message stringlengths 2 44.5k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 276 109k | cluster float64 23 23 | __index_level_0__ int64 552 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
Your math teacher gave you the following problem:
There are n segments on the x-axis, [l_1; r_1], [l_2; r_2], …, [l_n; r_n]. The segment [l; r] includes the bounds, i.e. it is a set of such x that l ≤ x ≤ r. The length of the segment [l; r] is equal to r - l.
Two segments [a; b] and [c; d] have a common point (intersect) if there exists x that a ≤ x ≤ b and c ≤ x ≤ d. For example, [2; 5] and [3; 10] have a common point, but [5; 6] and [1; 4] don't have.
You should add one segment, which has at least one common point with each of the given segments and as short as possible (i.e. has minimal length). The required segment can degenerate to be a point (i.e a segment with length zero). The added segment may or may not be among the given n segments.
In other words, you need to find a segment [a; b], such that [a; b] and every [l_i; r_i] have a common point for each i, and b-a is minimal.
Input
The first line contains integer number t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.
The first line of each test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of segments. The following n lines contain segment descriptions: the i-th of them contains two integers l_i,r_i (1 ≤ l_i ≤ r_i ≤ 10^{9}).
The sum of all values n over all the test cases in the input doesn't exceed 10^5.
Output
For each test case, output one integer — the smallest possible length of the segment which has at least one common point with all given segments.
Example
Input
4
3
4 5
5 9
7 7
5
11 19
4 17
16 16
3 12
14 17
1
1 10
1
1 1
Output
2
4
0
0
Note
In the first test case of the example, we can choose the segment [5;7] as the answer. It is the shortest segment that has at least one common point with all given segments. | instruction | 0 | 72,594 | 23 | 145,188 |
Tags: math
Correct Solution:
```
otvet = []
t = int(input())
for i in range(t):
n = int(input())
for j in range(n):
if j == 0:
min2, max1 = reversed(list(map(int, input().split())))
else:
a, b = map(int, input().split())
if a > max1:
max1 = a
if b < min2:
min2 = b
z = max1 - min2
if z > 0:
otvet.append(z)
else:
otvet.append(0)
for i in otvet:
print(i)
``` | output | 1 | 72,594 | 23 | 145,189 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Your math teacher gave you the following problem:
There are n segments on the x-axis, [l_1; r_1], [l_2; r_2], …, [l_n; r_n]. The segment [l; r] includes the bounds, i.e. it is a set of such x that l ≤ x ≤ r. The length of the segment [l; r] is equal to r - l.
Two segments [a; b] and [c; d] have a common point (intersect) if there exists x that a ≤ x ≤ b and c ≤ x ≤ d. For example, [2; 5] and [3; 10] have a common point, but [5; 6] and [1; 4] don't have.
You should add one segment, which has at least one common point with each of the given segments and as short as possible (i.e. has minimal length). The required segment can degenerate to be a point (i.e a segment with length zero). The added segment may or may not be among the given n segments.
In other words, you need to find a segment [a; b], such that [a; b] and every [l_i; r_i] have a common point for each i, and b-a is minimal.
Input
The first line contains integer number t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.
The first line of each test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of segments. The following n lines contain segment descriptions: the i-th of them contains two integers l_i,r_i (1 ≤ l_i ≤ r_i ≤ 10^{9}).
The sum of all values n over all the test cases in the input doesn't exceed 10^5.
Output
For each test case, output one integer — the smallest possible length of the segment which has at least one common point with all given segments.
Example
Input
4
3
4 5
5 9
7 7
5
11 19
4 17
16 16
3 12
14 17
1
1 10
1
1 1
Output
2
4
0
0
Note
In the first test case of the example, we can choose the segment [5;7] as the answer. It is the shortest segment that has at least one common point with all given segments.
Submitted Solution:
```
number_of_sets = int(input())
sets = []
for i in range(number_of_sets):
temp = []
numbers_of_linesegments = int(input())
for k in range(numbers_of_linesegments):
temp.append(tuple(map(int, input().split())))
sets.append(temp)
for elem in sets:
start = -1
end = 10000000000
for object in elem:
if object[0] > start:
start = object[0]
if object[1] < end:
end = object[1]
if end > start:
print(0)
else:
print(start - end)
``` | instruction | 0 | 72,595 | 23 | 145,190 |
Yes | output | 1 | 72,595 | 23 | 145,191 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Your math teacher gave you the following problem:
There are n segments on the x-axis, [l_1; r_1], [l_2; r_2], …, [l_n; r_n]. The segment [l; r] includes the bounds, i.e. it is a set of such x that l ≤ x ≤ r. The length of the segment [l; r] is equal to r - l.
Two segments [a; b] and [c; d] have a common point (intersect) if there exists x that a ≤ x ≤ b and c ≤ x ≤ d. For example, [2; 5] and [3; 10] have a common point, but [5; 6] and [1; 4] don't have.
You should add one segment, which has at least one common point with each of the given segments and as short as possible (i.e. has minimal length). The required segment can degenerate to be a point (i.e a segment with length zero). The added segment may or may not be among the given n segments.
In other words, you need to find a segment [a; b], such that [a; b] and every [l_i; r_i] have a common point for each i, and b-a is minimal.
Input
The first line contains integer number t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.
The first line of each test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of segments. The following n lines contain segment descriptions: the i-th of them contains two integers l_i,r_i (1 ≤ l_i ≤ r_i ≤ 10^{9}).
The sum of all values n over all the test cases in the input doesn't exceed 10^5.
Output
For each test case, output one integer — the smallest possible length of the segment which has at least one common point with all given segments.
Example
Input
4
3
4 5
5 9
7 7
5
11 19
4 17
16 16
3 12
14 17
1
1 10
1
1 1
Output
2
4
0
0
Note
In the first test case of the example, we can choose the segment [5;7] as the answer. It is the shortest segment that has at least one common point with all given segments.
Submitted Solution:
```
for _ in range(int(input())):
L, R = 0, 10 ** 9 + 1
for _ in range(int(input())):
l, r = map(int, input().split())
L = max(L, l)
R = min(R, r)
print(max(0, L - R))
``` | instruction | 0 | 72,596 | 23 | 145,192 |
Yes | output | 1 | 72,596 | 23 | 145,193 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Your math teacher gave you the following problem:
There are n segments on the x-axis, [l_1; r_1], [l_2; r_2], …, [l_n; r_n]. The segment [l; r] includes the bounds, i.e. it is a set of such x that l ≤ x ≤ r. The length of the segment [l; r] is equal to r - l.
Two segments [a; b] and [c; d] have a common point (intersect) if there exists x that a ≤ x ≤ b and c ≤ x ≤ d. For example, [2; 5] and [3; 10] have a common point, but [5; 6] and [1; 4] don't have.
You should add one segment, which has at least one common point with each of the given segments and as short as possible (i.e. has minimal length). The required segment can degenerate to be a point (i.e a segment with length zero). The added segment may or may not be among the given n segments.
