Problem:


Score : 200 points

Problem Statement

In a factory, there are N robots placed on a number line.
Robot i is placed at coordinate X_i and can extend its arms of length L_i in both directions, positive and negative.

We want to remove zero or more robots so that the movable ranges of arms of no two remaining robots intersect.
Here, for each i (1 \leq i \leq N), the movable range of arms of Robot i is the part of the number line between the coordinates X_i - L_i and X_i + L_i, excluding the endpoints.

Find the maximum number of robots that we can keep.

Constraints

1 \leq N \leq 100,000

0 \leq X_i \leq 10^9 (1 \leq i \leq N)

1 \leq L_i \leq 10^9 (1 \leq i \leq N)

If i \neq j, X_i \neq X_j.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 L_1
X_2 L_2
\vdots
X_N L_N

Output

Print the maximum number of robots that we can keep.

Sample Input 1

4
2 4
4 3
9 3
100 5

Sample Output 1

3

By removing Robot 2, we can keep the other three robots.

Sample Input 2

2
8 20
1 10

Sample Output 2

1

Sample Input 3

5
10 1
2 1
4 1
6 1
8 1

Sample Output 3

5



Sample input:
4
2 4
4 3
9 3
100 5


Sample output:
3

Submission status: Wrong Answer

Solution code:
import math
import fractions

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    # divisors.sort()
    return divisors

def bitlist(x,digit):
    res = [0 for i in range(digit)]
    now = x
    for i in range(digit):
        res[i]=now%2
        now = now >> 1
    return res

#a = list(map(int, input().split()))

robos = []
n = int(input())

for i in range(n):
    robos.append(list(map(int, input().split())))

robos.sort(key=lambda x:x[0])

ans=0
prev=-999999999999
for i in range(n):
    if(prev<=robos[i][0]-robos[i][1]):
        ans+=1
        prev = robos[i][0]+robos[i][1]
        
print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())
x = sorted([list(map(int, input().split())) for _ in range(n)])

if n == 1:
    print(1)
    exit()

cnt = n
l = 0
r = 1
for i in range(n):
    if x[l][0] + x[l][1] > x[r][0] - x[r][1]:
        cnt -= 1
        r += 1
    else:
        l = r
        r = l + 1
    if r >= n - 1:
        break
print(cnt)

Submission status: Wrong Answer

Solution code:
import numpy as np

n = int(input())

left = np.zeros(n)
right = np.zeros(n)
for i in range(n):
    x, l = map(int, input().split())
    left[i] = x-l
    right[i] = x+l

sort_ind = np.argsort(right)
left = left[sort_ind]
right = right[sort_ind]

ans = 0
right_now = -1
for i in range(n):
    if(left[i] >= right_now):
        ans += 1
        tright_now = right[i]

print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
# X, L = [], []
A = []
for i in range(N):
    x, l = map(int, input().split())
    # X.append(x)
    # L.append(l)
    A.append((x - l, x + l))

A.sort(key=lambda x: x[1])
ans = 0
x = -10e50
for i in range(N):
    l, r = A[i]
    if x <= l:
        ans += 1
        x = r-1

print(ans)


# 選べるロボットの中で最もX+Lが小さいもの

Submission status: Wrong Answer

Solution code:
def main():
    N = int(input())
    L = [list(map(int, input().split())) for _ in range(N)]
    tmp = []
    for a, b in L:
        tmp.append([a-b, a+b])
    tmp.sort()
    t = tmp[0][0]- 1
    c = 0

    for i in range(N):

        if t > tmp[i][0]:
            c += 1
        else:
            t = tmp[i][1]
    print(N-c)

if __name__ == '__main__':
    main()

