.append(to)
to = next(to)
continue
stack.pop()
if not stack: break
to = stack[-1].send(to)
return to
return wrapped_func
#### END ITERATE RECURSION ####
#===============================================================================================
#some shortcuts
mod = 10**9+7
def inp(): return sys.stdin.readline().rstrip("\r\n") #for fast input
def out(var): sys.stdout.write(str(var)) #for fast output, always take string
def lis(): return list(map(int, inp().split()))
def stringlis(): return list(map(str, inp().split()))
def sep(): return map(int, inp().split())
def strsep(): return map(str, inp().split())
# def graph(vertex): return [[] for i in range(0,vertex+1)]
def zerolist(n): return [0]*n
def nextline(): out("\n") #as stdout.write always print sring.
def testcase(t):
for pp in range(t):
solve(pp)
def printlist(a) :
for p in range(0,len(a)):
out(str(a[p]) + ' ')
def google(p):
print('Case #'+str(p)+': ',end='')
def lcm(a,b): return (a*b)//gcd(a,b)
def power(x, y, p) :
res = 1 # Initialize result
x = x % p # Update x if it is more , than or equal to p
if (x == 0) :
return 0
while (y > 0) :
if ((y & 1) == 1) : # If y is odd, multiply, x with result
res = (res * x) % p
y = y >> 1 # y = y/2
x = (x * x) % p
return res
def ncr(n,r): return factorial(n) // (factorial(r) * factorial(max(n - r, 1)))
def isPrime(n) :
if (n <= 1) : return False
if (n <= 3) : return True
if (n % 2 == 0 or n % 3 == 0) : return False
i = 5
while(i * i <= n) :
if (n % i == 0 or n % (i + 2) == 0) :
return False
i = i + 6
return True
#===============================================================================================
# code here ;))
def safe(x,y,n,m):
return (0<=x<n and 0<=y<m)
def solve(case):
n,m = sep()
a = []
b = []
while(n!=0):
a.append(n%3)
n//=3
while(m!=0):
b.append(m%3)
m//=3
if(len(a)<=len(b)):
for i in range(len(b) - len(a)):
a.append(0)
else:
for i in range(len(a) - len(b)):
b.append(0)
# print(a)
# print(b)
ans = []
for i in range(len(a)):
ans.append(( - a[i] + b[i])%3)
# print(ans)
num = 0
for i in range(len(ans)):
num+=(3**i)*ans[i]
print(num)
testcase(1)
# testcase(int(inp()))
``` | output | 1 | 58,187 | 20 | 116,375 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0 | instruction | 0 | 58,188 | 20 | 116,376 |
Tags: implementation, math
Correct Solution:
```
from math import floor , sqrt
from sys import stdin
# input = stdin.readline
def convertToTernary(a):
if a == 0:
return ''
return convertToTernary(a//3) + str(a%3)
for _ in range(1):
a , c = map(int , input().split())
A = convertToTernary(a)
C = convertToTernary(c)
# print(A, C)
# print(len(A), len(C))
A = '0'*(max(0, len(C) - len(A))) + A
C = '0'*(max(0, len(A) - len(C))) + C
B = ''
for i in range(len(A)):
if A[i] == '0':
B = B + str(int(C[i]) - int(A[i]))
elif A[i] == '1':
if C[i] == '0':
B = B + '2'
elif C[i] == '1':
B = B + '0'
else:
B = B + '1'
else:
if C[i] == '0':
B = B + '1'
elif C[i] == '1':
B = B + '2'
else:
B = B + '0'
b = 0
# print(B)
for i in range(len(A) - 1 , -1, -1):
b += int(B[i])*(3**(len(A) - 1 - i))
print(b)
``` | output | 1 | 58,188 | 20 | 116,377 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0 | instruction | 0 | 58,189 | 20 | 116,378 |
Tags: implementation, math
Correct Solution:
```
nk = input().split(' ')
a = int(nk[0])
c = int(nk[1])
a_arr = []