In other words, you need to find a segment [a; b], such that [a; b] and every [l_i; r_i] have a common point for each i, and b-a is minimal.
Input
The first line contains integer number t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.
The first line of each test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of segments. The following n lines contain segment descriptions: the i-th of them contains two integers l_i,r_i (1 ≤ l_i ≤ r_i ≤ 10^{9}).
The sum of all values n over all the test cases in the input doesn't exceed 10^5.
Output
For each test case, output one integer — the smallest possible length of the segment which has at least one common point with all given segments.
Example
Input
4
3
4 5
5 9
7 7
5
11 19
4 17
16 16
3 12
14 17
1
1 10
1
1 1
Output
2
4
0
0
Note
In the first test case of the example, we can choose the segment [5;7] as the answer. It is the shortest segment that has at least one common point with all given segments.
Submitted Solution:
```
from math import *
import os, sys
from io import BytesIO
input = BytesIO(os.read(0, os.fstat(0).st_size)).readline
for i in range(int(input())):
n = int(input())
a = []
b = []
for i in range(n):
x, y = map(int, input().split())
a.append((x, y))
b.append((y, x))
#print()
a.sort()
b.sort()
if n == 1:
print(0)
else:
l = b[0][0]
r = a[-1][0]
print(max(r - l, 0))
``` | instruction | 0 | 72,597 | 23 | 145,194 |
Yes | output | 1 | 72,597 | 23 | 145,195 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Your math teacher gave you the following problem:
There are n segments on the x-axis, [l_1; r_1], [l_2; r_2], …, [l_n; r_n]. The segment [l; r] includes the bounds, i.e. it is a set of such x that l ≤ x ≤ r. The length of the segment [l; r] is equal to r - l.
Two segments [a; b] and [c; d] have a common point (intersect) if there exists x that a ≤ x ≤ b and c ≤ x ≤ d. For example, [2; 5] and [3; 10] have a common point, but [5; 6] and [1; 4] don't have.
You should add one segment, which has at least one common point with each of the given segments and as short as possible (i.e. has minimal length). The required segment can degenerate to be a point (i.e a segment with length zero). The added segment may or may not be among the given n segments.
In other words, you need to find a segment [a; b], such that [a; b] and every [l_i; r_i] have a common point for each i, and b-a is minimal.
Input
The first line contains integer number t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.
The first line of each test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of segments. The following n lines contain segment descriptions: the i-th of them contains two integers l_i,r_i (1 ≤ l_i ≤ r_i ≤ 10^{9}).
The sum of all values n over all the test cases in the input doesn't exceed 10^5.
Output
For each test case, output one integer — the smallest possible length of the segment which has at least one common point with all given segments.
Example
Input
4
3
4 5
5 9
7 7
5
11 19
4 17
16 16
3 12
14 17
1
1 10
1
1 1
Output
2
4
0
0
Note
In the first test case of the example, we can choose the segment [5;7] as the answer. It is the shortest segment that has at least one common point with all given segments.
Submitted Solution:
```
# math_prob.py
for z in range(int(input())):
n = int(input())
f = 10e9
s = 0
for i in range(n):
x,y = map(int,input().split())
f = min(f,y)
s = max(s,x)
if n==1:
print(0)
else:
if s-f>=0:
print(s-f)
else:
print(0)
``` | instruction | 0 | 72,598 | 23 | 145,196 |
Yes | output | 1 | 72,598 | 23 | 145,197 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Your math teacher gave you the following problem:
There are n segments on the x-axis, [l_1; r_1], [l_2; r_2], …, [l_n; r_n]. The segment [l; r] includes the bounds, i.e. it is a set of such x that l ≤ x ≤ r. The length of the segment [l; r] is equal to r - l.
Two segments [a; b] and [c; d] have a common point (intersect) if there exists x that a ≤ x ≤ b and c ≤ x ≤ d. For example, [2; 5] and [3; 10] have a common point, but [5; 6] and [1; 4] don't have.
You should add one segment, which has at least one common point with each of the given segments and as short as possible (i.e. has minimal length). The required segment can degenerate to be a point (i.e a segment with length zero). The added segment may or may not be among the given n segments.
In other words, you need to find a segment [a; b], such that [a; b] and every [l_i; r_i] have a common point for each i, and b-a is minimal.
Input
The first line contains integer number t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.
The first line of each test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of segments. The following n lines contain segment descriptions: the i-th of them contains two integers l_i,r_i (1 ≤ l_i ≤ r_i ≤ 10^{9}).
The sum of all values n over all the test cases in the input doesn't exceed 10^5.
Output
For each test case, output one integer — the smallest possible length of the segment which has at least one common point with all given segments.
Example
Input
4
3
4 5
5 9
7 7
5
11 19
4 17
16 16
3 12
14 17
1
1 10
1
1 1
Output
2
4
0
0
Note
In the first test case of the example, we can choose the segment [5;7] as the answer. It is the shortest segment that has at least one common point with all given segments.
Submitted Solution:
```
t = int(input())
minn = 10000
maxx = 0
for test in range(t):
n = int(input())
for line in range(n):
x1, x2 = input().split()
x1 = int(x1)
x2 = int(x2)
minn = min(x2, minn)
maxx = max(x1, maxx)
ans = maxx - minn
minn = 10000
maxx = 0
if ans < 0:
print(0)
else:
print(ans)
``` | instruction | 0 | 72,599 | 23 | 145,198 |
No | output | 1 | 72,599 | 23 | 145,199 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Your math teacher gave you the following problem:
There are n segments on the x-axis, [l_1; r_1], [l_2; r_2], …, [l_n; r_n]. The segment [l; r] includes the bounds, i.e. it is a set of such x that l ≤ x ≤ r. The length of the segment [l; r] is equal to r - l.
Two segments [a; b] and [c; d] have a common point (intersect) if there exists x that a ≤ x ≤ b and c ≤ x ≤ d. For example, [2; 5] and [3; 10] have a common point, but [5; 6] and [1; 4] don't have.
You should add one segment, which has at least one common point with each of the given segments and as short as possible (i.e. has minimal length). The required segment can degenerate to be a point (i.e a segment with length zero). The added segment may or may not be among the given n segments.
In other words, you need to find a segment [a; b], such that [a; b] and every [l_i; r_i] have a common point for each i, and b-a is minimal.
Input
The first line contains integer number t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.
The first line of each test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of segments. The following n lines contain segment descriptions: the i-th of them contains two integers l_i,r_i (1 ≤ l_i ≤ r_i ≤ 10^{9}).
The sum of all values n over all the test cases in the input doesn't exceed 10^5.
Output
For each test case, output one integer — the smallest possible length of the segment which has at least one common point with all given segments.
Example
Input
4
3
4 5
5 9
7 7
5
11 19
4 17
16 16
3 12
14 17
1
1 10
1
1 1
Output
2
4
0
0
Note
In the first test case of the example, we can choose the segment [5;7] as the answer. It is the shortest segment that has at least one common point with all given segments.
