Problem:


Score : 500 points

Problem Statement

There are N integers X_1, X_2, \cdots, X_N, and we know that A_i \leq X_i \leq B_i.
Find the number of different values that the median of X_1, X_2, \cdots, X_N can take.

Notes

The median of X_1, X_2, \cdots, X_N is defined as follows. Let x_1, x_2, \cdots, x_N be the result of sorting X_1, X_2, \cdots, X_N in ascending order.

If N is odd, the median is x_{(N+1)/2};

if N is even, the median is (x_{N/2} + x_{N/2+1}) / 2.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq A_i \leq B_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 B_1
A_2 B_2
:
A_N B_N

Output

Print the answer.

Sample Input 1

2
1 2
2 3

Sample Output 1

3

If X_1 = 1 and X_2 = 2, the median is \frac{3}{2};

if X_1 = 1 and X_2 = 3, the median is 2;

if X_1 = 2 and X_2 = 2, the median is 2;

if X_1 = 2 and X_2 = 3, the median is \frac{5}{2}.

Thus, the median can take three values: \frac{3}{2}, 2, and \frac{5}{2}.

Sample Input 2

3
100 100
10 10000
1 1000000000

Sample Output 2

9991



Sample input:
2
1 2
2 3


Sample output:
3

Submission status: Accepted

Solution code:
n = int(input())
t = []
for i in range(n):
    ai,bi = map(int,input().split())
    t.append([ai,bi])
# t.sort(key=lambda x:x[1],reverse=True)
t.sort(key=lambda x:x[0])
if n % 2 == 1:
    a = t[n//2][0]
    t.sort(key=lambda x:x[1])
    b = t[n//2][1]
    print(b-a+1)
    exit()
if n % 2 == 0:
    a1 = t[n//2-1][0]
    a2 = t[n//2][0]
    t.sort(key=lambda x:x[1])
    b1 = t[n//2-1][1]
    b2 = t[n//2][1]
    print(b1+b2-a1-a2+1)

Submission status: Accepted

Solution code:
N = int(input())

A = []
B = []
for _ in range(N):
    a, b = map(int, input().split())
    A.append(a)
    B.append(b)
A = sorted(A)
B = sorted(B)

if N % 2 == 0:
    Amed = A[N//2-1]+A[N//2]
    Bmed = B[N//2-1]+B[N//2]
    print(Bmed-Amed+1)
else:
    Amed = A[N//2]
    Bmed = B[N//2]
    print(Bmed-Amed+1)

Submission status: Accepted

Solution code:
def e_count_median():
    N = int(input())
    # Intervals = [[int(i) for i in input().split()] for j in range(N)]
    Min, Max = [], []
    for _ in range(N):
        a, b = [int(i) for i in input().split()]
        Min.append(a)
        Max.append(b)

    Min.sort()
    Max.sort()
    if N % 2 == 0:
        median_min, median_max = Min[N // 2] + Min[N // 2 - 1], Max[N // 2] + Max[N // 2 - 1]
    else:
        median_min, median_max = Min[N // 2], Max[N // 2]
    return median_max - median_min + 1

print(e_count_median())

Submission status: Accepted

Solution code:
N = int(input())
E = [list(map(int,input().split())) for _ in range(N)]

E = sorted(E,key=lambda x:x[0])

A=[v[0] for v in E]
B=[v[1] for v in E]

A = sorted(A)
B = sorted(B)


if N%2==0:
    A_mid = (A[N//2]+A[N//2-1])
    B_mid = (B[N//2]+B[N//2-1])
    print(B_mid-A_mid+1)
else:
    A_mid = A[N//2]
    B_mid=B[N//2]
    print(B_mid-A_mid+1)

Submission status: Accepted

Solution code:
n = int(input())
a, b = [], []
for _ in range(n):
    tmp = list(map(int, input().split()))
    a.append(tmp[0])
    b.append(tmp[1])

a.sort()
b.sort()

if n%2:
    print(b[(n+1)//2-1]-a[(n+1)//2-1]+1)
else:
    print(b[n//2-1]+b[n//2]-a[n//2-1]-a[n//2]+1)

Submission status: Accepted

Solution code:
from bisect import *
from collections import *

N = int(input())
# AB = [list(map(int, input().split())) for i in range(N)]
A, B = [None]*N, [None]*N
for i in range(N):
    A[i], B[i] = map(int, input().split())
A.sort()
B.sort()
if N % 2:
    a = A[N//2]
    b = B[N//2]
    ans = b-a+1
else:
    a = A[N//2-1] + A[N//2] 
    b = B[N//2-1] + B[N//2]
    ans = b-a+1
print(ans)

Submission status: Accepted

Solution code:
import statistics

N = int(input())
A = []
B = []
for i in range(N):
    a, b = map(int, input().split())
    A.append(a)
    B.append(b)

