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 |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix a consisting of n rows and m columns, determine the minimum number of cells you need to change to make it good, or report that there is no way to make it good at all.
All the terms above have their usual meanings β refer to the Notes section for their formal definitions.
Input
The first line of input contains two integers n and m (1 β€ n β€ m β€ 10^6 and nβ
m β€ 10^6) β the number of rows and columns in a, respectively.
The following n lines each contain m characters, each of which is one of 0 and 1. If the j-th character on the i-th line is 1, then a_{i,j} = 1. Similarly, if the j-th character on the i-th line is 0, then a_{i,j} = 0.
Output
Output the minimum number of cells you need to change to make a good, or output -1 if it's not possible at all.
Examples
Input
3 3
101
001
110
Output
2
Input
7 15
000100001010010
100111010110001
101101111100100
010000111111010
111010010100001
000011001111101
111111011010011
Output
-1
Note
In the first case, changing a_{1,1} to 0 and a_{2,2} to 1 is enough.
You can verify that there is no way to make the matrix in the second case good.
Some definitions β
* A binary matrix is one in which every element is either 1 or 0.
* A sub-matrix is described by 4 parameters β r_1, r_2, c_1, and c_2; here, 1 β€ r_1 β€ r_2 β€ n and 1 β€ c_1 β€ c_2 β€ m.
* This sub-matrix contains all elements a_{i,j} that satisfy both r_1 β€ i β€ r_2 and c_1 β€ j β€ c_2.
* A sub-matrix is, further, called an even length square if r_2-r_1 = c_2-c_1 and r_2-r_1+1 is divisible by 2.
Submitted Solution:
```
# Coding is about expressing your feeling and there is always a better way to express your feeling _feelme
import sys,math
try:sys.stdin,sys.stdout=open('input.txt','r'),open('out.txt','w')
except:pass
from sys import stdin,stdout;mod=int(1e9 + 7);from statistics import mode
from collections import *;from math import ceil,floor,inf,factorial,gcd,log2,sqrt,log
ii1=lambda:int(stdin.readline().strip())
is1=lambda:stdin.readline().strip()
iia=lambda:list(map(int,stdin.readline().strip().split()))
isa=lambda:stdin.readline().strip().split()
# print('{:.3f}'.format(1),round(1.123456789,4))
# sys.setrecursionlimit(500000)
def lcm(a,b): return (a*b)//gcd(a,b)
def setbits(n):return bin(n).count('1')
def resetbits(n):return bin(n).count('0')
def modinv(n,p):return pow(n,p-2,p)
def ncr(n,r):
num,den=1,1;r=min(n,n-r)
for i in range(r):num*=(n-i);den*=(i+1)
return num//den
def ncr_p(n, r, p):
num,den=1,1;r=min(r,n-r)
for i in range(r):num = (num * (n - i)) % p ;den = (den * (i + 1)) % p
return (num * modinv(den,p)) % p
def isPrime(num) :
if num<=1:return False
if num==2 or n==3:return True
if (num % 2 == 0 or num % 3 == 0) :return False
m = int(num**0.5)+1
for i in range(5,m,6):
if (num % i == 0 or num % (i + 2) == 0) :return False
return True
def bin_search(arr, low, high, val):
while low <= high:
mid = low + (high - low) // 2;
if arr[mid] == val:return mid
elif arr[mid] < val:low = mid + 1
else:high = mid - 1
return -1
def sumofdigit(num):
count=0;
while num : count+=num % 10;num //= 10;
return count;
def inputmatrix():
r,c=iia();mat=[0]*r;
for i in range(r):mat[i]=iia();
return r,c,mat;
def prefix_sum(n,arr):
for i in range(1,n):arr[i]+=arr[i-1]
return arr;
def binomial(n, k):
if 0 <= k <= n:
ntok = 1;ktok = 1
for t in range(1, min(k, n - k) + 1):ntok *= n;ktok *= t;n -= 1
return ntok // ktok
else:return 0
def divisors(n):
res = [];
for i in range(1,ceil(sqrt(n))+1):
if n%i == 0:
if i==n//i:res.append(i)
else:res.append(i);res.append(n//i)
return res;
# @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ code here @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
n,m = iia()
arr=[[] for i in range(n)]
s=0
for i in range(n):
arr[i]=is1()
for i in range(n):
s+=(arr[i].count('0'))
# print(s)
a=bin(s).count('1')
if a==1:
print(len(bin(n))-3)
else:
print(-1)
``` | instruction | 0 | 83,588 | 23 | 167,176 |
No | output | 1 | 83,588 | 23 | 167,177 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya likes points a lot. Recently his mom has presented him n points lying on the line OX. Now Petya is wondering in how many ways he can choose three distinct points so that the distance between the two farthest of them doesn't exceed d.
Note that the order of the points inside the group of three chosen points doesn't matter.
Input
The first line contains two integers: n and d (1 β€ n β€ 105; 1 β€ d β€ 109). The next line contains n integers x1, x2, ..., xn, their absolute value doesn't exceed 109 β the x-coordinates of the points that Petya has got.
It is guaranteed that the coordinates of the points in the input strictly increase.
Output
Print a single integer β the number of groups of three points, where the distance between two farthest points doesn't exceed d.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
4 3
1 2 3 4
Output
4
Input
4 2
-3 -2 -1 0
Output
2
Input
5 19
1 10 20 30 50
Output
1
Note
In the first sample any group of three points meets our conditions.
In the seconds sample only 2 groups of three points meet our conditions: {-3, -2, -1} and {-2, -1, 0}.
In the third sample only one group does: {1, 10, 20}. | instruction | 0 | 83,692 | 23 | 167,384 |
Tags: binary search, combinatorics, two pointers
Correct Solution:
```
from sys import stdin
from bisect import *
from math import factorial
def nCr(n, r):
f, m = factorial, 1
for i in range(n, n - r, -1):
m *= i
return int(m // f(r))
def arr_inp(n):
if n == 1:
return [int(x) for x in stdin.readline().split()]
elif n == 2:
return [float(x) for x in stdin.readline().split()]
else:
return [str(x) for x in stdin.readline().split()]
n, d = arr_inp(1)
a, ans = arr_inp(1), 0
for i in range(2, n):
en = bisect_left(a, a[i] - d)
ans += nCr(i - en, 2)
print(ans)
``` | output | 1 | 83,692 | 23 | 167,385 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes points a lot. Recently his mom has presented him n points lying on the line OX. Now Petya is wondering in how many ways he can choose three distinct points so that the distance between the two farthest of them doesn't exceed d.
Note that the order of the points inside the group of three chosen points doesn't matter.
Input
The first line contains two integers: n and d (1 β€ n β€ 105; 1 β€ d β€ 109). The next line contains n integers x1, x2, ..., xn, their absolute value doesn't exceed 109 β the x-coordinates of the points that Petya has got.
It is guaranteed that the coordinates of the points in the input strictly increase.
Output
Print a single integer β the number of groups of three points, where the distance between two farthest points doesn't exceed d.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
4 3
1 2 3 4
Output
4
Input
4 2
-3 -2 -1 0
Output
2
Input
5 19
1 10 20 30 50
Output
1
Note
In the first sample any group of three points meets our conditions.
In the seconds sample only 2 groups of three points meet our conditions: {-3, -2, -1} and {-2, -1, 0}.
In the third sample only one group does: {1, 10, 20}.
Submitted Solution:
```
n, d = (int(x) for x in input().split())
x = [int(i) for i in input().split()]
r = 0
ans = 0
for l in range(n):
while r < n-1 and abs(x[r] - x[l]) <= d:
r += 1
if abs(x[r] - x[l]) > d and r > l+1:
r -= 1
temp = r - l - 1
if temp <= 0: continue
ans += temp * (temp+1) // 2
print(ans)
``` | instruction | 0 | 83,700 | 23 | 167,400 |
Yes | output | 1 | 83,700 | 23 | 167,401 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes points a lot. Recently his mom has presented him n points lying on the line OX. Now Petya is wondering in how many ways he can choose three distinct points so that the distance between the two farthest of them doesn't exceed d.
Note that the order of the points inside the group of three chosen points doesn't matter.
Input
The first line contains two integers: n and d (1 β€ n β€ 105; 1 β€ d β€ 109). The next line contains n integers x1, x2, ..., xn, their absolute value doesn't exceed 109 β the x-coordinates of the points that Petya has got.
It is guaranteed that the coordinates of the points in the input strictly increase.
Output
Print a single integer β the number of groups of three points, where the distance between two farthest points doesn't exceed d.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
4 3
1 2 3 4
Output
4
Input
4 2
-3 -2 -1 0
Output
2
Input
5 19
1 10 20 30 50
Output
1
Note
In the first sample any group of three points meets our conditions.
In the seconds sample only 2 groups of three points meet our conditions: {-3, -2, -1} and {-2, -1, 0}.
In the third sample only one group does: {1, 10, 20}.
Submitted Solution:
```
n,d=map(int,input().split())
arr=list(map(int,input().split()))
arr.sort()
if n<3:
print(0)
else:
i=0
j=2
count=0
while i<len(arr):
while (j<len(arr) and (arr[j]-arr[i])<=d):
j+=1
count+=((j-i-1)*(j-i-2))//2
i+=1
print(count)
``` | instruction | 0 | 83,701 | 23 | 167,402 |
Yes | output | 1 | 83,701 | 23 | 167,403 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes points a lot. Recently his mom has presented him n points lying on the line OX. Now Petya is wondering in how many ways he can choose three distinct points so that the distance between the two farthest of them doesn't exceed d.
Note that the order of the points inside the group of three chosen points doesn't matter.
Input
The first line contains two integers: n and d (1 β€ n β€ 105; 1 β€ d β€ 109). The next line contains n integers x1, x2, ..., xn, their absolute value doesn't exceed 109 β the x-coordinates of the points that Petya has got.
It is guaranteed that the coordinates of the points in the input strictly increase.
Output
Print a single integer β the number of groups of three points, where the distance between two farthest points doesn't exceed d.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
4 3
1 2 3 4
Output
4
Input
4 2
-3 -2 -1 0
Output
2
Input
5 19
1 10 20 30 50
Output
1
Note
In the first sample any group of three points meets our conditions.
In the seconds sample only 2 groups of three points meet our conditions: {-3, -2, -1} and {-2, -1, 0}.
In the third sample only one group does: {1, 10, 20}.