Submitted Solution:
```
t=int(input())
for g in range(t):
n=int(input())
a=list(range(n))
b=list(range(n))
for i in range(n):
a[i],b[i]=map(int,input().split())
if n==1:
print(0)
else:
print(max(a)-min(b))
``` | instruction | 0 | 72,600 | 23 | 145,200 |
No | output | 1 | 72,600 | 23 | 145,201 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Your math teacher gave you the following problem:
There are n segments on the x-axis, [l_1; r_1], [l_2; r_2], …, [l_n; r_n]. The segment [l; r] includes the bounds, i.e. it is a set of such x that l ≤ x ≤ r. The length of the segment [l; r] is equal to r - l.
Two segments [a; b] and [c; d] have a common point (intersect) if there exists x that a ≤ x ≤ b and c ≤ x ≤ d. For example, [2; 5] and [3; 10] have a common point, but [5; 6] and [1; 4] don't have.
You should add one segment, which has at least one common point with each of the given segments and as short as possible (i.e. has minimal length). The required segment can degenerate to be a point (i.e a segment with length zero). The added segment may or may not be among the given n segments.
In other words, you need to find a segment [a; b], such that [a; b] and every [l_i; r_i] have a common point for each i, and b-a is minimal.
Input
The first line contains integer number t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.
The first line of each test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of segments. The following n lines contain segment descriptions: the i-th of them contains two integers l_i,r_i (1 ≤ l_i ≤ r_i ≤ 10^{9}).
The sum of all values n over all the test cases in the input doesn't exceed 10^5.
Output
For each test case, output one integer — the smallest possible length of the segment which has at least one common point with all given segments.
Example
Input
4
3
4 5
5 9
7 7
5
11 19
4 17
16 16
3 12
14 17
1
1 10
1
1 1
Output
2
4
0
0
Note
In the first test case of the example, we can choose the segment [5;7] as the answer. It is the shortest segment that has at least one common point with all given segments.
Submitted Solution:
```
t=int(input())
qq=[]
for i in range(t):
n = int(input())
minn = 0
maxx = 1000000
if n>1:
for j in range(n):
a,b=map(int,input().split())
if a>minn:
minn=a
if b<maxx or b<minn:
maxx=b
qq.append((abs(maxx - minn)))
else:
a, b = map(int, input().split())
qq.append(0)
print(qq)
``` | instruction | 0 | 72,601 | 23 | 145,202 |
No | output | 1 | 72,601 | 23 | 145,203 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Your math teacher gave you the following problem:
There are n segments on the x-axis, [l_1; r_1], [l_2; r_2], …, [l_n; r_n]. The segment [l; r] includes the bounds, i.e. it is a set of such x that l ≤ x ≤ r. The length of the segment [l; r] is equal to r - l.
Two segments [a; b] and [c; d] have a common point (intersect) if there exists x that a ≤ x ≤ b and c ≤ x ≤ d. For example, [2; 5] and [3; 10] have a common point, but [5; 6] and [1; 4] don't have.
You should add one segment, which has at least one common point with each of the given segments and as short as possible (i.e. has minimal length). The required segment can degenerate to be a point (i.e a segment with length zero). The added segment may or may not be among the given n segments.
In other words, you need to find a segment [a; b], such that [a; b] and every [l_i; r_i] have a common point for each i, and b-a is minimal.
Input
The first line contains integer number t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.
The first line of each test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of segments. The following n lines contain segment descriptions: the i-th of them contains two integers l_i,r_i (1 ≤ l_i ≤ r_i ≤ 10^{9}).
The sum of all values n over all the test cases in the input doesn't exceed 10^5.
Output
For each test case, output one integer — the smallest possible length of the segment which has at least one common point with all given segments.
Example
Input
4
3
4 5
5 9
7 7
5
11 19
4 17
16 16
3 12
14 17
1
1 10
1
1 1
Output
2
4
0
0
Note
In the first test case of the example, we can choose the segment [5;7] as the answer. It is the shortest segment that has at least one common point with all given segments.
Submitted Solution:
```
for i in range(int(input())):
n=int(input())
maxl=0
minr=100000000
if n==1:
l,r=map(int,input().split())
print(0)
else:
f=0
prevl=-1
prevr=-1
for i in range(n):
l,r=map(int,input().split())
if f==0:
if prevl==-1:
prevl=l
prevr=r
else:
if not((l<=prevr and l>=prevl) or (r>=prevl and r<=prevr)or (r>=prevr and l<=prevl)):
f=1
prevl=l
prevr=r
elif f==0:
prevl=max(l,prevl)
prevr=min(r,prevr)
if maxl<l:
maxl=l
if minr>r:
minr=r
if f==0:
print(0)
else:
print(max(maxl,minr)-min(maxl,minr))
``` | instruction | 0 | 72,602 | 23 | 145,204 |
No | output | 1 | 72,602 | 23 | 145,205 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595 | instruction | 0 | 72,672 | 23 | 145,344 |
Tags: binary search, brute force, geometry, math
Correct Solution:
```
import math
import sys;input=sys.stdin.readline
T, = map(int, input().split())
for t in range(T):
n=int(input())
print(math.cos(math.pi/(4*n))/math.sin(math.pi/(2*n)))
``` | output | 1 | 72,672 | 23 | 145,345 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595 | instruction | 0 | 72,673 | 23 | 145,346 |
Tags: binary search, brute force, geometry, math
Correct Solution:
```
from math import pi, sin, sqrt
t = int(input())
for _ in range(t):
n = int(input())
r = 0.5/sin((pi/n/2))
al = pi/n * (n//2) / 2
x = sin(al)*r*sqrt(2)
al2 = pi/n * (n//2+1) / 2
y = sin(al2)*r*sqrt(2)
print(x+y)
``` | output | 1 | 72,673 | 23 | 145,347 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595 | instruction | 0 | 72,674 | 23 | 145,348 |
Tags: binary search, brute force, geometry, math
Correct Solution:
```
#------------------------------warmup----------------------------
import os
import sys
from io import BytesIO, IOBase
import math
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")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
#-------------------game starts now----------------------------------------------------
for _ in range((int)(input())):
n=(int)(input())
print(1/(2*(math.sin(math.pi/(n*4)))))
``` | output | 1 | 72,674 | 23 | 145,349 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595 | instruction | 0 | 72,675 | 23 | 145,350 |
Tags: binary search, brute force, geometry, math
Correct Solution:
```
import sys
import math
t=int(sys.stdin.readline())
for i in range(t):
n=int(sys.stdin.readline())
pi=math.pi
theta=0
ans=0
while 2*theta<pi:
ans+=math.cos(theta)
theta+=pi/n
k=(2*ans-1)
theta=0
while 4*theta<pi:
theta+=pi/n
if abs(theta-pi/n-pi/4)<abs(theta-pi/4):