c_arr = []
i = 0
while a!= 0:
a_arr.append(a%3)
a = a//3
i += 1
i = 0
while c!= 0:
c_arr.append(c%3)
c = c//3
i += 1
if len(a_arr) < len(c_arr):
while len(a_arr) != len(c_arr):
a_arr.append(0)
elif len(a_arr) > len(c_arr):
while len(a_arr) != len(c_arr):
c_arr.append(0)
t = []
for i in range(len(a_arr)):
t.append((3 - (a_arr[i] - c_arr[i])) %3)
sum = 0
for i in range(len(t)):
sum += t[i]* 3**i
print(sum)
``` | output | 1 | 58,189 | 20 | 116,379 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0 | instruction | 0 | 58,190 | 20 | 116,380 |
Tags: implementation, math
Correct Solution:
```
def main():
a, c = map(int, input().split())
x, m = 0, 1
while a or c:
x += (c - a) % 3 * m
a //= 3
c //= 3
m *= 3
print(x)
if __name__ == '__main__':
main()
``` | output | 1 | 58,190 | 20 | 116,381 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0 | instruction | 0 | 58,191 | 20 | 116,382 |
Tags: implementation, math
Correct Solution:
```
#(っ◔◡◔)っ ♥ GLHF ♥
import os #(っ◔◡◔)っ
import sys #(っ◔◡◔)っ
from io import BytesIO, IOBase #(っ◔◡◔)っ
def main(): #(っ◔◡◔)っ
line = input().split()
x, ans = int(line[0]), int(line[1])
x3 = []
ans3 = []
while(x > 0):
x3.append(x%3)
x //= 3
while(ans>0):
ans3.append(ans%3)
ans //= 3
x3.reverse()
ans3.reverse()
while(len(x3) < len(ans3)):
x3.insert(0, 0)
while(len(x3) > len(ans3)):
ans3.insert(0, 0)
# print(x3, ans3)
b = []
for i in range(len(ans3)):
b.append((ans3[i] - x3[i])%3)
summ = 0
b.reverse()
for i in range(len(b)):
summ += (3**i)*(b[i])
print(summ)
# print(b)
BUFSIZE = 8192 #(っ◔◡◔)っ
class FastIO(IOBase): #(っ◔◡◔)っ
newlines = 0 #(っ◔◡◔)っ
def __init__(self, file): #(っ◔◡◔)っ
self._fd = file.fileno() #(っ◔◡◔)っ
self.buffer = BytesIO() #(っ◔◡◔)っ
self.writable = "x" in file.mode or "r" not in file.mode #(っ◔◡◔)っ
self.write = self.buffer.write if self.writable else None #(っ◔◡◔)っ
def read(self): #(っ◔◡◔)っ
while True: #(っ◔◡◔)っ
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) #(っ◔◡◔)っ
if not b: #(っ◔◡◔)っ
break #(っ◔◡◔)っ
ptr = self.buffer.tell() #(っ◔◡◔)っ
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) #(っ◔◡◔)っ
self.newlines = 0 #(っ◔◡◔)っ
return self.buffer.read() #(っ◔◡◔)っ
def readline(self): #(っ◔◡◔)っ
while self.newlines == 0: #(っ◔◡◔)っ
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) #(っ◔◡◔)っ
self.newlines = b.count(b"\n") + (not b) #(っ◔◡◔)っ
ptr = self.buffer.tell() #(っ◔◡◔)っ
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) #(っ◔◡◔)っ
self.newlines -= 1 #(っ◔◡◔)っ
return self.buffer.readline() #(っ◔◡◔)っ
def flush(self): #(っ◔◡◔)っ
if self.writable: #(っ◔◡◔)っ
os.write(self._fd, self.buffer.getvalue()) #(っ◔◡◔)っ
self.buffer.truncate(0), self.buffer.seek(0) #(っ◔◡◔)っ
class IOWrapper(IOBase): #(っ◔◡◔)っ
def __init__(self, file): #(っ◔◡◔)っ
self.buffer = FastIO(file) #(っ◔◡◔)っ
self.flush = self.buffer.flush #(っ◔◡◔)っ
self.writable = self.buffer.writable #(っ◔◡◔)っ
self.write = lambda s: self.buffer.write(s.encode("ascii")) #(っ◔◡◔)っ
self.read = lambda: self.buffer.read().decode("ascii") #(っ◔◡◔)っ
self.readline = lambda: self.buffer.readline().decode("ascii") #(っ◔◡◔)っ
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) #(っ◔◡◔)っ
input = lambda: sys.stdin.readline().rstrip("\r\n") #(っ◔◡◔)っ
if __name__ == "__main__": #(っ◔◡◔)っ
main() #(っ◔◡◔)っ
#██╗░░░██╗██╗██████╗░██████╗░██╗░░██╗
#██║░░░██║██║██╔══██╗╚════██╗██║░██╔╝