Submitted Solution:
```
import sys
from functools import lru_cache, cmp_to_key
from heapq import merge, heapify, heappop, heappush
from math import *
from collections import defaultdict as dd, deque, Counter as C
from itertools import combinations as comb, permutations as perm
from bisect import bisect_left as bl, bisect_right as br, bisect
from time import perf_counter
from fractions import Fraction
import copy
import time
starttime = time.time()
mod = int(pow(10, 9) + 7)
mod2 = 998244353
# from sys import stdin
# input = stdin.readline
def data(): return sys.stdin.readline().strip()
def out(*var, end="\n"): sys.stdout.write(' '.join(map(str, var))+end)
def L(): return list(sp())
def sl(): return list(ssp())
def sp(): return map(int, data().split())
def ssp(): return map(str, data().split())
def l1d(n, val=0): return [val for i in range(n)]
def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)]
try:
# sys.setrecursionlimit(int(pow(10,7)))
sys.stdin = open("input.txt", "r")
# sys.stdout = open("../output.txt", "w")
except:
pass
def pmat(A):
for ele in A:
print(*ele,end="\n")
def seive():
prime=[1 for i in range(10**6+1)]
prime[0]=0
prime[1]=0
for i in range(10**6+1):
if(prime[i]):
for j in range(2*i,10**6+1,i):
prime[j]=0
return prime
n,d=L()
A=L()
ans=0
for i in range(n):
x=br(A,A[i]+d)
x-=(1 if x==n else int(A[x]>A[i]+d))
# print(x,A[i],A[i]+d,A[x])
f=(x-i)
if f<2:
continue
ans+=(f*(f-1)//2)
# print(ans)
print(ans)
endtime = time.time()
# print(f"Runtime of the program is {endtime - starttime}")
``` | instruction | 0 | 83,702 | 23 | 167,404 |
Yes | output | 1 | 83,702 | 23 | 167,405 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes points a lot. Recently his mom has presented him n points lying on the line OX. Now Petya is wondering in how many ways he can choose three distinct points so that the distance between the two farthest of them doesn't exceed d.
Note that the order of the points inside the group of three chosen points doesn't matter.
Input
The first line contains two integers: n and d (1 β€ n β€ 105; 1 β€ d β€ 109). The next line contains n integers x1, x2, ..., xn, their absolute value doesn't exceed 109 β the x-coordinates of the points that Petya has got.
It is guaranteed that the coordinates of the points in the input strictly increase.
Output
Print a single integer β the number of groups of three points, where the distance between two farthest points doesn't exceed d.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
4 3
1 2 3 4
Output
4
Input
4 2
-3 -2 -1 0
Output
2
Input
5 19
1 10 20 30 50
Output
1
Note
In the first sample any group of three points meets our conditions.
In the seconds sample only 2 groups of three points meet our conditions: {-3, -2, -1} and {-2, -1, 0}.
In the third sample only one group does: {1, 10, 20}.
Submitted Solution:
```
from bisect import bisect
def binarySearch(arr, x):
l = 0
r = len(arr) - 1
while l <= r:
mid = (l + r) // 2
if arr[mid] == x:
return mid
elif arr[mid] < x:
l = mid + 1
else:
r = mid - 1
return r
n, d = map(int, input().split())
ls = list(map(int, input().split()))
sm = 0
for i in range(n):
r = binarySearch(ls, ls[i] + d)
k = r - i
sm += k * (k - 1) // 2
print(sm)
``` | instruction | 0 | 83,703 | 23 | 167,406 |
Yes | output | 1 | 83,703 | 23 | 167,407 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes points a lot. Recently his mom has presented him n points lying on the line OX. Now Petya is wondering in how many ways he can choose three distinct points so that the distance between the two farthest of them doesn't exceed d.
Note that the order of the points inside the group of three chosen points doesn't matter.
Input
The first line contains two integers: n and d (1 β€ n β€ 105; 1 β€ d β€ 109). The next line contains n integers x1, x2, ..., xn, their absolute value doesn't exceed 109 β the x-coordinates of the points that Petya has got.
It is guaranteed that the coordinates of the points in the input strictly increase.
Output
Print a single integer β the number of groups of three points, where the distance between two farthest points doesn't exceed d.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
4 3
1 2 3 4
Output
4
Input
4 2
-3 -2 -1 0
Output
2
Input
5 19
1 10 20 30 50
Output
1
Note
In the first sample any group of three points meets our conditions.
In the seconds sample only 2 groups of three points meet our conditions: {-3, -2, -1} and {-2, -1, 0}.
In the third sample only one group does: {1, 10, 20}.
Submitted Solution:
```
######### ## ## ## #### ##### ## # ## # ##
# # # # # # # # # # # # # # # # # # #
# # # # ### # # # # # # # # # # # #
# ##### # # # # ### # # # # # # # # #####
# # # # # # # # # # # # # # # # # #
######### # # # # ##### # ##### # ## # ## # #
"""
PPPPPPP RRRRRRR OOOO VV VV EEEEEEEEEE
PPPPPPPP RRRRRRRR OOOOOO VV VV EE
PPPPPPPPP RRRRRRRRR OOOOOOOO VV VV EE
PPPPPPPP RRRRRRRR OOOOOOOO VV VV EEEEEE
PPPPPPP RRRRRRR OOOOOOOO VV VV EEEEEEE
PP RRRR OOOOOOOO VV VV EEEEEE
PP RR RR OOOOOOOO VV VV EE
PP RR RR OOOOOO VV VV EE
PP RR RR OOOO VVVV EEEEEEEEEE
"""
"""
Perfection is achieved not when there is nothing more to add, but rather when there is nothing more to take away.
"""
import sys
input = sys.stdin.readline
read = lambda: map(int, input().split())
read_float = lambda: map(float, input().split())
# from bisect import bisect_left as lower_bound;
# from bisect import bisect_right as upper_bound;
# from math import ceil, factorial;
def ceil(x):
if x != int(x):
x = int(x) + 1
return x
def factorial(x, m):
val = 1
while x>0:
val = (val * x) % m
x -= 1
return val
def fact(x):
val = 1
while x > 0:
val *= x
x -= 1
return val
# swap_array function
def swaparr(arr, a,b):
temp = arr[a];
arr[a] = arr[b];
arr[b] = temp;
## gcd function
def gcd(a,b):
if b == 0:
return a;
return gcd(b, a % b);
## lcm function
def lcm(a, b):
return (a * b) // math.gcd(a, b)
## nCr function efficient using Binomial Cofficient
def nCr(n, k):
if k > n:
return 0
if(k > n - k):
k = n - k
res = 1
for i in range(k):
res = res * (n - i)
res = res / (i + 1)
return int(res)
## upper bound function code -- such that e in a[:i] e < x;
## prime factorization
def primefs(n):
## if n == 1 ## calculating primes
primes = {}
while(n%2 == 0 and n > 0):
primes[2] = primes.get(2, 0) + 1
n = n//2
for i in range(3, int(n**0.5)+2, 2):
while(n%i == 0 and n > 0):
primes[i] = primes.get(i, 0) + 1
n = n//i
if n > 2:
primes[n] = primes.get(n, 0) + 1
## prime factoriazation of n is stored in dictionary
## primes and can be accesed. O(sqrt n)
return primes
## MODULAR EXPONENTIATION FUNCTION
def power(x, y, p):
res = 1
x = x % p
if (x == 0) :
return 0
while (y > 0) :
if ((y & 1) == 1) :
res = (res * x) % p
y = y >> 1
x = (x * x) % p
return res
## DISJOINT SET UNINON FUNCTIONS
def swap(a,b):
temp = a
a = b
b = temp
return a,b;
# find function with path compression included (recursive)
# def find(x, link):
# if link[x] == x:
# return x
# link[x] = find(link[x], link);
# return link[x];
# find function with path compression (ITERATIVE)
def find(x, link):
p = x;
while( p != link[p]):
p = link[p];
while( x != p):
nex = link[x];
link[x] = p;
x = nex;
return p;
# the union function which makes union(x,y)
# of two nodes x and y
def union(x, y, link, size):
x = find(x, link)
y = find(y, link)
if size[x] < size[y]:
x,y = swap(x,y)
if x != y:
size[x] += size[y]
link[y] = x
## returns an array of boolean if primes or not USING SIEVE OF ERATOSTHANES
def sieve(n):
prime = [True for i in range(n+1)]
prime[0], prime[1] = False, False
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
return prime
# Euler's Toitent Function phi
def phi(n) :
result = n
p = 2
while(p * p<= n) :
if (n % p == 0) :
while (n % p == 0) :
n = n // p
result = result * (1.0 - (1.0 / (float) (p)))
p = p + 1
if (n > 1) :
result = result * (1.0 - (1.0 / (float)(n)))
return (int)(result)
def is_prime(n):
if n == 0:
return False
if n == 1:
return True
for i in range(2, int(n ** (1 / 2)) + 1):
if not n % i:
return False
return True
#### PRIME FACTORIZATION IN O(log n) using Sieve ####
MAXN = int(1e5 + 5)
def spf_sieve():
spf[1] = 1;
for i in range(2, MAXN):
spf[i] = i;
for i in range(4, MAXN, 2):
spf[i] = 2;
for i in range(3, ceil(MAXN ** 0.5), 2):
if spf[i] == i:
for j in range(i*i, MAXN, i):
if spf[j] == j:
spf[j] = i;
## function for storing smallest prime factors (spf) in the array
################## un-comment below 2 lines when using factorization #################
spf = [0 for i in range(MAXN)]
# spf_sieve();
def factoriazation(x):
res = []
for i in range(2, int(x ** 0.5) + 1):
while x % i == 0:
res.append(i)
x //= i
if x != 1:
res.append(x)
return res
## this function is useful for multiple queries only, o/w use
## primefs function above. complexity O(log n)
def factors(n):
res = []
for i in range(1, int(n ** 0.5) + 1):
if n % i == 0:
res.append(i)
res.append(n // i)
return list(set(res))
## taking integer array input
def int_array():
return list(map(int, input().strip().split()));
def float_array():
return list(map(float, input().strip().split()));
## taking string array input
def str_array():
return input().strip().split();
def binary_search(low, high, w, h, n):
while low < high:
mid = low + (high - low) // 2
# print(low, mid, high)
if check(mid, w, h, n):
low = mid + 1
else:
high = mid
return low
## for checking any conditions
def check(councils, a, k):
summ = 0
for x in a:
summ += min(x, councils)
return summ // councils >= k
#defining a couple constants
MOD = int(1e9)+7;
CMOD = 998244353;
INF = float('inf'); NINF = -float('inf');
################### ---------------- TEMPLATE ENDS HERE ---------------- ###################
from itertools import permutations
import math
import bisect as bis
import random
import sys
def solve():
n, d = read()
coordinates = list(read())
m = {}
s = 0
for i in range(n - 2):
a = bis.bisect_right(coordinates, coordinates[i] + d)
if m.get(a) != None:
continue
m[a] = 1
s += nCr(a - i, 3)
print(s)
if __name__ == '__main__':
for _ in range(1):
solve()
# fin_time = datetime.now()
# print("Execution time (for loop): ", (fin_time-init_time))
``` | instruction | 0 | 83,704 | 23 | 167,408 |
No | output | 1 | 83,704 | 23 | 167,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes points a lot. Recently his mom has presented him n points lying on the line OX. Now Petya is wondering in how many ways he can choose three distinct points so that the distance between the two farthest of them doesn't exceed d.
Note that the order of the points inside the group of three chosen points doesn't matter.
Input
The first line contains two integers: n and d (1 β€ n β€ 105; 1 β€ d β€ 109). The next line contains n integers x1, x2, ..., xn, their absolute value doesn't exceed 109 β the x-coordinates of the points that Petya has got.