theta-=pi/n
ans=k*math.sin(theta)/math.sin(pi/4)+k*math.sin(pi/2-theta)/math.sin(pi/4)
print(ans/2)
``` | output | 1 | 72,675 | 23 | 145,351 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595 | instruction | 0 | 72,676 | 23 | 145,352 |
Tags: binary search, brute force, geometry, math
Correct Solution:
```
import math
for q in range(int(input())):
n=int(input())
ans = 1/(2*math.sin(math.radians(180/(4*n))))
print(ans)
``` | output | 1 | 72,676 | 23 | 145,353 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595 | instruction | 0 | 72,677 | 23 | 145,354 |
Tags: binary search, brute force, geometry, math
Correct Solution:
```
import math
for _ in range(int(input())):
x=int(input());print(1/(2*math.sin(math.pi/(4*x))))
``` | output | 1 | 72,677 | 23 | 145,355 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595 | instruction | 0 | 72,678 | 23 | 145,356 |
Tags: binary search, brute force, geometry, math
Correct Solution:
```
from math import tan,pi,sin,cos
t = int(input())
for i in range(t):
n = int(input())
if n % 2 == 0:
print()
else:
alpha = pi/n
x = 0.5/sin(alpha/2)
ans = 2*(x*(cos(3*alpha/4)) + sin(alpha/4))
print(ans)
``` | output | 1 | 72,678 | 23 | 145,357 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595 | instruction | 0 | 72,679 | 23 | 145,358 |
Tags: binary search, brute force, geometry, math
Correct Solution:
```
from math import sin,pi
for i in range(int(input())):
n=int(input())
print(1/(2*sin(pi/(4*n))))
``` | output | 1 | 72,679 | 23 | 145,359 |
Provide tags and a correct Python 2 solution for this coding contest problem.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595 | instruction | 0 | 72,680 | 23 | 145,360 |
Tags: binary search, brute force, geometry, math
Correct Solution:
```
from sys import stdin, stdout
from collections import Counter, defaultdict
from itertools import permutations, combinations
from math import sin,sqrt,pi
raw_input = stdin.readline
pr = stdout.write
mod=10**9+7
def ni():
return int(raw_input())
def li():
return map(int,raw_input().split())
def pn(n):
stdout.write(str(n)+'\n')
def pa(arr):
pr(' '.join(map(str,arr))+'\n')
# fast read function for total integer input
def inp():
# this function returns whole input of
# space/line seperated integers
# Use Ctrl+D to flush stdin.
return map(int,stdin.read().split())
range = xrange # not for python 3.0+
# main code
def polydiagonal(n, a):
# Side and side length cannot
# be negative
if (a < 0 and n < 0):
return -1
# diagonal degree converted to radians
return (2 * a * sin((((n - 2) * 180) /(2 * n)) * 3.14159 / 180))
for t in range(ni()):
n=ni()
n*=2
#pn(polydiagonal(n,1))
dig=0.5/sin(pi/(2*n))
#dig/=sqrt(2)
pn(dig)
``` | output | 1 | 72,680 | 23 | 145,361 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595
Submitted Solution:
```
import math
def rad(angle) :
return (angle / 180) * math.pi
def dist(a, b, c, d) :
return math.sqrt((a - c) * (a - c) + (b - d) * (b - d))
tt = int(input())
while tt > 0 :
tt -= 1
n = int(input())
angle = rad(360 / (2 * n))
l1, l2 = n // 2, n - n // 2
px, py = 0, 0
vx, vy = 1, 0
ans = 0
cur = 0
for i in range(1, n + 1) :
px += vx
py += vy
if i == l1 or i == l2 :
ans += dist(0, 0, px, py)
cur += angle
vx = math.cos(cur)
vy = math.sin(cur)
print(ans / math.sqrt(2))
``` | instruction | 0 | 72,681 | 23 | 145,362 |
Yes | output | 1 | 72,681 | 23 | 145,363 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595
Submitted Solution:
```
from math import *
for _ in range(int(input())):
n = int(input())
print("{:.9f}".format(cos(pi / (4 * n)) / sin(pi / (2 * n))))
``` | instruction | 0 | 72,682 | 23 | 145,364 |
Yes | output | 1 | 72,682 | 23 | 145,365 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595
Submitted Solution:
```
import sys
import math
readline = sys.stdin.readline
read = sys.stdin.read
ns = lambda: readline().rstrip()
ni = lambda: int(readline().rstrip())
nm = lambda: map(int, readline().split())
nl = lambda: list(map(int, readline().split()))
prn = lambda x: print(*x, sep='\n')
def solve():
n = ni()
print(math.cos(math.pi / (4 * n)) / math.sin(math.pi / (2 * n)))
return
# solve()
T = ni()
for _ in range(T):
solve()
``` | instruction | 0 | 72,683 | 23 | 145,366 |
Yes | output | 1 | 72,683 | 23 | 145,367 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595
Submitted Solution:
```
from math import tan, pi, sin, cos
def test(n, an):
r = 0.5/tan(pi/n)
b = r*tan(an)
c = 0.5-b
compl = pi/2-an
#print(r/cos(an))
return r/cos(an)+c*cos(compl)
for _ in range(int(input())):
n = int(input())
n *= 2
print(2*test(n, pi/2/n))
``` | instruction | 0 | 72,684 | 23 | 145,368 |
Yes | output | 1 | 72,684 | 23 | 145,369 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595
Submitted Solution:
```
from collections import *
from bisect import *
from math import *
from heapq import *
import sys
input=sys.stdin.readline
t=int(input())
while(t):
t-=1
n=int(input())
cir=pi/(2*n)
s=1/(2*(sin(cir)))
print(s*2)
continue
if(n%2):
q=n//2
else:
q=(n//2)-1
q=q*(360/(2*n))
q=(q*pi)/180
si=sin(q)
si=si*si
co=pow(1-si,0.5)
d=2*s*s
d*=(1-co)
c=d/2
c=pow(c,0.5)
print(1+(2*c))
``` | instruction | 0 | 72,685 | 23 | 145,370 |
No | output | 1 | 72,685 | 23 | 145,371 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595
Submitted Solution:
```
from __future__ import division, print_function
import sys
if sys.version_info[0] < 3:
from __builtin__ import xrange as range
from future_builtins import ascii, filter, hex, map, oct, zip
import os, sys, bisect, copy
from collections import defaultdict, Counter, deque
#from functools import lru_cache #use @lru_cache(None)
if os.path.exists('in.txt'): sys.stdin=open('in.txt','r')
if os.path.exists('out.txt'): sys.stdout=open('out.txt', 'w')
#
def input(): return sys.stdin.readline()
def mapi(arg=0): return map(int if arg==0 else str,input().split())
#------------------------------------------------------------------
from math import *
for _ in range(int(input())):
n = int(input())
angle = ((2*n-2)*180)//n
res = cos(pi/(2*n))/sin(pi/(2*n))
#tst = 1+sqrt(2)
print(res)
``` | instruction | 0 | 72,686 | 23 | 145,372 |
No | output | 1 | 72,686 | 23 | 145,373 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595
Submitted Solution:
```
from sys import stdin
import math
inp = lambda : stdin.readline().strip()
t = int(inp())
for _ in range(t):
n = int(inp())*2
o = 360/n * (math.pi/180)
ans = 2*(1/(2*math.sin(o/2)))
print(ans)
``` | instruction | 0 | 72,687 | 23 | 145,374 |
No | output | 1 | 72,687 | 23 | 145,375 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The statement of this problem is the same as the statement of problem C1. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.