#╚██╗░██╔╝██║██║░░██║░░███╔═╝█████═╝░
#░╚████╔╝░██║██║░░██║██╔══╝░░██╔═██╗░
#░░╚██╔╝░░██║██████╔╝███████╗██║░╚██╗
#░░░╚═╝░░░╚═╝╚═════╝░╚══════╝╚═╝░░╚═╝
``` | output | 1 | 58,191 | 20 | 116,383 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0 | instruction | 0 | 58,192 | 20 | 116,384 |
Tags: implementation, math
Correct Solution:
```
def Ternary(a):
res = ""
while a:
res += str(a%3)
a //= 3
return res[::-1]
def decimal(b):
cur = 1
res = 0
for ch in b[::-1]:
res += int(ch)*cur
cur *= 3
return res
def tor(s1,s2):
m = max(len(s1), len(s2))
s1 = (m - len(s1))*"0" + s1
s2 = (m - len(s2))*"0" + s2
s3=''
for i in range(m):
s3 += str((int(s1[i]) + int(s2[i]))%3)
return s3
a,c = map(int,input().split())
s1 = Ternary(a)
s2 = Ternary(c)
print(decimal(tor(s1, tor(s1, s2))))
``` | output | 1 | 58,192 | 20 | 116,385 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0
Submitted Solution:
```
a,c=map(int,input().split())
a1=""
while a>0:
a1=str(a%3)+a1
a//=3
if a1=="":a1="0"
c1=""
while c>0:
c1=str(c%3)+c1
c//=3
if c1=="":c1="0"
if len(c1)>len(a1):
a1='0'*(len(c1)-len(a1))+a1
else:
c1='0'*(len(a1)-len(c1))+c1
i,b1=len(c1)-1,""
while i>=0:
if c1[i]=='0':
if a1[i]=='0':
b1='0'+b1
elif a1[i]=='1':
b1='2'+b1
else:
b1='1'+b1
elif c1[i]=='1':
if a1[i]=='0':
b1='1'+b1
elif a1[i]=='1':
b1='0'+b1
else:
b1='2'+b1
else:
if a1[i]=='0':
b1='2'+b1
elif a1[i]=='1':
b1='1'+b1
else:
b1='0'+b1
i-=1
print(int(b1,3))
``` | instruction | 0 | 58,193 | 20 | 116,386 |
Yes | output | 1 | 58,193 | 20 | 116,387 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0
Submitted Solution:
```
def ternary(n):
m=''
while n>0:
m=str(n%3)+m
n=n//3
return m
a,b=map(int,input().split())
l1=ternary(a)
l2=ternary(b)
if len(l1)>len(l2):
for i in range(len(l1)-len(l2)):
l2='0'+l2
elif len(l2)>len(l1):
for i in range(len(l2)-len(l1)):
l1='0'+l1
m=''
for i in range(len(l1)):
g=int(l2[i])-int(l1[i])
if g>=0:
m+=str(g)
else:
m+=str(g+3)
if m=='':
print(0)
else:
print(int(str(m),3))
``` | instruction | 0 | 58,194 | 20 | 116,388 |
Yes | output | 1 | 58,194 | 20 | 116,389 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0
Submitted Solution:
```
a,c=map(int,input().split())
def arr(n):
array=[]
while n:
array.append(n%3)
n//=3
return array
a=arr(a)
c=arr(c)
while len(a)<len(c):a.append(0)
while len(c)<len(a):c.append(0)
array=[0]*len(a)
#print(a,c)
for i in range(len(a)):
for j in range(3):
if (j+a[i])%3==c[i]%3:
array[i]=j
break
b=0
#print(array)
for i in range(len(array)):
b+=3**i*array[i]
print(b)
``` | instruction | 0 | 58,195 | 20 | 116,390 |
Yes | output | 1 | 58,195 | 20 | 116,391 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).
It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.
Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.
Input
The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.
Output
Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.
Examples
Input
14 34
Output
50
Input
50 34
Output
14
Input
387420489 225159023
Output
1000000001
Input
5 5
Output
0
Submitted Solution:
```
a, c = map(int, input().split())
b, k = 0, 1
while a or c:
b += k * ((c % 3 - a % 3) % 3)
k *= 3
a //= 3
c //= 3
print(b)
# Made By Mostafa_Khaled
``` | instruction | 0 | 58,196 | 20 | 116,392 |
Yes | output | 1 | 58,196 | 20 | 116,393 |
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