It is guaranteed that the coordinates of the points in the input strictly increase.
Output
Print a single integer β the number of groups of three points, where the distance between two farthest points doesn't exceed d.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
4 3
1 2 3 4
Output
4
Input
4 2
-3 -2 -1 0
Output
2
Input
5 19
1 10 20 30 50
Output
1
Note
In the first sample any group of three points meets our conditions.
In the seconds sample only 2 groups of three points meet our conditions: {-3, -2, -1} and {-2, -1, 0}.
In the third sample only one group does: {1, 10, 20}.
Submitted Solution:
```
n, d = (int(x) for x in input().split())
x = [int(i) for i in input().split()]
r = 0
ans = 0
for l in range(n):
while r < n:
if abs(x[r] - x[l]) <= d:
r += 1
else:
r -= 1
break
if r >= n:
r -= 1
temp = r - l - 1
if temp <= 0: continue
ans += temp * (temp+1) // 2
print(ans)
``` | instruction | 0 | 83,705 | 23 | 167,410 |
No | output | 1 | 83,705 | 23 | 167,411 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes points a lot. Recently his mom has presented him n points lying on the line OX. Now Petya is wondering in how many ways he can choose three distinct points so that the distance between the two farthest of them doesn't exceed d.
Note that the order of the points inside the group of three chosen points doesn't matter.
Input
The first line contains two integers: n and d (1 β€ n β€ 105; 1 β€ d β€ 109). The next line contains n integers x1, x2, ..., xn, their absolute value doesn't exceed 109 β the x-coordinates of the points that Petya has got.
It is guaranteed that the coordinates of the points in the input strictly increase.
Output
Print a single integer β the number of groups of three points, where the distance between two farthest points doesn't exceed d.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
4 3
1 2 3 4
Output
4
Input
4 2
-3 -2 -1 0
Output
2
Input
5 19
1 10 20 30 50
Output
1
Note
In the first sample any group of three points meets our conditions.
In the seconds sample only 2 groups of three points meet our conditions: {-3, -2, -1} and {-2, -1, 0}.
In the third sample only one group does: {1, 10, 20}.
Submitted Solution:
```
from bisect import bisect_left
n, d = map(int, input().split())
points = list(map(int, input().split()))
final = 0
for i in range(len(points) - 2):
left = bisect_left(points, points[i] + d)
if left >= len(points) or points[left] != points[i] + d:
left -= 1
n = left - i
x = 1
for i in range(1, 3):
x = x * n / i
n -= 1
final += x
print(str(final)[:-2])
``` | instruction | 0 | 83,706 | 23 | 167,412 |
No | output | 1 | 83,706 | 23 | 167,413 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes points a lot. Recently his mom has presented him n points lying on the line OX. Now Petya is wondering in how many ways he can choose three distinct points so that the distance between the two farthest of them doesn't exceed d.
Note that the order of the points inside the group of three chosen points doesn't matter.
Input
The first line contains two integers: n and d (1 β€ n β€ 105; 1 β€ d β€ 109). The next line contains n integers x1, x2, ..., xn, their absolute value doesn't exceed 109 β the x-coordinates of the points that Petya has got.
It is guaranteed that the coordinates of the points in the input strictly increase.
Output
Print a single integer β the number of groups of three points, where the distance between two farthest points doesn't exceed d.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
4 3
1 2 3 4
Output
4
Input
4 2
-3 -2 -1 0
Output
2
Input
5 19
1 10 20 30 50
Output
1
Note
In the first sample any group of three points meets our conditions.
In the seconds sample only 2 groups of three points meet our conditions: {-3, -2, -1} and {-2, -1, 0}.
In the third sample only one group does: {1, 10, 20}.
Submitted Solution:
```
import bisect
import math
n, d = map(int, input().split())
x = list(map(int, input().split()))
count = 0
output = 0
for i in range(n):
ind = bisect.bisect_left(x, x[i] + d)
if ind <= n - 1 and abs(x[i] - x[ind]) <= d:
count = abs(ind - i) + 1
if count >= 3:
output += math.factorial(count) / (math.factorial(3) * math.factorial(count - 3))
print(int(output))
``` | instruction | 0 | 83,707 | 23 | 167,414 |
No | output | 1 | 83,707 | 23 | 167,415 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO | instruction | 0 | 83,724 | 23 | 167,448 |
Tags: implementation
Correct Solution:
```
n = int(input())
area = 0
minx = miny = 999999
maxx = maxy = 0
for _ in range(n):
x1, y1, x2, y2 = list(map(int, input().split()))
minx = min(minx, min(x1, x2))
miny = min(miny, min(y1, y2))
maxx = max(maxx, max(x1, x2))
maxy = max(maxy, max(y1, y2))
a = abs(x1 - x2) * abs(y1 - y2)
area += a
h = maxy - miny
w = maxx - minx
if h != w or h*h != area:
print('NO')
else:
print('YES')
``` | output | 1 | 83,724 | 23 | 167,449 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO | instruction | 0 | 83,725 | 23 | 167,450 |
Tags: implementation
Correct Solution:
```
xmin, ymin, xmax, ymax, a = 31400, 31400, 0, 0, 0
for i in range(int(input())):
x1, y1, x2, y2 = map(int, input().split())
xmin = min(xmin, x1)
ymin = min(ymin, y1)
xmax = max(xmax, x2)
ymax = max(ymax, y2)
a += (x2 - x1) * (y2 - y1)
print('YES' if xmax - xmin == ymax - ymin and a == (xmax - xmin) ** 2 else 'NO')
``` | output | 1 | 83,725 | 23 | 167,451 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO | instruction | 0 | 83,726 | 23 | 167,452 |
Tags: implementation
Correct Solution:
```
n = int(input())
x1 = []
x2 = []
y1 = []
y2 = []
S = 0
for i in range(n):
a, b, c, d = list(map(int, input().split()))
x1.append(a)
y1.append(b)
x2.append(c)
y2.append(d)
S += (c - a) * (d - b)
if (max(x2) - min(x1)) * (max(y2) - min(y1)) == S and max(x2) - min(x1) == max(y2) - min(y1):
print('YES')
else:
print('NO')
``` | output | 1 | 83,726 | 23 | 167,453 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO | instruction | 0 | 83,727 | 23 | 167,454 |
Tags: implementation
Correct Solution:
```
n = eval(input())
area = 0
p1, p2 = [], []
for i in range(n):
in_ = input().split()
p1.append(tuple(map(int, in_[0:2])))
p2.append(tuple(map(int, in_[2:4])))
area += (p2[i][0] - p1[i][0]) * (p2[i][1] - p1[i][1])
pl = min(p1)
pu = max(p2)
ok = True
for p in p1 + p2:
if pl[1] > p[1]:
ok = False
if pu[1] < p[1]:
ok = False
w, h = (pu[0] - pl[0]), (pu[1] - pl[1])
exp = w * h
print('YES' if ok and w == h and area == exp else 'NO')
``` | output | 1 | 83,727 | 23 | 167,455 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO | instruction | 0 | 83,728 | 23 | 167,456 |
Tags: implementation
Correct Solution:
```
def f(l, i):
return min(l) if i < 2 else max(l)
class CodeforcesTask325ASolution:
def __init__(self):
self.result = ''
self.n = 0
self.rectangles = []
def read_input(self):
self.n = int(input())
for _ in range(self.n):
self.rectangles.append([int(x) for x in input().split(" ")])
def process_task(self):
cords = [f([x[i] for x in self.rectangles], i) for i in range(4)]
fields = [(x[3] - x[1]) * (x[2] - x[0]) for x in self.rectangles]
ff = sum(fields)
if ff == (cords[3] - cords[1]) * (cords[2] - cords[0]) and cords[3] - cords[1] == cords[2] - cords[0]:
self.result = "YES"
else:
self.result = "NO"
def get_result(self):
return self.result
if __name__ == "__main__":
Solution = CodeforcesTask325ASolution()
Solution.read_input()
Solution.process_task()
print(Solution.get_result())
``` | output | 1 | 83,728 | 23 | 167,457 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO | instruction | 0 | 83,729 | 23 | 167,458 |
Tags: implementation
Correct Solution:
```
n = int(input())
a1, b1, a2, b2 = map(int, input().split())
s = (a2 - a1) * (b2 - b1)
for i in range(n - 1):
x1, y1, x2, y2 = map(int, input().split())
a1, b1, a2, b2 = min(a1, x1), min(b1, y1), max(a2, x2), max(b2, y2)
s += (x2 - x1) * (y2 - y1)
print('YES' if a2 - a1 == b2 - b1 and s == (a2 - a1) * (b2 - b1) else 'NO')
``` | output | 1 | 83,729 | 23 | 167,459 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO | instruction | 0 | 83,730 | 23 | 167,460 |
Tags: implementation
Correct Solution:
```
n = int(input())
#print(n)
l = [[int(x) for x in input().split()] for i in range(n)]
#print(l)
dx = (max([r[2] for r in l])-min([r[0] for r in l]))
dy = (max([r[3] for r in l])-min([r[1] for r in l]))
size = dx*dy
#print(size)
if dx == dy and sum([(r[2]-r[0])*(r[3]-r[1]) for r in l]) == size:
print("YES")
else:
print("NO")
``` | output | 1 | 83,730 | 23 | 167,461 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO | instruction | 0 | 83,731 | 23 | 167,462 |
Tags: implementation
Correct Solution:
```
x0=[]; x1=[]; y0=[]; y1=[]
n=int(input())
s=0 # Variable to add rects. areas together
for i in range(n):
l=list(map(int,input().split()))
x0.extend([l[0]])
x1.extend([l[2]])
y0.extend([l[1]])
y1.extend([l[3]])
s+=(l[3]-l[1])*(l[2]-l[0])
lx=max(x1)-min(x0)
ly=max(y1)-min(y0)
if lx==ly and lx*ly==s:
print('YES')
else:
print('NO')
``` | output | 1 | 83,731 | 23 | 167,463 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO
Submitted Solution:
```
n = int(input())
x1, y1, x2, y2 = map(int, input().split())
l, r, u, d = x1, x2, y2, y1
s = (x2 - x1) * (y2 - y1)
for i in range(n - 1):
x1, y1, x2, y2 = map(int, input().split())
s += (x2 - x1) * (y2 - y1)
l = min(l, x1)
r = max(r, x2)
u = max(u, y2)
d = min(d, y1)
if r - l == u - d and (r - l) * (u - d) == s:
print('YES')
else:
print('NO')
``` | instruction | 0 | 83,732 | 23 | 167,464 |
Yes | output | 1 | 83,732 | 23 | 167,465 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO
Submitted Solution:
```
xmin, ymin, xmax, ymax, a = 31400, 31400, 0, 0, 0
for i in range(int(input())):
x1, y1, x2, y2 = map(int, input().split())
xmin = min(xmin, x1)
ymin = min(ymin, y1)
xmax = max(xmax, x2)
ymax = max(ymax, y2)
a += (x2 - x1) * (y2 - y1)
#print(xmax,xmin,ymax,ymin,a,end="")
print('YES' if xmax - xmin == ymax - ymin and a == (xmax - xmin) ** 2 else 'NO')
``` | instruction | 0 | 83,733 | 23 | 167,466 |