You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.
Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.
You can rotate 2n-gon and/or the square.
Input
The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.
Next T lines contain descriptions of test cases — one per line. Each line contains single odd integer n (3 ≤ n ≤ 199). Don't forget you need to embed 2n-gon, not an n-gon.
Output
Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.
Example
Input
3
3
5
199
Output
1.931851653
3.196226611
126.687663595
Submitted Solution:
```
import math, sys
input = sys.stdin.readline
for _ in range(int(input())):
n = int(input()) * 2
if n == 4: # square
print(1)
else:
large_angle = (((n - 2) * 180) / n) / 2
small_angle = 180 - 2 * large_angle
alt = math.sin(math.radians(large_angle)) / math.sin(math.radians(small_angle)) # law of sines
print(math.sqrt(alt ** 2 - 0.5 ** 2) * 2)
``` | instruction | 0 | 72,688 | 23 | 145,376 |
No | output | 1 | 72,688 | 23 | 145,377 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him.
Input
The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.
Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.
Output
Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
3 0 0
0 1
-1 2
1 2
Output
12.566370614359172464
Input
4 1 -1
0 0
1 2
2 0
1 1
Output
21.991148575128551812
Note
In the first sample snow will be removed from that area:
<image> | instruction | 0 | 72,916 | 23 | 145,832 |
Tags: binary search, geometry, ternary search
Correct Solution:
```
def main():
n, a, b = map(int, input().split())
l, res = [], []
for _ in range(n):
u, v = input().split()
l.append((int(u) - a, int(v) - b))
x0, y0 = l[-1]
for x1, y1 in l:
res.append(x1 * x1 + y1 * y1)
dx, dy = x1 - x0, y1 - y0
if (x0 * dx + y0 * dy) * (x1 * dx + y1 * dy) < 0:
x0 = x0 * y1 - x1 * y0
res.append(x0 * x0 / (dx * dx + dy * dy))
x0, y0 = x1, y1
print((max(res) - min(res)) * 3.141592653589793)
if __name__ == '__main__':
main()
# Made By Mostafa_Khaled
``` | output | 1 | 72,916 | 23 | 145,833 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him.
Input
The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.
Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.
Output
Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
3 0 0
0 1
-1 2
1 2
Output
12.566370614359172464
Input
4 1 -1
0 0
1 2
2 0
1 1
Output
21.991148575128551812
Note
In the first sample snow will be removed from that area:
<image> | instruction | 0 | 72,917 | 23 | 145,834 |
Tags: binary search, geometry, ternary search
Correct Solution:
```
import math
def dist(p_x, p_y, p0_x, p0_y, p1_x, p1_y):
v_x = p1_x - p0_x
v_y = p1_y - p0_y
w_x = p_x - p0_x
w_y = p_y - p0_y
c1 = w_x * v_x + w_y * v_y
if c1 <= 0:
return math.hypot(p_x - p0_x, p_y - p0_y)
c2 = v_x * v_x + v_y * v_y
if c2 <= c1:
return math.hypot(p_x - p1_x, p_y - p1_y)
b = c1 / c2
pb_x = p0_x + b * v_x
pb_y = p0_y + b * v_y
return math.hypot(p_x - pb_x, p_y - pb_y)
r_max = 0
r_min = 1000000000
n, x0, y0 = [int(i) for i in input().split()]
x0 = float(x0)
y0 = float(y0)
x_prev, y_prev = input().split()
x_initial = x_prev = float(x_prev)
y_initial = y_prev = float(y_prev)
r_prev = math.hypot(x_prev - x0, y_prev - y0)
r_max = max(r_max, r_prev)
for i in range(n):
if i < n - 1:
x1, y1 = input().split()
x1 = float(x1)
y1 = float(y1)
else:
x1 = x_initial
y1 = y_initial
dx = x1 - x0
dy = y1 - y0
r = math.hypot(dx, dy)
r_max = max(r_max, r)
# w_x = x0 - x_prev
# w_y = y0 - y_prev
# v_x = x1 - x_prev
# v_y = y1 - y_prev
# dist = fabs(v_x * w_y - v_y * w_x) / math.hypot(v_x, v_y)
# dist1 = max(min(r, r_prev)
d = dist(x0, y0, x_prev, y_prev, x1, y1)
# print('d', d)
r_min = min(r_min, d)
x_prev = x1
y_prev = y1
r_prev = r
print(math.pi * (r_max * r_max - r_min * r_min))
``` | output | 1 | 72,917 | 23 | 145,835 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him.
Input
The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.
Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.
Output
Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
3 0 0
0 1
-1 2
1 2
Output
12.566370614359172464
Input
4 1 -1
0 0
1 2
2 0
1 1
Output
21.991148575128551812
Note
In the first sample snow will be removed from that area:
<image> | instruction | 0 | 72,918 | 23 | 145,836 |
Tags: binary search, geometry, ternary search
Correct Solution:
```
import math
n, px, py = map(int, input().split())
xs, ys, l = list(), list(), list()
for _ in range(n):
x, y = map(int, input().split())
xs.append(x - px)
ys.append(y - py)
x0, y0 = xs[-1], ys[-1]
for x, y in zip(xs, ys):
l.append(x * x + y * y)
dx, dy = x - x0, y - y0
if (x0 * dx + y0 * dy) * (x * dx + y * dy) < 0:
x0 = x0 * y - x * y0
l.append(x0 * x0 / (dx * dx + dy * dy))
x0, y0 = x, y
print(math.pi * (max(l) - min(l)))
``` | output | 1 | 72,918 | 23 | 145,837 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him.
Input
The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.
Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.