Submission status: Wrong Answer

Solution code:
n = int(input())
dic = {}

for i in range(n):
    inp = list(map(int, input().split()))
    dic[inp[0]] = inp[1]

dic = sorted(dic.items())
pre = dic[0][0]+dic[0][1]
ans = 1

for i in range(n-1):
    if pre <= dic[i+1][0]-dic[i][1]:
        pre = dic[i+1][0]+dic[i][1]
        ans += 1

print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())
pos = []
L = []
for i in range(n):
    x, l = map(int, input().split())
    pos.append([x - l, x + l])
    L.extend([x - l, x + l])
zero = -1 * min(pos)[0]
for i in range(len(pos)):
    for j in range(2):
        pos[i][j] += zero
for i in range(len(L)):
    L[i] += zero
L = sorted(L)
arr = [0 for i in range(L[-1] + 1)]
for i in pos:
    arr[i[0]] += 1
    arr[i[1]] -= 1
for i in range(1, L[-1] + 1):
    arr[i] += arr[i - 1]
print(n - max(arr) + 1)

Submission status: Wrong Answer

Solution code:
n = int(input())
xl = [list(map(int, input().split())) for i in range(n)]
xl = sorted([[x-l+1,x+l-1] for x,l in xl], key = lambda x: x[1])
now = xl[0][1]
ans = n
for s,e in xl[1:]:
  if s <= now:
    ans -= 1
  else:
    now = e
xl = sorted(xl)
now = xl[-1][0]
ans2 = n
for s,e in reversed(xl[:-1]):
  if e >= now:
    ans2 -= 1
  else:
    now = s
ans = max(ans,ans2)
print(ans)

Submission status: Wrong Answer

Solution code:
n=int(input())
xl=[list(map(int,input().split())) for _ in range(n)]
xl.sort(key=lambda x: x[0])
ans=1
nx=xl[0][0]
for i in range(1,n):
  x,l=xl[i]
  if nx<x-l:
    ans+=1
    nx=x
print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())

la = -10000000000
cnt=0

robots = []
for i in range(n):
  x,l = map(int,input().split())
  robots.append((x,l))

sr = sorted(robots)

for i in range(n): 
  x = sr[i][0]
  l = sr[i][1]
  if la <= x-l:
    la = x+l
    cnt+=1

print(cnt)

Submission status: Wrong Answer

Solution code:
n=int(input())

L=[]
for i in range(n):
    x,l=map(int,input().split())
    L.append([x,l])
L.sort(key=lambda x:x[0])

ans=1
before=L[0][0]+L[0][1]
for i in range(1,n):
    if before<=L[i][0]-L[i][1]:
        ans+=1
        before=max(before,L[i][0]+L[i][1])
print(ans)

Submission status: Wrong Answer

Solution code:
import sys
input = sys.stdin.readline

N = 100000
n = int(input())

x_list = [0]*N
l = [0]*N
x_list = [0]*N

x, l = map(int, input().split())
x_min = max(0, x-l-1)
x_max = min(N-1, x+l-1)
temp = [1] * (x_max - x_min)
x_list[x_min:x_max] = temp


ans = n
for i in range(n-1):
    x, l = map(int, input().split())
    x_min = max(0, x-l-1)
    x_max = min(N-1, x+l-1)
    if 1 in x_list[x_min:x_max]:
        ans -= 1
    else:
        temp = [1] * (x_max - x_min)
        x_list[x_min:x_max] = temp
print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
# X, L = [], []
A = []
for i in range(N):
    x, l = map(int, input().split())
    # X.append(x)
    # L.append(l)
    A.append((x - l, x + l))

A.sort()
ans = 0
x = -10e50
for i in range(N):
    l, r = A[i]
    if x <= l:
        ans += 1
        x = r-1

print(ans)


# 選べるロボットの中で最もX+Lが小さいもの

Submission status: Wrong Answer

Solution code:
n = int(input())

xl = [tuple(map(int, input().split())) for _ in range(n)]
xl = sorted(xl)


def run(xl):
    res = 1
    x, l = xl[0]
    cur = x + l
    for (x, l) in xl:
        if x - l >= cur:
            cur = x + l
            res += 1
    return res


res = max(run(xl), run(list(reversed([(-x, l) for x, l in xl]))))

print(res)

Submission status: Wrong Answer

Solution code:
n = int(input())
ls = []
for i in range(n):
    x,l = map(int,input().split())
    ls.append([x-l,l+x])
    
r = n
ls = sorted(ls)
for i in range(1,n):
    if ls[i][0] < ls[i-1][1]:
      ls[i][1] = ls[i-1][1]
      r -=1
        
print(r)