Yes | output | 1 | 83,733 | 23 | 167,467 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO
Submitted Solution:
```
n = int(input())
s = 0
INF = 10**9
minx = miny = INF
maxx = maxy = -INF
for i in range(n):
x1, y1, x2, y2 = map(int, input().split())
s += abs(x1 - x2) * abs(y1 - y2)
minx = min(minx, x1, x2)
maxx = max(maxx, x1, x2)
miny = min(miny, y1, y2)
maxy = max(maxy, y1, y2)
if (maxx - minx) == (maxy - miny) and s == (maxx - minx) ** 2:
print ("YES")
else:
print ("NO")
``` | instruction | 0 | 83,734 | 23 | 167,468 |
Yes | output | 1 | 83,734 | 23 | 167,469 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO
Submitted Solution:
```
n = eval(input())
area = 0
p1 = []
p2 = []
ps = []
xl, xu, yl, yu = 1 << 28, 0, 1 << 28, 0
for i in range(n):
in_ = input().split()
p1.append(tuple(map(int, in_[0:2])))
p2.append(tuple(map(int, in_[2:4])))
ps.append(tuple(map(int, in_[0:2])))
ps.append(tuple(map(int, in_[2:4])))
xl = min(xl, p1[-1][0], p2[-1][0])
xu = max(xu, p1[-1][0], p2[-1][0])
yl = min(yl, p1[-1][1], p2[-1][1])
yu = max(yu, p1[-1][1], p2[-1][1])
ok = True
for p in ps:
for dx in (-0.5, 0, 0.5):
for dy in (-0.5, 0, 0.5):
q = (p[0] + dx, p[1] + dy)
if not (xl < q[0] < xu and yl < q[1] < yu):
continue
c = False
for i in range(n):
if p1[i][0] <= q[0] <= p2[i][0] and p1[i][1] <= q[1] <= p2[i][1]:
c = True
if not c:
ok = False
print('YES' if ok and (xu - xl) == (yu - yl) else 'NO')
``` | instruction | 0 | 83,735 | 23 | 167,470 |
Yes | output | 1 | 83,735 | 23 | 167,471 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO
Submitted Solution:
```
n = eval(input())
area = 0
p1 = []
p2 = []
ps = []
xl, xu, yl, yu = 0, 1 << 28, 0, 1 << 28
for i in range(n):
in_ = input().split()
p1.append(tuple(map(int, in_[0:2])))
p2.append(tuple(map(int, in_[2:4])))
xl = min(xl, p1[-1][0], p2[-1][0])
xu = max(xu, p1[-1][0], p2[-1][0])
yl = min(yl, p1[-1][1], p2[-1][1])
yu = max(yu, p1[-1][1], p2[-1][1])
ok = True
for p in p2:
q = p
if p[0] < xu:
q = (q[0] + 0.5, q[1])
if p[1] < yu:
q = (q[0], q[1] + 0.5)
for i in range(n):
if not (p1[i][0] <= p[0] <= p2[i][0] and p1[i][1] <= p[1] <= p2[i][1]):
ok = False
for p in p1:
q = p
if xl < p[0]:
q = (q[0] - 0.5, q[1])
if yl < p[1]:
q = (q[0], q[1] - 0.5)
for i in range(n):
if not (p1[i][0] <= p[0] <= p2[i][0] and p1[i][1] <= p[1] <= p2[i][1]):
ok = False
print('YES' if ok and (xu - xl) == (yu - yl)else 'NO')
``` | instruction | 0 | 83,736 | 23 | 167,472 |
No | output | 1 | 83,736 | 23 | 167,473 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO
Submitted Solution:
```
n = int(input())
x1, y1, x2, y2 = 0, 0, 0, 0
for i in range(n):
ex1, wy1, ex2, wy2 = map(int, input().split())
x1 = min(x1, ex1)
y1 = min(y1, wy1)
x2 = max(x2, ex2)
y2 = max(y2, wy2)
if x2-x1 == y2 - y1:
print('YES')
else:
print('NO')
``` | instruction | 0 | 83,737 | 23 | 167,474 |
No | output | 1 | 83,737 | 23 | 167,475 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO
Submitted Solution:
```
n = int(input())
x1, y1, x2, y2 = map(int, input().split())
u_r, d_r, u_l, d_l = [x2, y2], [x2, y1], [x1, y2], [x1, y1]
s = (x2 - x1) * (y2 - y1)
for i in range(n - 1):
x1, y1, x2, y2 = map(int, input().split())
s += (x2 - x1) * (y2 - y1)
if x2 >= u_r[0] and y2 >= u_r[1]:
u_r = [x2, y2]
if x2 >= u_r[0] and y1 <= d_r[1]:
d_r = [x2, y1]
if x1 <= u_l[0] and y2 >= u_l[1]:
u_l = [x1, y2]
if x1 <= d_l[0] and y1 <= d_l[1]:
d_l = [x1, y1]
if u_r[0] != d_r[0] or u_r[1] != u_l[1] or u_l[0] != d_l[0] or d_l[1] != d_r[1]:
print('NO')
elif u_r[1] - d_r[1] == u_r[0] - u_l[0] == u_l[1] - d_l[1] == d_r[0] - d_l[0]:
if (u_r[0] - d_l[0]) * (u_r[1] - d_l[1]) == s:
print('YES')
else:
print('NO')
else:
print('NO')
``` | instruction | 0 | 83,738 | 23 | 167,476 |
No | output | 1 | 83,738 | 23 | 167,477 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).
Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.
Input
The first line contains a single integer n (1 β€ n β€ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 β€ x1 < x2 β€ 31400, 0 β€ y1 < y2 β€ 31400) β x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.
No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).
Output
In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.
Examples
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3
Output
YES
Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
Output
NO
Submitted Solution:
```
n = int(input())
x1 = []
x2 = []
y1 = []
y2 = []
S = 0
for i in range(n):
a, b, c, d = list(map(int, input().split()))
x1.append(a)
y1.append(b)
x2.append(c)
y2.append(d)
S += (c - a) * (d - b)
if (max(x2) - min(x1)) * (max(y2) - min(y1)) == S:
print('YES')
else:
print('NO')
``` | instruction | 0 | 83,739 | 23 | 167,478 |
No | output | 1 | 83,739 | 23 | 167,479 |
Provide a correct Python 3 solution for this coding contest problem.
A mobile phone company ACMICPC (Advanced Cellular, Mobile, and Internet-Connected Phone Corporation) is planning to set up a collection of antennas for mobile phones in a city called Maxnorm. The company ACMICPC has several collections for locations of antennas as their candidate plans, and now they want to know which collection is the best choice.
for this purpose, they want to develop a computer program to find the coverage of a collection of antenna locations. Each antenna Ai has power ri, corresponding to "radius". Usually, the coverage region of the antenna may be modeled as a disk centered at the location of the antenna (xi, yi) with radius ri. However, in this city Maxnorm such a coverage region becomes the square [xi β ri, xi + ri] Γ [yi β ri, yi + ri]. In other words, the distance between two points (xp, yp) and (xq, yq) is measured by the max norm max{ |xp β xq|, |yp β yq|}, or, the Lβ norm, in this city Maxnorm instead of the ordinary Euclidean norm β {(xp β xq)2 + (yp β yq)2}.
As an example, consider the following collection of 3 antennas
4.0 4.0 3.0
5.0 6.0 3.0
5.5 4.5 1.0
depicted in the following figure
<image>
where the i-th row represents xi, yi ri such that (xi, yi) is the position of the i-th antenna and ri is its power. The area of regions of points covered by at least one antenna is 52.00 in this case.
Write a program that finds the area of coverage by a given collection of antenna locations.
Input
The input contains multiple data sets, each representing a collection of antenna locations. A data set is given in the following format.
n
x1 y1 r1
x2 y2 r2
. . .
xn yn rn
The first integer n is the number of antennas, such that 2 β€ n β€ 100. The coordinate of the i-th antenna is given by (xi, yi), and its power is ri. xi, yi and ri are fractional numbers between 0 and 200 inclusive.
The end of the input is indicated by a data set with 0 as the value of n.
Output
For each data set, your program should output its sequence number (1 for the first data set, 2 for the second, etc.) and the area of the coverage region. The area should be printed with two digits to the right of the decimal point, after rounding it to two decimal places.
The sequence number and the area should be printed on the same line with no spaces at the beginning and end of the line. The two numbers should be separated by a space.
Example
Input
3
4.0 4.0 3.0
5.0 6.0 3.0
5.5 4.5 1.0
2
3.0 3.0 3.0
1.5 1.5 1.0
0
Output
1 52.00
2 36.00 | instruction | 0 | 84,151 | 23 | 168,302 |
"Correct Solution:
```
import sys
def is_contained(a, area):
rx1, ry1, rx2, ry2 = a
for r in area:
x1, y1, x2, y2 = r
if x1 <= rx1 <= x2 and x1 <= rx2 <= x2 and \
y1 <= ry1 <= y2 and y1 <= ry2 <= y2:
return True
return False
def add_area(a, area):
if is_contained(a, area):
return area
xs, ys, xe, ye = a
if xs >= xe or ys >= ye:
return area
ret = area
if area == []:
return [a]
rr = []
for r in area:
rxs, rys, rxe, rye = r
if xs < rxs < xe and ys < rys < ye and xe <= rxe and ye <= rye:
rr = [[xs, ys, xe, rys], [xs, rys, rxs, ye]]
elif xs < rxs < xe and ys < rye < ye and rys <= ys and xe <= rxe:
rr = [[xs, ys, rxs, rye], [xs, rye, xe, ye]]
elif xs < rxe < xe and ys < rys < ye and rxs <= xs and ye <= rye:
rr = [[xs, ys, rxe, rys], [rxe, ys, xe, ye]]
elif xs < rxe < xe and ys < rye < ye and rxs <= xs and rys <= ys:
rr = [[xs, rye, rxe, ye], [rxe, ys, xe, ye]]
elif xs < rxs and ys <= rys < ye and rxe < xe and ye <= rye:
rr = [[xs, ys, xe, rys], [xs, rys, rxs, ye], [rxe, rys, xe, ye]]
elif xs < rxs and ys < rye <= ye and rxe < xe and rys <= ys:
rr = [[xs, rye, xe, ye], [xs, ys, rxs, rye], [rxe, ys, xe, rye]]
elif xs <= rxs < xe and ys < rys and rye < ye and xe <= rxe:
rr = [[xs, ys, rxs, ye], [rxs, ys, xe, rys], [rxs, rye, xe, ye]]
elif xs < rxe <= xe and ys < rys and rye < ye and rxs <= xs:
rr = [[rxe, ys, xe, ye], [xs, ys, rxe, rys], [xs, rye, rxe, ye]]
elif rxs <= xs and xe <= rxe and ys < rys < ye and ye <= rye:
rr = [[xs, ys, xe, rys]]
elif rys <= ys and ye <= rye and xs < rxs < xe and xe <= rxe:
rr = [[xs, ys, rxs, ye]]
elif rxs <= xs and xe <= rxe and ys < rye < ye and rys <= ys:
rr = [[xs, rye, xe, ye]]
elif rys <= ys and ye <= rye and xs < rxe < xe and rxs <= xs:
rr = [[rxe, ys, xe, ye]]
elif xs < rxs < xe and xs < rxe < xe and ys < rys < ye and ys < rye < ye:
rr = [[xs, ys, rxs, rye], [xs, rye, rxe, ye], [rxe, rys, xe, ye], [rxs, ys, xe, rys]]
elif rxs <= xs and xe <= rxe and ys < rys and rye < ye:
rr = [[xs, ys, xe, rys], [xs, rye, xe, ye]]
elif rys <= ys and ye <= rye and xs < rxs and rxe < xe:
rr = [[xs, ys, rxs, ye], [rxe, ys, xe, ye]]
if rr != []:
for q in rr:
ret = add_area(q, ret)
break
if rr == []:
ret.append(a)
return ret
def calc_area(area):
s = 0.0
for r in area:
s += (r[2]- r[0]) * (r[3] - r[1])
return s
n = 0
c = 0
area = []
for line in sys.stdin:
if n == 0:
n = int(line)
c += 1
area = []
if n == 0:
break
else:
ant = list(map(float, line.strip().split()))
r = [ant[0] - ant[2], ant[1] - ant[2], ant[0] + ant[2], ant[1] + ant[2]]
area = add_area(r, area)
n -= 1
if n == 0:
print("%d %.2f" % (c, calc_area(area)))
``` | output | 1 | 84,151 | 23 | 168,303 |
Provide a correct Python 3 solution for this coding contest problem.