Output
Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
3 0 0
0 1
-1 2
1 2
Output
12.566370614359172464
Input
4 1 -1
0 0
1 2
2 0
1 1
Output
21.991148575128551812
Note
In the first sample snow will be removed from that area:
<image> | instruction | 0 | 72,919 | 23 | 145,838 |
Tags: binary search, geometry, ternary search
Correct Solution:
```
import math
import sys
def calculate_area(n, x, y, vertices):
r_max = -sys.maxsize
r_min = sys.maxsize
last_d = -1
for v in vertices:
d = distance_two_points(v, (x, y))
if d > r_max:
r_max = d
if d < r_min:
r_min = d
last_v = vertices[0]
for i in range(1,n):
d_min, i_point = distance_point_to_line(last_v, vertices[i], (x, y))
if d_min < r_min and is_in_range(i_point, last_v, vertices[i]):
r_min = d_min
last_v = vertices[i]
d_min, i_point = distance_point_to_line(last_v, vertices[0], (x, y))
if d_min < r_min and is_in_range(i_point, last_v, vertices[0]):
r_min = d_min
return math.pi * (r_max**2 - r_min**2)
def distance_two_points(p1, p2):
return math.sqrt((p1[0]-p2[0])**2 + (p1[1]-p2[1])**2)
def distance_point_to_line(p1, p2, p0):
a = p2[1] - p1[1]
b = p1[0] - p2[0]
c = p2[0]*p1[1] - p2[1]*p1[0]
dist = math.fabs(a*p0[0] + b*p0[1] + c) / math.sqrt(a**2 + b**2)
x_int = (b*(b*p0[0]-a*p0[1]) - a*c)/(a**2 + b**2)
y_int = (a*(-b*p0[0]+a*p0[1]) - b*c)/(a**2 + b**2)
return dist, (x_int, y_int)
def is_in_range(i_point, p1, p2):
x_min = p1[0] if p1[0] <= p2[0] else p2[0]
x_max = p1[0] if p1[0] > p2[0] else p2[0]
y_min = p1[1] if p1[1] <= p2[1] else p2[1]
y_max = p1[1] if p1[1] > p2[1] else p2[1]
return x_min <= i_point[0] <= x_max and y_min <= i_point[1] <= y_max
if __name__ == "__main__":
n, x, y = input().split()
n, x, y = int(n), int(x), int(y)
vertices = [None]*n
for i in range(n):
x_i, y_i = input().split()
vertices[i] = (int(x_i), int(y_i))
area = calculate_area(n, x, y, vertices)
print(area)
``` | output | 1 | 72,919 | 23 | 145,839 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him.
Input
The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.
Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.
Output
Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
3 0 0
0 1
-1 2
1 2
Output
12.566370614359172464
Input
4 1 -1
0 0
1 2
2 0
1 1
Output
21.991148575128551812
Note
In the first sample snow will be removed from that area:
<image> | instruction | 0 | 72,920 | 23 | 145,840 |
Tags: binary search, geometry, ternary search
Correct Solution:
```
#!/usr/bin/python3
import math
class StdIO:
def read_int(self):
return int(self.read_string())
def read_ints(self, sep=None):
return [int(i) for i in self.read_strings(sep)]
def read_float(self):
return float(self.read_string())
def read_floats(self, sep=None):
return [float(i) for i in self.read_strings(sep)]
def read_string(self):
return input()
def read_strings(self, sep=None):
return self.read_string().split(sep)
io = StdIO()
def closest(a, b, p):
ax, ay = a
bx, by = b
px, py = p
lx, ly = bx - ax, by - ay
# print(lx, ly)
num = ax*lx - px*lx + ay*ly - py*ly
den = lx*lx + ly*ly
t = - num / den
if t > 1.0:
return b
elif t < 0.0:
return a
else:
return (ax + t*lx, ay + t*ly)
def dist(a, b):
ax, ay = a
bx, by = b
return math.hypot(ax - bx, ay - by)
def main():
n, px, py = io.read_ints()
p = (px, py)
prev = None
first = None
min_dst = float('inf')
max_dst = 0
for i in range(n):
qx, qy = io.read_ints()
q = (qx, qy)
dst = dist(p, q)
max_dst = max(max_dst, dst)
if prev is None:
prev = q
first = q
continue
r = closest(prev, q, p)
dst = dist(p, r)
min_dst = min(min_dst, dst)
prev = q
r = closest(prev, first, p)
dst = dist(p, r)
min_dst = min(min_dst, dst)
r = min_dst
R = max_dst
A = math.pi * (R*R - r*r)
print(A)
if __name__ == '__main__':
main()
``` | output | 1 | 72,920 | 23 | 145,841 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him.
Input
The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.
Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.
Output
Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
3 0 0
0 1
-1 2
1 2
Output
12.566370614359172464
Input
4 1 -1
0 0
1 2
2 0
1 1
Output
21.991148575128551812
Note
In the first sample snow will be removed from that area:
<image> | instruction | 0 | 72,921 | 23 | 145,842 |
Tags: binary search, geometry, ternary search
Correct Solution:
```
import math
n, a, b = [int(x) for x in input().split()]
distances = []
x, y = [int(x) for x in input().split()]
distances.append(math.hypot(x - a, y - b))
prevx, prevy = x, y
firstx, firsty = x, y
for i in range(n-1):
x, y = [int(x) for x in input().split()]
distances.append(math.hypot(x - a, y - b))
scalar_mult = (a-x)*(prevx-x) + (b-y)*(prevy-y)
sq = (prevx - x)**2 + (prevy - y)**2
if 0 < scalar_mult < sq:
distances.append(((a-x)**2 + (b-y)**2 - scalar_mult**2/sq) ** 0.5)
prevx, prevy = x, y
scalar_mult = (a-prevx)*(firstx-prevx) + (b-prevy)*(firsty-prevy)
sq = (firstx - prevx)**2 + (firsty - prevy)**2
if 0 < scalar_mult < sq:
distances.append(((a-prevx)**2 + (b-prevy)**2 - scalar_mult**2/sq) ** 0.5)
distances.sort()
print((distances[-1] - distances[0])*(distances[-1] + distances[0])*math.pi)
``` | output | 1 | 72,921 | 23 | 145,843 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him.
Input
The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.
Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.
Output
Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
3 0 0
0 1
-1 2
1 2
Output
12.566370614359172464
Input
4 1 -1
0 0
1 2
2 0
1 1
Output
21.991148575128551812
Note
In the first sample snow will be removed from that area:
<image> | instruction | 0 | 72,922 | 23 | 145,844 |
Tags: binary search, geometry, ternary search
Correct Solution:
```
from math import pi
def getl(p1, p2):
x1, y1 = p1
x2, y2 = p2
return(pow((x1-x2)**2+(y1-y2)**2, 0.5))
def geth(a, b, c):
z = getl(c,b)
return abs((b[1] - c[1])*a[0]+(c[0]-b[0])*a[1]+b[0]*c[1]-c[0]*b[1]) / z
def getp(a, b):
return(pow(abs(a**2-b**2), 0.5))
n, x, y = map(int, input().split())
P = (x, y)
p = [0] * n
for i in range(n):
p[i] = tuple(map(int,input().split()))\
mini = int(2e9)
maxi = 0
for i in range(n):
if maxi < getl(P, p[i]): maxi = getl(P, p[i])
if mini > getl(P, p[i]): mini = getl(P, p[i])
for i in range(-1, n-1):
h = geth(P, p[i], p[i+1])
t = getp(getl(P, p[i]), h) + getp(getl(P, p[i+1]), h)
if t + 1e-3 >= getl(p[i], p[i + 1]) >= t - 1e-3:
if h < mini: mini = h
print(pi * (maxi ** 2 - mini ** 2))
``` | output | 1 | 72,922 | 23 | 145,845 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him.