A_med = statistics.median(A)
B_med = statistics.median(B)

if N % 2 == 0:
    ans = int((B_med - A_med) * 2 + 1)
else:
    ans = int((B_med - A_med) + 1)

print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
import numpy as np
from decimal import *

n = int(input())

Li = [[int(e) for e in input().split()] for _ in range(n)]

Li = np.array(Li)
LA = Li[:,0]
LB = Li[:,1]

LA.sort()
LB.sort()


if n %2 == 0: # n = 2m
    idx =n //2 -1
    min = (LA[idx] + LA[idx+1])
    max = (LB[idx] + LB[idx+1])

else: # n = 2m - 1
    idx =(n+1) //2 -1
    min = LA[idx]
    max = LB[idx]

print(max - min +1 )

Submission status: Accepted

Solution code:
n = int(input())
a = []
b = []
for i in range(n):
  c, d = map(int, input().split())
  a.append(c)
  b.append(d)
a.sort()
b.sort()
if n % 2 == 1:
  t = int((n-1)/2)
  ans = b[t] - a[t] + 1
else:
  t = int(n/2)
  s = (b[t] + b[t-1])/2 - (a[t] + a[t-1])/2
  ans = int(2*s+1)
print(ans)

Submission status: Accepted

Solution code:
def main():
    n = int(input())
    ranges = [[int(x) for x in input().split()] for _ in range(n)]

    mins = []
    maxs = []
    for a, b in ranges:
        mins.append(a)
        maxs.append(b)
    mins.sort()
    maxs.sort()
    if n % 2 == 0:
        min_mid = mins[n // 2 - 1] + mins[n // 2]
        max_mid = maxs[n // 2 - 1] + maxs[n // 2]
        ans = max_mid - min_mid + 1
    else:
        min_mid = mins[(n + 1) // 2 - 1]
        max_mid = maxs[(n + 1) // 2 - 1]
        ans = max_mid - min_mid + 1
    print(ans)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
n = int(input())
a_ = [0]*n
b_ = [0]*n
c = [0]*n
for i in range(n):
    a_[i],b_[i] = map(int,input().split())
    c[i] = a_[i]
lb_ = 1
ub_ = 10**9
c.sort()
med = c[(n-1)//2]
med_ub = c[(n-1)//2+1]


def ok_odd(m):
    cnt = 0
    for i in range(n):
        a = a_[i]
        if a <= m:
            cnt += 1
    if cnt < (n+1)//2:
        return False
    cnt = 0
    for i in range(n):
        b = b_[i]
        if b >= m:
            cnt += 1
    if cnt < (n+1)//2:
        return False
    cnt = 0
    for i in range(n):
        a,b = a_[i],b_[i]
        if a <= m and m <= b:
            return True
    return False

def ok_even_lb(m):
    cnt = 0
    for i in range(n):
        a = a_[i]
        if a <= m:
            cnt += 1
    if cnt < n//2:
        return False
    cnt = 0
    for i in range(n):
        b = b_[i]
        if b >= m:
            cnt += 1
    if cnt < n//2 + 1:
        return False
    cnt = 0
    for i in range(n):
        a,b = a_[i],b_[i]
        if a <= m and m <= b:
            return True
    return False

def ok_even_ub(m):
    cnt = 0
    for i in range(n):
        a = a_[i]
        if a <= m:
            cnt += 1
    if cnt < n//2 + 1:
        return False
    cnt = 0
    for i in range(n):
        b = b_[i]
        if b >= m:
            cnt += 1
    if cnt < n//2:
        return False
    cnt = 0
    for i in range(n):
        a,b = a_[i],b_[i]
        if a <= m and m <= b:
            return True
    return False

if n % 2 == 1:
    lb = 1
    ub = med
    while lb < ub:
        mid = (lb+ub)//2
        if ok_odd(mid):
            ub = mid
        else:
            lb = mid+1
    lb_ret = lb
    lb = med
    ub = 10**9
    while lb < ub:
        mid = (lb+ub+1)//2
        if ok_odd(mid):
            lb = mid
        else:
            ub = mid-1
    ub_ret = lb
    print(ub_ret-lb_ret+1)
else:
    lb = 1
    ub = med
    while lb < ub:
        mid = (lb+ub)//2
        if ok_even_lb(mid):
            ub = mid
        else:
            lb = mid+1
    lb_lb = lb
    lb = med
    ub = 10**9
    while lb < ub:
        mid = (lb+ub+1)//2
        if ok_even_lb(mid):
            lb = mid
        else:
            ub = mid-1
    lb_ub = lb