A mobile phone company ACMICPC (Advanced Cellular, Mobile, and Internet-Connected Phone Corporation) is planning to set up a collection of antennas for mobile phones in a city called Maxnorm. The company ACMICPC has several collections for locations of antennas as their candidate plans, and now they want to know which collection is the best choice.
for this purpose, they want to develop a computer program to find the coverage of a collection of antenna locations. Each antenna Ai has power ri, corresponding to "radius". Usually, the coverage region of the antenna may be modeled as a disk centered at the location of the antenna (xi, yi) with radius ri. However, in this city Maxnorm such a coverage region becomes the square [xi β ri, xi + ri] Γ [yi β ri, yi + ri]. In other words, the distance between two points (xp, yp) and (xq, yq) is measured by the max norm max{ |xp β xq|, |yp β yq|}, or, the Lβ norm, in this city Maxnorm instead of the ordinary Euclidean norm β {(xp β xq)2 + (yp β yq)2}.
As an example, consider the following collection of 3 antennas
4.0 4.0 3.0
5.0 6.0 3.0
5.5 4.5 1.0
depicted in the following figure
<image>
where the i-th row represents xi, yi ri such that (xi, yi) is the position of the i-th antenna and ri is its power. The area of regions of points covered by at least one antenna is 52.00 in this case.
Write a program that finds the area of coverage by a given collection of antenna locations.
Input
The input contains multiple data sets, each representing a collection of antenna locations. A data set is given in the following format.
n
x1 y1 r1
x2 y2 r2
. . .
xn yn rn
The first integer n is the number of antennas, such that 2 β€ n β€ 100. The coordinate of the i-th antenna is given by (xi, yi), and its power is ri. xi, yi and ri are fractional numbers between 0 and 200 inclusive.
The end of the input is indicated by a data set with 0 as the value of n.
Output
For each data set, your program should output its sequence number (1 for the first data set, 2 for the second, etc.) and the area of the coverage region. The area should be printed with two digits to the right of the decimal point, after rounding it to two decimal places.
The sequence number and the area should be printed on the same line with no spaces at the beginning and end of the line. The two numbers should be separated by a space.
Example
Input
3
4.0 4.0 3.0
5.0 6.0 3.0
5.5 4.5 1.0
2
3.0 3.0 3.0
1.5 1.5 1.0
0
Output
1 52.00
2 36.00 | instruction | 0 | 84,152 | 23 | 168,304 |
"Correct Solution:
```
# AOJ 1202: Mobile Phone Coverage
# Python3 2018.7.28
from bisect import bisect_left
cno = 0
while True:
n = int(input())
if n == 0: break
tbl, xx, yy = [], set(), set()
for i in range(n):
x, y, r = map(float, input().split())
x, y, r = int(100*x), int(100*y), int(100*r)
x1, y1, x2, y2 = x-r, y-r, x+r, y+r
tbl.append((x1, y1, x2, y2))
xx.add(x1); xx.add(x2)
yy.add(y1); yy.add(y2)
xx = sorted(xx); yy = sorted(yy)
arr = [[0 for c in range(201)] for r in range(201)]
for x1, y1, x2, y2 in tbl:
l = bisect_left(xx, x1); r = bisect_left(xx, x2)
u = bisect_left(yy, y1); d = bisect_left(yy, y2)
for y in range(u, d):
for x in range(l, r): arr[y][x] = 1
ans = 0
for r in range(1, len(yy)):
t = yy[r]-yy[r-1]
for c in range(1, len(xx)):
if arr[r-1][c-1]: ans += t * (xx[c]-xx[c-1])
ans //= 100
cno += 1
print(cno, "{:d}.{:02d}".format(ans//100, ans%100))
``` | output | 1 | 84,152 | 23 | 168,305 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A mobile phone company ACMICPC (Advanced Cellular, Mobile, and Internet-Connected Phone Corporation) is planning to set up a collection of antennas for mobile phones in a city called Maxnorm. The company ACMICPC has several collections for locations of antennas as their candidate plans, and now they want to know which collection is the best choice.
for this purpose, they want to develop a computer program to find the coverage of a collection of antenna locations. Each antenna Ai has power ri, corresponding to "radius". Usually, the coverage region of the antenna may be modeled as a disk centered at the location of the antenna (xi, yi) with radius ri. However, in this city Maxnorm such a coverage region becomes the square [xi β ri, xi + ri] Γ [yi β ri, yi + ri]. In other words, the distance between two points (xp, yp) and (xq, yq) is measured by the max norm max{ |xp β xq|, |yp β yq|}, or, the Lβ norm, in this city Maxnorm instead of the ordinary Euclidean norm β {(xp β xq)2 + (yp β yq)2}.
As an example, consider the following collection of 3 antennas
4.0 4.0 3.0
5.0 6.0 3.0
5.5 4.5 1.0
depicted in the following figure
<image>
where the i-th row represents xi, yi ri such that (xi, yi) is the position of the i-th antenna and ri is its power. The area of regions of points covered by at least one antenna is 52.00 in this case.
Write a program that finds the area of coverage by a given collection of antenna locations.
Input
The input contains multiple data sets, each representing a collection of antenna locations. A data set is given in the following format.
n
x1 y1 r1
x2 y2 r2
. . .
xn yn rn
The first integer n is the number of antennas, such that 2 β€ n β€ 100. The coordinate of the i-th antenna is given by (xi, yi), and its power is ri. xi, yi and ri are fractional numbers between 0 and 200 inclusive.
The end of the input is indicated by a data set with 0 as the value of n.
Output
For each data set, your program should output its sequence number (1 for the first data set, 2 for the second, etc.) and the area of the coverage region. The area should be printed with two digits to the right of the decimal point, after rounding it to two decimal places.
The sequence number and the area should be printed on the same line with no spaces at the beginning and end of the line. The two numbers should be separated by a space.
Example
Input
3
4.0 4.0 3.0
5.0 6.0 3.0
5.5 4.5 1.0
2
3.0 3.0 3.0
1.5 1.5 1.0
0
Output
1 52.00
2 36.00
Submitted Solution:
```
import sys
def is_contained(a, area):
rx1, ry1, rx2, ry2 = a
for r in area:
x1, y1, x2, y2 = r
if x1 <= rx1 <= x2 and x1 <= rx2 <= x2 and \
y1 <= ry1 <= y2 and y1 <= ry2 <= y2:
return True
return False
def is_inside(x, y, rect):
rx1, ry1, rx2, ry2 = rect
return (rx1 <= x <= rx2) and (ry1 <= y <= ry2)
def add_area(a, area):
if is_contained(a, area):
return area
xs, ys, xe, ye = a
if xs >= xe or ys >= ye:
return area
ret = area
if area == []:
return [a]
rr = []
for r in area:
rxs, rys, rxe, rye = r
if xs <= rxs < xe and ys <= rys < ye and xe <= rxe and ye <= rye:
rr = [[xs, ys, xe, rys], [xs, rys, rxs, ye]]
elif xs <= rxs < xe and ys < rye <= ye and rys <= ys and xe <= rxe:
rr = [[xs, ys, rxs, rye], [xs, rye, xe, ye]]
elif xs < rxe <= xe and ys <= rys < ye and rxs <= xs and ye <= rye:
rr = [[xs, ys, rxe, rys], [rxe, ys, xe, ye]]
elif xs < rxe <= xe and ys < rye <= ye and rxs <= xs and rys <= ys:
rr = [[xs, rye, rxe, ye], [rxe, ys, xe, ye]]
elif xs <= rxs and ys <= rys < ye and rxe <= xe and ye <= rye:
rr = [[xs, ys, xe, rys], [xs, rys, rxs, ye], [rxe, rys, xe, ye]]
elif xs <= rxs and ys < rye <= ye and rxe <= xe and rys <= ys:
rr = [[xs, rye, xe, ye], [xs, ys, rxs, rye], [rxe, ys, xe, rye]]
elif xs <= rxs < xe and ys <= rys and rye <= ye and xe <= rxe:
rr = [[xs, ys, rxs, ye], [rxs, ys, xe, rys], [rxs, rye, xe, ye]]
elif xs < rxe <= xe and ys <= rys and rye <= ye and rxs <= xs:
rr = [[rxe, ys, xe, ye], [xs, ys, rxe, rys], [xs, rye, rxe, ye]]
elif rxs <= xs and xe <= rxe and ys <= rys < ye:
rr = [[xs, ys, xe, rys]]
elif rys <= ys and ye <= rye and xs <= rxs < xe:
rr = [[xs, ys, rxs, ye]]
elif rxs <= xs and xe <= rxe and ys < rye <= ye:
rr = [[xs, rye, xe, ye]]
elif rys <= ys and ye <= rye and xs < rxe <= xe:
rr = [[rxe, ys, xe, ye]]
if rr != []:
for q in rr:
ret = add_area(q, ret)
break
if rr == []:
ret.append(a)
return ret
def calc_area(area):
s = 0.0
for r in area:
s += (r[2]- r[0]) * (r[3] - r[1])
return s
n = 0
c = 0
area = []
for line in sys.stdin:
if n == 0:
n = int(line)
c += 1
area = []
if n == 0:
break
else:
ant = list(map(float, line.strip().split()))
r = [ant[0] - ant[2], ant[1] - ant[2], ant[0] + ant[2], ant[1] + ant[2]]
area = add_area(r, area)
n -= 1
if n == 0:
print("%d %.2f" % (c, calc_area(area)))
``` | instruction | 0 | 84,153 | 23 | 168,306 |
No | output | 1 | 84,153 | 23 | 168,307 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A mobile phone company ACMICPC (Advanced Cellular, Mobile, and Internet-Connected Phone Corporation) is planning to set up a collection of antennas for mobile phones in a city called Maxnorm. The company ACMICPC has several collections for locations of antennas as their candidate plans, and now they want to know which collection is the best choice.
for this purpose, they want to develop a computer program to find the coverage of a collection of antenna locations. Each antenna Ai has power ri, corresponding to "radius". Usually, the coverage region of the antenna may be modeled as a disk centered at the location of the antenna (xi, yi) with radius ri. However, in this city Maxnorm such a coverage region becomes the square [xi β ri, xi + ri] Γ [yi β ri, yi + ri]. In other words, the distance between two points (xp, yp) and (xq, yq) is measured by the max norm max{ |xp β xq|, |yp β yq|}, or, the Lβ norm, in this city Maxnorm instead of the ordinary Euclidean norm β {(xp β xq)2 + (yp β yq)2}.