Input
The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.
Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.
Output
Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
3 0 0
0 1
-1 2
1 2
Output
12.566370614359172464
Input
4 1 -1
0 0
1 2
2 0
1 1
Output
21.991148575128551812
Note
In the first sample snow will be removed from that area:
<image> | instruction | 0 | 72,923 | 23 | 145,846 |
Tags: binary search, geometry, ternary search
Correct Solution:
```
from math import pi
def vadd(v1, v2):
return v1[0]+v2[0], v1[1]+v2[1]
def vsub(v1, v2):
return v1[0]-v2[0], v1[1]-v2[1]
def smul(s, v):
return s*v[0], s*v[1]
def dot(v1, v2):
return v1[0]*v2[0] + v1[1]*v2[1]
def vmag2(v):
return v[0]*v[0] + v[1]*v[1]
def segment_dist2(p, v, w):
vp = vsub(p, v)
vw = vsub(w, v)
l2 = vmag2(vw)
t = dot(vp, vw) / float(l2)
if t <= 0:
proj = v
elif t >= 1:
proj = w
else:
proj = vadd(v, smul(t, vw))
return vmag2(vsub(p, proj))
def area(p, q):
r2min, r2max = None, None
qprev = q[-1]
for qi in q:
r2 = vmag2(vsub(p, qi))
sd2 = segment_dist2(p, qi, qprev)
if r2max is None or r2 > r2max:
r2max = r2
if r2min is None or sd2 < r2min:
r2min = sd2
qprev = qi
return pi * (r2max-r2min)
if __name__ == '__main__':
n, px, py = map(int, input().split())
q = [tuple(map(int, input().split())) for _ in range(n)]
print(area((px, py), q))
``` | output | 1 | 72,923 | 23 | 145,847 |
Provide tags and a correct Python 2 solution for this coding contest problem.
Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him.
Input
The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.
Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.
Output
Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
3 0 0
0 1
-1 2
1 2
Output
12.566370614359172464
Input
4 1 -1
0 0
1 2
2 0
1 1
Output
21.991148575128551812
Note
In the first sample snow will be removed from that area:
<image> | instruction | 0 | 72,924 | 23 | 145,848 |
Tags: binary search, geometry, ternary search
Correct Solution:
```
from sys import stdin, stdout
from collections import Counter, defaultdict
from itertools import permutations, combinations
from bisect import bisect
raw_input = stdin.readline
pr = stdout.write
import math
def in_num():
return int(raw_input())
def in_arr():
return map(int,raw_input().split())
def pr_num(n):
stdout.write(str(n)+'\n')
def pr_arr(arr):
pr(' '.join(map(str,arr))+'\n')
# fast read function for total integer input
def inp():
# this function returns whole input of
# space/line seperated integers
# Use Ctrl+D to flush stdin.
return map(int,stdin.read().split())
range = xrange # not for python 3.0+
def get_par(x1,y1,x2,y2):
if x1==x2:
return 1,0,-x1
elif y1==y2:
return 0,1,-y1
else:
return y2-y1,x1-x2,(y1*(x2-x1))-(x1*(y2-y1))
def get_dis1(x1,y1,x2,y2):
return ((x1-x2)**2)+((y1-y2)**2)
def get_dis2(x1,y1,x2,y2,x3,y3):
a,b,c=get_par(x2,y2,x3,y3)
#print a,b,c
a1=-b
b1=a
c1=-(a1*x1+b1*y1)
#print (a1*x2+b1*y2+c1)*(a1*x3+b1*y3+c1)
if (a1*x2+b1*y2+c1)*(a1*x3+b1*y3+c1)<=0:
return ((((a*x1)+(b*y1)+c)**2)/float(a**2+b**2))
else:
return 10**18
n,x,y=in_arr()
l=[]
for i in range(n):
l.append(tuple(in_arr()))
l.append(l[0])
mx=0
mn=10**18
for i in range(n):
mx=max(mx,get_dis1(x,y,l[i][0],l[i][1]))
mn=min(mn,get_dis1(x,y,l[i][0],l[i][1]))
for i in range(n):
mn=min(mn,get_dis2(x,y,l[i][0],l[i][1],l[i+1][0],l[i+1][1]))
print math.pi*(mx-mn)
``` | output | 1 | 72,924 | 23 | 145,849 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.
Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.
Peter decided to tie his car to point P and now he is wondering what is the area of the region that will be cleared from snow. Help him.
Input
The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.
Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.
All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.
Output
Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
3 0 0
0 1
-1 2
1 2
Output
12.566370614359172464
Input
4 1 -1
0 0
1 2
2 0
1 1
Output
21.991148575128551812
Note
In the first sample snow will be removed from that area:
<image>
Submitted Solution:
```
import math
import sys
def area(x_center, y_center, x_coor, y_coor):
delta_x = abs(x_coor - x_center)
delta_y = abs(y_coor - y_center)
radius = math.sqrt(delta_x ** 2 + delta_y ** 2)
return math.pi * radius ** 2
n, x_p, y_p = map(int, input().split())
# print('n:', n, 'Xp:', x_p, 'Yp:', x_p)
x_i, y_i = [], []
for i in range(n):
x, y = map(int, input().split())
x_i += [x]
y_i += [y]
x_i_2, y_i_2 = [], []
n_2 = 0
for i in range(n - 1):
print(i)
new_x = (x_i[i] + x_i[i + 1]) / 2
new_y = (y_i[i] + y_i[i + 1]) / 2
x_i_2 += [new_x]
y_i_2 += [new_y]
n_2 += 1
new_x = (x_i[0] + x_i[-1]) / 2
new_y = (y_i[0] + y_i[-1]) / 2
x_i_2 += [new_x]
y_i_2 += [new_y]
n_2 += 1
x_i += x_i_2
y_i += y_i_2
n += n_2
min_area, max_area = sys.maxsize, -sys.maxsize
for i in range(n):
circle_area = area(x_p, y_p, x_i[i], y_i[i])
# print('Area:', circle_area)
if circle_area > max_area:
max_area = circle_area
if circle_area < min_area:
min_area = circle_area
# print('Min area:', min_area)
# print('Max area:', max_area)
covered_area = max_area - min_area
# print('Covered area:', covered_area)
print(covered_area)
``` | instruction | 0 | 72,930 | 23 | 145,860 |
No | output | 1 | 72,930 | 23 | 145,861 |
Provide a correct Python 3 solution for this coding contest problem.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2 | instruction | 0 | 73,195 | 23 | 146,390 |
"Correct Solution:
```
rect = 0
hish = 0
try:
while True:
a, b, c = map(float, input().split(","))
if a*a + b*b == c*c:
rect += 1
if a == b:
hish += 1
except:
pass
print(rect)
print(hish)
``` | output | 1 | 73,195 | 23 | 146,391 |
Provide a correct Python 3 solution for this coding contest problem.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2 | instruction | 0 | 73,196 | 23 | 146,392 |
"Correct Solution:
```
import sys
rect = 0
rhom = 0
for line in sys.stdin:
try:
a, b, c = [int(i) for i in line.split(',')]
if a**2 + b**2 == c**2:
rect += 1
elif a == b:
rhom += 1
except:
break
print(rect)
print(rhom)
``` | output | 1 | 73,196 | 23 | 146,393 |
Provide a correct Python 3 solution for this coding contest problem.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2 | instruction | 0 | 73,197 | 23 | 146,394 |
"Correct Solution:
```
s = 0
t = 0
while 1:
try:
a,b,c = map(int,input().split(","))
if a**2 + b**2 == c**2:
s += 1
elif a == b :
t += 1
except EOFError:
print(s)
print(t)
break
``` | output | 1 | 73,197 | 23 | 146,395 |
Provide a correct Python 3 solution for this coding contest problem.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2 | instruction | 0 | 73,198 | 23 | 146,396 |
"Correct Solution:
```
s=0
h=0
while True:
try:
a,b,c =map(int,input().split(","))
except:break
if a**2+b**2==c**2:
s = s+1
elif a==b:
h = h+1
print(s)
print(h)
``` | output | 1 | 73,198 | 23 | 146,397 |
Provide a correct Python 3 solution for this coding contest problem.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2 | instruction | 0 | 73,199 | 23 | 146,398 |
"Correct Solution:
```
cho = 0
hishi = 0
while True:
try:
a, b, c = map(int, input().split(','))
except:
break
if a**2 + b**2 == c**2 and a!=b:
cho += 1
elif a**2 + b**2 != c**2 and a==b:
hishi += 1
print(cho)
print(hishi)
``` | output | 1 | 73,199 | 23 | 146,399 |
Provide a correct Python 3 solution for this coding contest problem.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2 | instruction | 0 | 73,200 | 23 | 146,400 |
"Correct Solution:
```
rect_cnt = dia_cnt = 0
while True:
try:
a, b, c = map(int, input().split(","))
rect_cnt += (a ** 2 + b ** 2 == c ** 2)
dia_cnt += (a == b)
except EOFError:
break
print(rect_cnt)
print(dia_cnt)
``` | output | 1 | 73,200 | 23 | 146,401 |
Provide a correct Python 3 solution for this coding contest problem.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2 | instruction | 0 | 73,201 | 23 | 146,402 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
import sys
import os
rectangle = 0
diamond = 0
parallelogram = 0
for s in sys.stdin:
a, b, c = map(int, s.split(','))
if a**2 + b**2 == c**2:
rectangle += 1
elif a == b:
diamond += 1
else:
parallelogram += 1
print(rectangle)
print(diamond)
``` | output | 1 | 73,201 | 23 | 146,403 |
Provide a correct Python 3 solution for this coding contest problem.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2 | instruction | 0 | 73,202 | 23 | 146,404 |
"Correct Solution:
```
rec = rho = 0
while True:
try:
a, b, c = map(int, input().split(','))
except:
break
if a ** 2 + b ** 2 == c ** 2:
rec += 1
if a == b:
rho += 1
print(rec, rho, sep='\n')
``` | output | 1 | 73,202 | 23 | 146,405 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2
Submitted Solution:
```
import sys
rect = 0
dia = 0
for line in sys.stdin:
a,b,c = [int(i) for i in line.split(",")]
if a**2 + b**2 == c**2:
rect += 1
if a == b:
dia += 1
print(rect)
print(dia)
``` | instruction | 0 | 73,203 | 23 | 146,406 |
Yes | output | 1 | 73,203 | 23 | 146,407 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2
Submitted Solution:
```
sq=ss=0
while 1:
try: a,b,c=map(int,input().split(','))
except: break
if a**2 + b**2 == c**2:
sq+=1
elif a == b:
ss+=1
print(sq)
print(ss)
``` | instruction | 0 | 73,204 | 23 | 146,408 |
Yes | output | 1 | 73,204 | 23 | 146,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2
Submitted Solution:
```
if __name__ == '__main__':
x = y = 0
while True:
try:
a,b,c = map(int,input().split(","))
if a*a + b*b == c*c:
x += 1
elif a == b:
y += 1
except EOFError:
break
print(x)
print(y)
``` | instruction | 0 | 73,205 | 23 | 146,410 |
Yes | output | 1 | 73,205 | 23 | 146,411 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2
Submitted Solution:
```
def get_input():
while True:
try:
yield ''.join(input())
except EOFError:
break
N = list(get_input())
ans1 = 0
ans2 = 0
for l in range(len(N)):
a, b, c = [int(i) for i in N[l].split(",")]
if a*a + b*b == c*c:
ans1 += 1
if a == b:
ans2 += 1
print(ans1)
print(ans2)
``` | instruction | 0 | 73,206 | 23 | 146,412 |
Yes | output | 1 | 73,206 | 23 | 146,413 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2
Submitted Solution:
```
n1 = n2 = 0
while True:
try:
a, b, c = map(int, line.split(','))
if a**2 + b**2 == c**2:
n1 += 1
elif a == b:
n2 += 1
except EOFError: break
print(n1)
print(n2)
``` | instruction | 0 | 73,207 | 23 | 146,414 |
No | output | 1 | 73,207 | 23 | 146,415 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a factory that inputs the data of the side and diagonal lengths to the machine and cuts out the plastic plate. At this factory, we cut out only parallelogram molds, although they vary in size. You have been ordered by your boss to count the number of rectangles and rhombuses produced among the parallelograms that are cut out.
Create a program that reads "Data to be input to the machine" and outputs the number of rectangles and diamonds manufactured.
<image>
Input
The input is given in the following format:
a1, b1, c1
a2, b2, c2
::
The data to be entered into the machine is given in multiple lines. On line i, the integers ai, bi, which represent the lengths of two adjacent sides of the i-th parallelogram, and the integer ci, which represents the length of the diagonal, are given, separated by commas (1 ≤ ai, bi, ci ≤ 1000). , ai + bi> ci). The number of data does not exceed 100.
Output
The first line outputs the number of rectangles manufactured, and the second line outputs the number of diamonds manufactured.
Example
Input
3,4,5
5,5,8
4,4,4
5,4,3
Output
1
2
Submitted Solution:
```
while True:
try:
a, b, c = map(int, input().split(","))
rect_cnt += (a ** 2 + b ** 2 == c ** 2)
dia_cnt += (a == b)
except EOFError:
break
print(rect_cnt)
print(dia_cnt)
``` | instruction | 0 | 73,208 | 23 | 146,416 |
No | output | 1 | 73,208 | 23 | 146,417 |
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