    lb = 1
    ub = med_ub
    while lb < ub:
        mid = (lb+ub)//2
        if ok_even_ub(mid):
            ub = mid
        else:
            lb = mid+1
    ub_lb = lb
    lb = med_ub
    ub = 10**9
    while lb < ub:
        mid = (lb+ub+1)//2
        if ok_even_ub(mid):
            lb = mid
        else:
            ub = mid-1
    ub_ub = lb
    print(ub_ub+lb_ub-lb_lb-ub_lb+1)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(1 << 25)
read = sys.stdin.readline
ra = range
enu = enumerate


def mina(*argv, sub=1): return list(map(lambda x: x - sub, argv))
# 受け渡されたすべての要素からsubだけ引く.リストを*をつけて展開しておくこと


def read_a_int(): return int(read())


def read_ints(): return list(map(int, read().split()))


def read_col(H):
    '''H is number of rows
    A列、B列が与えられるようなとき
    ex1)A,B=read_col(H)    ex2) A,=read_col(H) #一列の場合'''
    ret = []
    for _ in range(H):
        ret.append(list(map(int, read().split())))
    return tuple(map(list, zip(*ret)))


def read_tuple(H):
    '''H is number of rows'''
    ret = []
    for _ in range(H):
        ret.append(tuple(map(int, read().split())))
    return ret


def read_matrix(H):
    '''H is number of rows'''
    ret = []
    for _ in range(H):
        ret.append(list(map(int, read().split())))
    return ret
    # return [list(map(int, read().split())) for _ in range(H)] # 内包表記はpypyでは遅いため


MOD = 10**9 + 7
INF = 2**31  # 2147483648 > 10**9
# default import
from collections import defaultdict, Counter, deque
from operator import itemgetter
from itertools import product, permutations, combinations
from bisect import bisect_left, bisect_right  # , insort_left, insort_right


class Compress:
    def __init__(self, ls):
        # 座標圧縮クラス(仮) #どうしたら使いやすくなるのか知らんけど
        self.i_to_orig = sorted(set(ls))
        self.orig_to_i = {}
        for i, zahyou in enumerate(self.i_to_orig):
            self.orig_to_i[zahyou] = i
        self.len = len(self.i_to_orig)

    def __len__(self):
        return len(self.i_to_orig)


N = read_a_int()
A, B = read_col(N)
A.sort()
B.sort()
if N & 1:
    print(B[N // 2] - A[N // 2] + 1)
else:
    l = (A[N // 2 - 1] + A[N // 2])
    r = (B[N // 2] + B[N // 2 - 1])
    print(abs(r - l) + 1)


# 偶数奇数でちょっとわけて考えよう
# Nが奇数なら→X[N//2]の候補の数

# 2つの領域の重なり方は3種類
# 1. 重なっていない
# 2. 一部重なっている
# 3. 完全に内包関係にある(ちょうどの場合も含む)

# 座標圧縮と前後ろから累積和で行けない？
# 一番lをXにしたときと一番rをXにしたとき,中央値の始まる端と終わる端がわかればよい

# 奇数の場合は

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(200000)
import bisect


def read():
    N = int(input().strip())
    AB = []
    for i in range(N):
        a, b = map(int, input().strip().split())
        AB.append((a, b))
    return N, AB


def solve(N, AB, MOD=1000000007):
    A = list(sorted([a for a, b in AB]))
    B = list(sorted([b for a, b in AB]))
    if N % 2 == 1:
        m = N // 2
        low = A[m]
        high = B[m]
        return high - low + 1
    else:
        m = N // 2
        low = A[m-1] + A[m]
        high = B[m-1] + B[m]
        return high - low + 1
    return -1


if __name__ == '__main__':
    inputs = read()
    outputs = solve(*inputs)
    if outputs is not None:
        print("%s" % str(outputs))

Submission status: Accepted

Solution code:
import statistics
N = int(input())
A = []
B = []
for _ in range(N):
  a, b = map(int, input().split())
  A.append(a)
  B.append(b)
left = statistics.median(A)
right = statistics.median(B)
if N%2 == 0:
  print(int(right*2 - left*2 + 1))
else: 
  print(right-left+1)

Submission status: Accepted

Solution code:
from statistics import median

N = int(input())
A = []
B = []
for _ in range(N):
    a, b = map(int, input().split())
    A.append(a)
    B.append(b)

m = median(A)
M = median(B)

if N % 2 == 0:
    m *= 2
    M *= 2

print(int(M-m+1))

Submission status: Accepted

Solution code:
N = int(input())
X = [list(map(int,input().split())) for _ in range(N)]

Y = sorted(X, key=lambda x:x[0])
Z = sorted(X, key=lambda x:x[1])

ans = 0
if N % 2:
    ans = Z[N//2][1]-Y[N//2][0]+1

else:
    ans = Z[N//2][1]-Y[N//2][0]+1
    ans += Z[N//2-1][1]-Y[N//2-1][0]

print(ans)