As an example, consider the following collection of 3 antennas
4.0 4.0 3.0
5.0 6.0 3.0
5.5 4.5 1.0
depicted in the following figure
<image>
where the i-th row represents xi, yi ri such that (xi, yi) is the position of the i-th antenna and ri is its power. The area of regions of points covered by at least one antenna is 52.00 in this case.
Write a program that finds the area of coverage by a given collection of antenna locations.
Input
The input contains multiple data sets, each representing a collection of antenna locations. A data set is given in the following format.
n
x1 y1 r1
x2 y2 r2
. . .
xn yn rn
The first integer n is the number of antennas, such that 2 β€ n β€ 100. The coordinate of the i-th antenna is given by (xi, yi), and its power is ri. xi, yi and ri are fractional numbers between 0 and 200 inclusive.
The end of the input is indicated by a data set with 0 as the value of n.
Output
For each data set, your program should output its sequence number (1 for the first data set, 2 for the second, etc.) and the area of the coverage region. The area should be printed with two digits to the right of the decimal point, after rounding it to two decimal places.
The sequence number and the area should be printed on the same line with no spaces at the beginning and end of the line. The two numbers should be separated by a space.
Example
Input
3
4.0 4.0 3.0
5.0 6.0 3.0
5.5 4.5 1.0
2
3.0 3.0 3.0
1.5 1.5 1.0
0
Output
1 52.00
2 36.00
Submitted Solution:
```
import sys
def is_contained(a, area):
rx1, ry1, rx2, ry2 = a
for r in area:
x1, y1, x2, y2 = r
if x1 <= rx1 <= x2 and x1 <= rx2 <= x2 and \
y1 <= ry1 <= y2 and y1 <= ry2 <= y2:
return True
return False
def is_inside(x, y, rect):
rx1, ry1, rx2, ry2 = rect
return (rx1 < x < rx2) and (ry1 < y < ry2)
def add_area(a, area):
if is_contained(a, area):
return area
xs, ys, xe, ye = a
if xs >= xe or ys >= ye:
return area
ret = area
if area == []:
return [a]
rr = []
for r in area:
rxs, rys, rxe, rye = r
if is_inside(rxs, rys, a) and xe < rxe and ye < rye:
rr = [[xs, ys, xe, rys], [xs, rys, rxs, ye]]
elif is_inside(rxs, rye, a) and rys < ys and xe < rxe:
rr = [[xs, ys, rxs, rye], [xs, rye, xe, ye]]
elif is_inside(rxe, rys, a) and rxs < xs and ye < rye:
rr = [[xs, ys, rxe, rys], [rxe, ys, xe, ye]]
elif is_inside(rxe, rye, a) and rxs < xs and rys < ys:
rr = [[xs, rye, rxe, ye], [rxe, ys, xe, ye]]
elif is_inside(rxs, rys, a) and is_inside(rxe, rys, a) and ye < rye:
rr = [[xs, ys, xe, rys], [xs, rys, rxs, ye], [rxe, rys, xe, ye]]
elif is_inside(rxs, rye, a) and is_inside(rxe, rye, a) and rys < ys:
rr = [[xs, rye, xe, ye], [xs, ys, rxs, rye], [rxe, ys, xe, rye]]
elif is_inside(rxs, rys, a) and is_inside(rxs, rye, a) and xe < rxe:
rr = [[xs, ys, rxs, ye], [rxs, ys, xe, rys], [rxs, rye, xe, ye]]
elif is_inside(rxe, rys, a) and is_inside(rxe, rye, a) and rxs < xs:
rr = [[rxe, ys, xe, ye], [xs, ys, rxe, rys], [xs, rye, rxe, ye]]
elif rxs < xs and xe < rxe and ys < rys < ye:
rr = [[xs, ys, xe, rys]]
elif rys < ys and ye < rye and xs < rxs < xe:
rr = [[xs, ys, rxs, ye]]
elif rxs < xs and xe < rxe and ys < rye < ye:
rr = [[xs, rye, xe, ye]]
elif rys < ys and ye < rye and xs < rxe < xe:
rr = [[rxe, ys, xe, ye]]
if rr != []:
for q in rr:
ret = add_area(q, ret)
break
if rr == []:
ret.append(a)
return ret
def calc_area(area):
s = 0.0
for r in area:
s += (r[2]- r[0]) * (r[3] - r[1])
return s
n = 0
c = 0
area = []
for line in sys.stdin:
if n == 0:
n = int(line)
c += 1
area = []
if n == 0:
break
else:
ant = list(map(float, line.strip().split()))
r = [ant[0] - ant[2], ant[1] - ant[2], ant[0] + ant[2], ant[1] + ant[2]]
area = add_area(r, area)
n -= 1
if n == 0:
print("%d %.2f" % (c, calc_area(area)))
``` | instruction | 0 | 84,154 | 23 | 168,308 |
No | output | 1 | 84,154 | 23 | 168,309 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A mobile phone company ACMICPC (Advanced Cellular, Mobile, and Internet-Connected Phone Corporation) is planning to set up a collection of antennas for mobile phones in a city called Maxnorm. The company ACMICPC has several collections for locations of antennas as their candidate plans, and now they want to know which collection is the best choice.
for this purpose, they want to develop a computer program to find the coverage of a collection of antenna locations. Each antenna Ai has power ri, corresponding to "radius". Usually, the coverage region of the antenna may be modeled as a disk centered at the location of the antenna (xi, yi) with radius ri. However, in this city Maxnorm such a coverage region becomes the square [xi β ri, xi + ri] Γ [yi β ri, yi + ri]. In other words, the distance between two points (xp, yp) and (xq, yq) is measured by the max norm max{ |xp β xq|, |yp β yq|}, or, the Lβ norm, in this city Maxnorm instead of the ordinary Euclidean norm β {(xp β xq)2 + (yp β yq)2}.
As an example, consider the following collection of 3 antennas
4.0 4.0 3.0
5.0 6.0 3.0
5.5 4.5 1.0
depicted in the following figure
<image>
where the i-th row represents xi, yi ri such that (xi, yi) is the position of the i-th antenna and ri is its power. The area of regions of points covered by at least one antenna is 52.00 in this case.
Write a program that finds the area of coverage by a given collection of antenna locations.
Input
The input contains multiple data sets, each representing a collection of antenna locations. A data set is given in the following format.
n
x1 y1 r1
x2 y2 r2
. . .
xn yn rn
The first integer n is the number of antennas, such that 2 β€ n β€ 100. The coordinate of the i-th antenna is given by (xi, yi), and its power is ri. xi, yi and ri are fractional numbers between 0 and 200 inclusive.
The end of the input is indicated by a data set with 0 as the value of n.
Output
For each data set, your program should output its sequence number (1 for the first data set, 2 for the second, etc.) and the area of the coverage region. The area should be printed with two digits to the right of the decimal point, after rounding it to two decimal places.
The sequence number and the area should be printed on the same line with no spaces at the beginning and end of the line. The two numbers should be separated by a space.
Example
Input
3
4.0 4.0 3.0
5.0 6.0 3.0
5.5 4.5 1.0
2
3.0 3.0 3.0
1.5 1.5 1.0
0
Output
1 52.00
2 36.00
Submitted Solution:
```
import sys
def is_contained(a, area):
rx1, ry1, rx2, ry2 = a
for r in area:
x1, y1, x2, y2 = r
if x1 <= rx1 <= x2 and x1 <= rx2 <= x2 and \
y1 <= ry1 <= y2 and y1 <= ry2 <= y2:
return True
return False
def is_inside(x, y, rect):
rx1, ry1, rx2, ry2 = rect
return (rx1 < x < rx2) and (ry1 < y < ry2)
def add_area(a, area):
if is_contained(a, area):
return area
xs, ys, xe, ye = a
if xs >= xe or ys >= ye:
return area
ret = area
if area == []:
return [a]
rr = []
for r in area:
rxs, rys, rxe, rye = r
if is_inside(rxs, rys, a) and xe < rxe and ye < rye:
rr = [[xs, ys, xe, rys], [xs, rys, rxs, ye]]
elif is_inside(rxs, rye, a) and rys < ys and xe < rxe:
rr = [[xs, ys, rxs, rye], [xs, rye, xe, ye]]
elif is_inside(rxe, rys, a) and rxs < xs and ye < rye:
rr = [[xs, ys, rxe, rys], [rxe, ys, xe, ye]]
elif is_inside(rxe, rye, a) and rxs < xs and rys < ys:
rr = [[xs, rye, rxe, ye], [rxe, ys, xe, ye]]
elif is_inside(rxs, rys, a) and is_inside(rxe, rys, a) and ye < rye:
rr = [[xs, ys, xe, rys], [xs, rys, rxs, ye], [rxe, rys, xe, ye]]
elif is_inside(rxs, rye, a) and is_inside(rxe, rye, a) and rys < ys:
rr = [[xs, rye, xe, ye], [xs, ys, rxs, rye], [rxe, ys, xe, rye]]
elif is_inside(rxs, rys, a) and is_inside(rxs, rye, a) and xe < rxe:
rr = [[xs, ys, rxs, ye], [rxs, ys, xe, rys], [rxs, rye, xe, ye]]
elif is_inside(rxe, rys, a) and is_inside(rxe, rye, a) and rxs < xs:
rr = [[rxe, ys, xe, ye], [xs, ys, rxe, rys], [xs, rye, rxe, ye]]
elif rxs < xs and xe < rxe and ys < rys < ye:
rr = [[xs, ys, xe, rys]]
elif rys < ys and ye < rye and xs < rxs < xe:
rr = [[xs, ys, rxs, ye]]
elif rxs < xs and xe < rxe and ys < rye < ye:
rr = [[xs, rye, xe, ye]]
elif rys < ys and ye < rye and xs < rxe < xe:
rr = [[rxe, ys, xe, ye]]
if rr != []:
for q in rr:
ret = add_area(q, ret)
break
if rr == []:
ret.append(a)
return ret
def calc_area(area):
s = 0.0
for r in area:
s += (r[2]- r[0]) * (r[3] - r[1])
return s
n = 0
c = 0
area = []
for line in sys.stdin:
if n == 0:
n = int(line)
c += 1
area = []
if n == 0:
break
else:
ant = list(map(float, line.strip().split(" ")))
r = [ant[0] - ant[2], ant[1] - ant[2], ant[0] + ant[2], ant[1] + ant[2]]
area = add_area(r, area)
n -= 1
if n == 0:
print("%d %.2f" % (c, calc_area(area)))
``` | instruction | 0 | 84,155 | 23 | 168,310 |
No | output | 1 | 84,155 | 23 | 168,311 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N non-overlapping circles in xy-plane. The radius of each circle varies, but the radius of the largest circle is not double longer than that of the smallest.