Submission status: Accepted

Solution code:
import statistics
num = int(input())
aList = []
bList = []
for x in range(num):
    a, b = map(int, input().split())
    aList.append(a)
    bList.append(b)
a_median = statistics.median(aList)
b_median = statistics.median(bList)
if num % 2 == 1: print(b_median - a_median + 1)
else: print(int((b_median - a_median) * 2) + 1)

Submission status: Accepted

Solution code:
def main(sample_file = ''):

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz') # 26
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    class SegTree:
        """
        ref: https://qiita.com/takayg1/items/c811bd07c21923d7ec69
        init(init_val, ide_ele): 配列init_valで初期化 O(N)
        update(k, x): k番目の値をxに更新 O(logN)
        query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
        """
        def __init__(self, init_val, segfunc, ide_ele):
            """
            init_val: 配列の初期値
            segfunc: 区間にしたい操作
            ide_ele: 単位元
            n: 要素数
            num: n以上の最小の2のべき乗
            tree: セグメント木(1-index)
            """
            n = len(init_val)
            self.segfunc = segfunc
            self.ide_ele = ide_ele
            self.num = 1 << (n - 1).bit_length()
            self.tree = [ide_ele] * 2 * self.num
            # 配列の値を葉にセット
            for i in range(n):
                self.tree[self.num + i] = init_val[i]
            # 構築していく
            for i in range(self.num - 1, 0, -1):
                self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

        def update(self, k, x):
            """
            k番目の値をxに更新
            k: index(0-index)
            x: update value
            """
            k += self.num
            self.tree[k] = x
            while k > 1:
                self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
                k >>= 1

        def query(self, l, r):
            """
            [l, r)のsegfuncしたものを得る
            l: index(0-index)
            r: index(0-index)
            """
            res = self.ide_ele
            l += self.num
            r += self.num
            while l < r:
                if l & 1:
                    res = self.segfunc(res, self.tree[l])
                    l += 1
                if r & 1:
                    res = self.segfunc(res, self.tree[r - 1])
                l >>= 1
                r >>= 1
            return res

    # ************ Graph ************
    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # 最短経路問題: https://ja.wikipedia.org/wiki/%E6%9C%80%E7%9F%AD%E7%B5%8C%E8%B7%AF%E5%95%8F%E9%A1%8C
    
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    # Warshall Floyd O(V**3)
    def warshall_floyd(number_vertex, XYD, shift_one_for_vertex=False):
        # ref: https://juppy.hatenablog.com/entry/2018/11/01/%E8%9F%BB%E6%9C%AC_python_%E5%85%A8%E7%82%B9%E5%AF%BE%E6%9C%80%E7%9F%AD%E7%B5%8C%E8%B7%AF%E6%B3%95%EF%BC%88%E3%83%AF%E3%83%BC%E3%82%B7%E3%83%A3%E3%83%AB%E3%83%95%E3%83%AD%E3%82%A4%E3%83%89%E6%B3%95
        # number_vertex: len(vertex)
        # XYD: list of distance from x to y
        # shift_one_for_vertex: XYDの値が1~Nの時(0~N-1でない時)に調整するフラグ。
        # d[i][j]: iからjへの最短距離
        d = [[float("inf")]*number_vertex for i in range(number_vertex)]
        for x, y, dist in XYD:
            if shift_one_for_vertex:
                x = x - 1
                y = y - 1
            d[x][y] = dist
            d[y][x] = dist
        for i in range(number_vertex):
            d[i][i] = 0 # distance of same vertex is 0
        for k in range(number_vertex):
            for i in range(number_vertex):
                for j in range(number_vertex):
                    d[i][j] = min(d[i][j],d[i][k] + d[k][j])
        return d


    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main
    #%%
    N = r_int()
    AB = [R() for _ in range(N)]
    
    ab_0 = sorted(AB, key=itemgetter(0))
    ab_1 = sorted(AB, key=itemgetter(1))
    
    if N%2 == 0: # 偶数の時
        left = N//2 - 1
        right = N//2
        l = ab_0[left][0] + ab_0[right][0]
        r = ab_1[left][1] + ab_1[right][1]
        print(r-l+1)
    else:
        c = N//2
        l = ab_0[c][0]
        r = ab_1[c][1]
        print(r-l+1)
    
    #%%
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
n=int(input())
a=sorted([list(map(int,input().split())) for i in range(n)])
b=sorted(a,key=lambda x:x[1])
if n%2==1:
    print(b[n//2][1]-a[n//2][0]+1)
else:
    print((b[n//2-1][1]+b[n//2][1])-(a[n//2-1][0]+a[n//2][0])+1)