<image>
Figure 1: The Sample Input
The distance between two circles C1 and C2 is given by the usual formula
<image>
where (xi, yi ) is the coordinates of the center of the circle Ci, and ri is the radius of Ci, for i = 1, 2.
Your task is to write a program that finds the closest pair of circles and print their distance.
Input
The input consists of a series of test cases, followed by a single line only containing a single zero, which indicates the end of input.
Each test case begins with a line containing an integer N (2 β€ N β€ 100000), which indicates the number of circles in the test case. N lines describing the circles follow. Each of the N lines has three decimal numbers R, X, and Y. R represents the radius of the circle. X and Y represent the x- and y-coordinates of the center of the circle, respectively.
Output
For each test case, print the distance between the closest circles. You may print any number of digits after the decimal point, but the error must not exceed 0.00001.
Example
Input
4
1.0 0.0 0.0
1.5 0.0 3.0
2.0 4.0 0.0
1.0 3.0 4.0
0
Output
0.5 | instruction | 0 | 84,169 | 23 | 168,338 |
"Correct Solution:
```
def _get_distance(c1, c2):
return ((c1[1] - c2[1]) ** 2 + (c1[2] - c2[2]) ** 2) ** 0.5 - c1[0] - c2[0]
from itertools import combinations
def _get_min_distance(circles):
min_d = float("inf")
for c1, c2 in combinations(circles, 2):
min_d = min(min_d, _get_distance(c1, c2))
return min_d
def closest_pair_distance(circles, axis =1):
# axis: x; 1, y; 2
n = len(circles)
if n <= 3:
return _get_min_distance(circles)
else:
mid = n // 2
r, x, y = zip(*circles)
if len(set(x)) > len(set(y)):
if axis == 2:
circles.sort(key = lambda c: c[1] - c[0])
axis1 = 1
axis2 = 2
else:
if axis == 1:
circles.sort(key = lambda c: c[2] - c[0])
axis1 = 2
axis2 = 1
A_circles = circles[:mid]
B_circles = circles[mid:]
d_Amin = closest_pair_distance(A_circles.copy(), axis1)
d_Bmin = closest_pair_distance(B_circles.copy(), axis1)
dist = min(d_Amin, d_Bmin)
min_d = dist
A_circles.sort(key = lambda c: c[axis] + c[0])
B_edge = B_circles[0][axis1] - B_circles[0][0]
for ac in A_circles[::-1]:
ac_r = ac[0]
ac_edge = ac[axis1] + ac_r
if B_edge - ac_edge >= dist:
break
for bc in B_circles:
bc_r = bc[0]
if bc[axis1] - bc_r - ac_edge >= dist:
break
if abs(ac[axis2] - bc[axis2]) - ac_r - bc_r < dist:
min_d = min(min_d, _get_distance(ac, bc))
return min_d
# solve
def solve():
import sys
input_lines = sys.stdin.readlines()
while True:
N = int(input_lines[0])
if N == 0:
break
circles = [tuple(map(float, l.split())) for l in input_lines[1:N+1]]
print('{:.8f}'.format(closest_pair_distance(circles)))
del input_lines[:N+1]
solve()
``` | output | 1 | 84,169 | 23 | 168,339 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N non-overlapping circles in xy-plane. The radius of each circle varies, but the radius of the largest circle is not double longer than that of the smallest.
<image>
Figure 1: The Sample Input
The distance between two circles C1 and C2 is given by the usual formula
<image>
where (xi, yi ) is the coordinates of the center of the circle Ci, and ri is the radius of Ci, for i = 1, 2.
Your task is to write a program that finds the closest pair of circles and print their distance.
Input
The input consists of a series of test cases, followed by a single line only containing a single zero, which indicates the end of input.
Each test case begins with a line containing an integer N (2 β€ N β€ 100000), which indicates the number of circles in the test case. N lines describing the circles follow. Each of the N lines has three decimal numbers R, X, and Y. R represents the radius of the circle. X and Y represent the x- and y-coordinates of the center of the circle, respectively.
Output
For each test case, print the distance between the closest circles. You may print any number of digits after the decimal point, but the error must not exceed 0.00001.
Example
Input
4
1.0 0.0 0.0
1.5 0.0 3.0
2.0 4.0 0.0
1.0 3.0 4.0
0
Output
0.5
Submitted Solution:
```
from itertools import combinations
def _get_distance(c1, c2):
return ((c1[1] - c2[1]) ** 2 + (c1[2] - c2[2]) ** 2) ** 0.5 - c1[0] - c2[0]
def _get_min_distance(circles):
min_d = float("inf")
for c1, c2 in combinations(circles, 2):
min_d = min(min_d, _get_distance(c1, c2))
return min_d
def closest_pair_distance(circles, axis =1):
# axis: x; 1, y; 2
n = len(circles)
if n <= 3:
return _get_min_distance(circles)
else:
mid = n // 2
r, x, y = zip(*circles)
if len(set(x)) > len(set(y)):
if axis == 2:
circles.sort(key = lambda c: c[1] - c[0])
axis1 = 1
axis2 = 2
else:
if axis == 1:
circles.sort(key = lambda c: c[2] - c[0])
axis1 = 2
axis2 = 1
A_circles = circles[:mid]
B_circles = circles[mid:]
d_Amin = closest_pair_distance(A_circles.copy(), axis1)
d_Bmin = closest_pair_distance(B_circles.copy(), axis1)
dist = min(d_Amin, d_Bmin)
min_d = dist
B_0_axis1 = B_circles[0][axis1]
B_0_r = B_circles[0][0]
for ac in A_circles[::-1]:
ac_r = ac[0]
ac_axis1 = ac[axis1]
ac_axis2 = ac[axis2]
if B_0_axis1 - ac_axis1 - B_0_r - ac_r >= dist:
break
for bc in B_circles:
bc_r = bc[0]
if bc[axis1] - ac_axis1 - bc_r - ac_r >= dist:
break
if abs(ac_axis2 - bc[axis2]) - ac_r - bc_r < dist:
min_d = min(min_d, _get_distance(ac, bc))
return min_d
# solve
def solve():
import sys
input_lines = sys.stdin.readlines()
while True:
N = int(input_lines[0])
if N == 0:
break
circles = [tuple(map(float, l.split())) for l in input_lines[1:N+1]]
print('{:.8f}'.format(closest_pair_distance(circles)))
del input_lines[:N+1]
solve()
``` | instruction | 0 | 84,170 | 23 | 168,340 |
No | output | 1 | 84,170 | 23 | 168,341 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N non-overlapping circles in xy-plane. The radius of each circle varies, but the radius of the largest circle is not double longer than that of the smallest.
<image>
Figure 1: The Sample Input
The distance between two circles C1 and C2 is given by the usual formula
<image>
where (xi, yi ) is the coordinates of the center of the circle Ci, and ri is the radius of Ci, for i = 1, 2.
Your task is to write a program that finds the closest pair of circles and print their distance.
Input
The input consists of a series of test cases, followed by a single line only containing a single zero, which indicates the end of input.
Each test case begins with a line containing an integer N (2 β€ N β€ 100000), which indicates the number of circles in the test case. N lines describing the circles follow. Each of the N lines has three decimal numbers R, X, and Y. R represents the radius of the circle. X and Y represent the x- and y-coordinates of the center of the circle, respectively.
Output
For each test case, print the distance between the closest circles. You may print any number of digits after the decimal point, but the error must not exceed 0.00001.
Example
Input
4
1.0 0.0 0.0
1.5 0.0 3.0
2.0 4.0 0.0
1.0 3.0 4.0
0
Output
0.5
Submitted Solution:
```
def solve():
import sys
from itertools import combinations
input_lines = sys.stdin.readlines()
while True:
N = int(input_lines[0])
if N == 0:
break
distance = []
for t1, t2 in combinations(input_lines[1:N+1], 2):
r1, x1, y1 = map(float, t1.split())
r2, x2, y2 = map(float, t2.split())
d = ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5 -r1 - r2
distance.append(d)
print(min(distance))
del input_lines[:N+1]
solve()
``` | instruction | 0 | 84,171 | 23 | 168,342 |
No | output | 1 | 84,171 | 23 | 168,343 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N non-overlapping circles in xy-plane. The radius of each circle varies, but the radius of the largest circle is not double longer than that of the smallest.
<image>
Figure 1: The Sample Input
The distance between two circles C1 and C2 is given by the usual formula
<image>
where (xi, yi ) is the coordinates of the center of the circle Ci, and ri is the radius of Ci, for i = 1, 2.
Your task is to write a program that finds the closest pair of circles and print their distance.
Input
The input consists of a series of test cases, followed by a single line only containing a single zero, which indicates the end of input.
Each test case begins with a line containing an integer N (2 β€ N β€ 100000), which indicates the number of circles in the test case. N lines describing the circles follow. Each of the N lines has three decimal numbers R, X, and Y. R represents the radius of the circle. X and Y represent the x- and y-coordinates of the center of the circle, respectively.
Output
For each test case, print the distance between the closest circles. You may print any number of digits after the decimal point, but the error must not exceed 0.00001.
Example
Input
4
1.0 0.0 0.0
1.5 0.0 3.0
2.0 4.0 0.0
1.0 3.0 4.0
0
Output
0.5
Submitted Solution:
```
from itertools import combinations
def _get_distance(c1, c2):
return ((c1[1] - c2[1]) ** 2 + (c1[2] - c2[2]) ** 2) ** 0.5 - c1[0] - c2[0]
def _get_min_distance(circles):
min_d = float("inf")
for c1, c2 in combinations(circles, 2):
min_d = min(min_d, _get_distance(c1, c2))
return min_d
def closest_pair_distance(circles, axis =1):
# axis: x; 1, y; 2
n = len(circles)
if n <= 3:
return _get_min_distance(circles)
else:
mid = n // 2
r, x, y = zip(*circles)
if len(set(x)) > len(set(y)):
if axis:
circles.sort(key = lambda c: c[1])
axis1 = 1
axis2 = 2
else:
if not axis:
circles.sort(key = lambda c: c[2])
axis1 = 2
axis2 = 1
A_circles = circles[:mid]
B_circles = circles[mid:]
d_Amin = closest_pair_distance(A_circles.copy(), axis1)
d_Bmin = closest_pair_distance(B_circles.copy(), axis1)
dist = min(d_Amin, d_Bmin)
min_d = dist
B_0_axis1 = B_circles[0][axis1]
B_0_r = B_circles[0][0]
for ac in A_circles[::-1]:
ac_r = ac[0]
ac_axis1 = ac[axis1]
ac_axis2 = ac[axis2]
if B_0_axis1 - ac_axis1 - B_0_r - ac_r >= dist:
break
for bc in B_circles:
bc_r = bc[0]
if bc[axis1] - ac_axis1 - bc_r - ac_r >= dist:
break
if abs(ac_axis2 - bc[axis2]) - ac_r - bc_r < dist:
min_d = min(min_d, _get_distance(ac, bc))
return min_d
# solve
def solve():
import sys
input_lines = sys.stdin.readlines()
while True:
N = int(input_lines[0])
if N == 0:
break
circles = [tuple(map(float, l.split())) for l in input_lines[1:N+1]]
print(closest_pair_distance(circles))
del input_lines[:N+1]
solve()
``` | instruction | 0 | 84,172 | 23 | 168,344 |
No | output | 1 | 84,172 | 23 | 168,345 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N non-overlapping circles in xy-plane. The radius of each circle varies, but the radius of the largest circle is not double longer than that of the smallest.
<image>
Figure 1: The Sample Input
The distance between two circles C1 and C2 is given by the usual formula
<image>
where (xi, yi ) is the coordinates of the center of the circle Ci, and ri is the radius of Ci, for i = 1, 2.
Your task is to write a program that finds the closest pair of circles and print their distance.
Input
The input consists of a series of test cases, followed by a single line only containing a single zero, which indicates the end of input.
Each test case begins with a line containing an integer N (2 β€ N β€ 100000), which indicates the number of circles in the test case. N lines describing the circles follow. Each of the N lines has three decimal numbers R, X, and Y. R represents the radius of the circle. X and Y represent the x- and y-coordinates of the center of the circle, respectively.
Output
For each test case, print the distance between the closest circles. You may print any number of digits after the decimal point, but the error must not exceed 0.00001.
Example
Input
4
1.0 0.0 0.0
1.5 0.0 3.0
2.0 4.0 0.0
1.0 3.0 4.0
0
Output
0.5
Submitted Solution:
```
from itertools import combinations
def _get_distance(c1, c2):
return ((c1[1] - c2[1]) ** 2 + (c1[2] - c2[2]) ** 2) ** 0.5 - c1[0] - c2[0]
def _get_min_distance(circles):
min_d = float("inf")
for c1, c2 in combinations(circles, 2):
min_d = min(min_d, _get_distance(c1, c2))
return min_d
def closest_pair_distance(circles, axis =1):
# axis: x; 1, y; 2
n = len(circles)
if n <= 3:
return _get_min_distance(circles)
else:
mid = n // 2
r, x, y = zip(*circles)
if len(set(x)) > len(set(y)):
if axis == 2:
circles.sort(key = lambda c: c[1] - c[0])
axis1 = 1
axis2 = 2
else:
if axis == 1:
circles.sort(key = lambda c: c[2] - c[0])
axis1 = 2
axis2 = 1
A_circles = circles[:mid]
B_circles = circles[mid:]
d_Amin = closest_pair_distance(A_circles.copy(), axis1)
d_Bmin = closest_pair_distance(B_circles.copy(), axis1)
dist = min(d_Amin, d_Bmin)
min_d = dist
B_0_axis1 = B_circles[0][axis1]
B_0_r = B_circles[0][0]
for ac in A_circles[::-1]:
ac_r = ac[0]
ac_axis1 = ac[axis1]
ac_axis2 = ac[axis2]
if B_0_axis1 - ac_axis1 - B_0_r - ac_r >= dist:
break
for bc in B_circles:
bc_r = bc[0]
if bc[axis1] - ac_axis1 - bc_r - ac_r >= dist:
break
if abs(ac_axis2 - bc[axis2]) - ac_r - bc_r < dist:
min_d = min(min_d, _get_distance(ac, bc))
return min_d
# solve
def solve():
import sys
input_lines = sys.stdin.readlines()
while True:
N = int(input_lines[0])
if N == 0:
break
circles = [tuple(map(float, l.split())) for l in input_lines[1:N+1]]
print(closest_pair_distance(circles))
del input_lines[:N+1]
solve()
``` | instruction | 0 | 84,173 | 23 | 168,346 |
No | output | 1 | 84,173 | 23 | 168,347 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7 | instruction | 0 | 84,269 | 23 | 168,538 |
Tags: implementation
Correct Solution:
```
n = int(input())
for _ in range(n):
a, b, c, d = map(int, input().split())
first_answer = a
second_answer = c
while second_answer == first_answer and c <= second_answer <= d:
second_answer += 1
print ('{} {}'.format(first_answer,second_answer))
``` | output | 1 | 84,269 | 23 | 168,539 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7 | instruction | 0 | 84,270 | 23 | 168,540 |
Tags: implementation
Correct Solution:
```
import math
q=eval(input())
i=1
while i<=q:
x=str(input())
l1,r1,l2,r2=x.split()
a=math.ceil(float(l1))
b=math.floor(float(r2))
if a==b:
a=math.floor(float(r1))
print (a,b)
i+=1
``` | output | 1 | 84,270 | 23 | 168,541 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7 | instruction | 0 | 84,271 | 23 | 168,542 |
Tags: implementation
Correct Solution:
```
def inpl(): return [int(i) for i in input().split()]
for _ in range(int(input())):
a, _, c, d = inpl()
if a != d:
print(*(a, d))
else:
print(*(a, c))
``` | output | 1 | 84,271 | 23 | 168,543 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7 | instruction | 0 | 84,272 | 23 | 168,544 |
Tags: implementation
Correct Solution:
```
q = int(input())
for l in range(q):
l1, r1, l2, r2 = [int(i) for i in input().split()]
if l1 == l2:
if l1 < r1:
print(r1, ' ', l2)
else:
print(l1, ' ', r2)
else:
print(l1, ' ', l2)
if __name__ == "__main__":
pass
``` | output | 1 | 84,272 | 23 | 168,545 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7 | instruction | 0 | 84,273 | 23 | 168,546 |
Tags: implementation
Correct Solution:
```
q = int(input())
for _ in range(q):
a, b, c, d = map(int, input().split())
if a != c:
print(a, c)
elif b != d:
print(b, d)
else:
print(a, d)
``` | output | 1 | 84,273 | 23 | 168,547 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7 | instruction | 0 | 84,274 | 23 | 168,548 |
Tags: implementation
Correct Solution:
```
import random
n=int(input())
for i in range(0,n):
a=list(map(int,str(input()).split()))
p=random.randint(a[0],a[1])
q=random.randint(a[2],a[3])
while(p==q and a[0]!=a[1] and a[3]!=a[2]):
q=random.randint(a[2],a[3])
print(p,q)
``` | output | 1 | 84,274 | 23 | 168,549 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7 | instruction | 0 | 84,275 | 23 | 168,550 |
Tags: implementation
Correct Solution:
```
q=lambda:map(int,input().split())
qi=lambda:int(input())
qs=lambda:input().split()
for _ in [0]*qi():
l1,r1,l2,r2=q()
print(*(l1,l2) if l1!=l2 else (l1,l2+1))
``` | output | 1 | 84,275 | 23 | 168,551 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7 | instruction | 0 | 84,276 | 23 | 168,552 |
Tags: implementation
Correct Solution:
```
q = int(input())
for _ in range(q):
l1,r1,l2,r2 = map(int, input().split())
if l1 != l2:
print(l1, l2)
else:
print(r1, l2)
``` | output | 1 | 84,276 | 23 | 168,553 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7
Submitted Solution:
```
n=int(input())
for z in range(n):
l1,r1,l2,r2=map(int,input().split())
i=l1
j=l2
while(i<=r1 and j<=r2):
if(i!=j):
print(i,j)
break
else:
j+=1
``` | instruction | 0 | 84,277 | 23 | 168,554 |
Yes | output | 1 | 84,277 | 23 | 168,555 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7
Submitted Solution:
```
q=int(input())
for i in range(q):
l1,r1,l2,r2=map(int,input().split())
if (l1==r2):
l1=r1
print(l1)
print(r2)
``` | instruction | 0 | 84,278 | 23 | 168,556 |
Yes | output | 1 | 84,278 | 23 | 168,557 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7
Submitted Solution:
```
q = int(input())
nums = []
for i in range(q):
nums.append(input())
for i in range(int(q)):
l_1, r_1, l_2, r_2 = map(int, nums[i].split(" "))
if l_1 <= l_2:
print(str(l_1)+" "+str(r_2))
else:
print(str(r_1)+" "+str(l_2))
``` | instruction | 0 | 84,279 | 23 | 168,558 |
Yes | output | 1 | 84,279 | 23 | 168,559 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7
Submitted Solution:
```
n=int(input())
for i in range(n):
d,b,k,s=map(int,input().split())
if d!=s:
print(d,s)
else:
print(d,s-1)
``` | instruction | 0 | 84,280 | 23 | 168,560 |
Yes | output | 1 | 84,280 | 23 | 168,561 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7
Submitted Solution:
```
q = int(input())
while q!=0:
a,b,c,d = map(int,input().split())
print(a,d)
q-=1
``` | instruction | 0 | 84,281 | 23 | 168,562 |
No | output | 1 | 84,281 | 23 | 168,563 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two segments [l_1; r_1] and [l_2; r_2] on the x-axis. It is guaranteed that l_1 < r_1 and l_2 < r_2. Segments may intersect, overlap or even coincide with each other.
<image> The example of two segments on the x-axis.
Your problem is to find two integers a and b such that l_1 β€ a β€ r_1, l_2 β€ b β€ r_2 and a β b. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment [l_1; r_1] and the second one belongs to the segment [l_2; r_2].
It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 β€ q β€ 500) β the number of queries.
Each of the next q lines contains four integers l_{1_i}, r_{1_i}, l_{2_i} and r_{2_i} (1 β€ l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} β€ 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}) β the ends of the segments in the i-th query.
Output
Print 2q integers. For the i-th query print two integers a_i and b_i β such numbers that l_{1_i} β€ a_i β€ r_{1_i}, l_{2_i} β€ b_i β€ r_{2_i} and a_i β b_i. Queries are numbered in order of the input.
It is guaranteed that the answer exists. If there are multiple answers, you can print any.
Example
Input
5
1 2 1 2
2 6 3 4
2 4 1 3
1 2 1 3
1 4 5 8
Output
2 1
3 4
3 2
1 2
3 7
Submitted Solution:
```
a=int(input())
r=0
m=0
for i in range (a):
b,c,d,e=map(int,input().split())
r=round((b+c)/2)
m=round((d+e)/2)
if r==m and m-1!=0:
m=m-1
print (r,' ',m)
``` | instruction | 0 | 84,282 | 23 | 168,564 |
No | output | 1 | 84,282 | 23 | 168,565 |
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