Submission status: Wrong Answer

Solution code:
robot_list = []
max_X = -1000000001
robot_count = 0
N = int(input())
for i in range(N):
    robot_list.append(list(map(int,input().split())))
robot_list.sort()
for i in range(N):
    if max_X <= int(robot_list[i][0]) - int(robot_list[i][1]):
        max_X = int(robot_list[i][0]) + int(robot_list[i][1])
        robot_count += 1
    else:
        continue
print(robot_count)

Submission status: Wrong Answer

Solution code:
n = int(input())

robots = []

for _ in range(n):
    x, l = map(int, input().split())
    left, right = x-l+1, x+l-1
    robots.append([left, right])

robots.sort()

DP = [0, -10**10]

for left, right in robots:
    count, now = DP[0], DP[1]
    if left > now:
        DP = [count+1, right]

    else:
        if right < now:
            DP = [count, right]
        else:
            continue

print(DP[0])

Submission status: Wrong Answer

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

XL.sort()

i = 0
result = 0
while i < N - 1:
    x1, l1 = XL[i]
    x2, l2 = XL[i + 1]
    if x1 + l1 > x2 - l2:
        result += 1
        i += 1
    i += 1
print(N - result)

Submission status: Wrong Answer

Solution code:
n = int(input())
xls = [list(map(int, input().split()))for i in range(n)]
xls.sort(key=lambda x:x[0])
ans1 = 1
x, l = xls[0]
for i in range(1, n):
    nx, nl = xls[i]
    if nx-nl+1<x+l: continue
    ans1 += 1
    x, l = nx, nl

ans2 = 1
x, l = xls[-1]
for i in range(n-1):
    nx, nl = xls[-2-i]
    if x-l+1<nx+nl: continue
    ans2 += 1
    x, l = nx, nl
print(max(ans1, ans2))

Submission status: Wrong Answer

Solution code:
#N=int(input())
#N,M=map(int, input().split())
#L=list(map(int, input().split()))
N=int(input())
x=0
l=0
count=N
xL=[]
for _ in range(N):
  x,l=map(int, input().split())
  xL.append([x-l,x+l])
  
xL.sort()
for i in range(N-1):
  if xL[i][1]>xL[i+1][0]:
    xL[i+1]=[-1,-1]
    count-=1

print(count)

Submission status: Wrong Answer

Solution code:
n = int(input())
XL = []
for _ in range(n):
    x, l = map(int, input().split())
    x_min = x - l + 1
    x_max = x + l -1
    XL.append((x,l, x_min, x_max))

XL = sorted(XL, key=lambda x: x[3])

check = True
now = 0
count = 0
for i in range(1,n):
    if XL[now][3] >= XL[i][2]:
        count += 1
    else:
        now = i
ans = n - count

print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
XL = [list(map(int,input().split())) for i in range(N)]
XL.sort(key=lambda x: x[0]+x[1])
M = XL[0][0]+XL[0][1]-1
ans = N
for i in range(1,N):
    if M >= XL[i][0]-XL[i][1]+1:
        ans -= 1
    else:
        M = XL[i][0]+XL[i][1]-1
print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())
Xl = [ list(map(int, input().split())) for _ in range(n) ]
Xl.sort()
cnt, prv = 0, sum(Xl[0])
for i in range(n-1):
    x, l = Xl[i+1][0], Xl[i+1][1]
    if prv <= x-l:
        continue
    else:
        prv = min(prv, x+l)
        cnt += 1
print(n-cnt)

Submission status: Wrong Answer

Solution code:
n=int(input())
x=[]
l=[]
for i in range(n):
  x1,l1=map(int,input().split())
  x.append(x1-l1)
  l.append(l1)
x.sort()
s=1
m=x[0]+2*l[0]
for i in range(n):
  if m<=x[i]:
    s+=1
    m=x[i]+2*l[i]
print(s)

Submission status: Wrong Answer

Solution code:
N = int(input())
robots = list(list(map(int,input().split())) for _ in range(N))
robots.sort()
now = robots[0][0] + robots[0][1]
remove_num = 0
for i in range(1 , N):
    if robots[i][0] - robots[i][1] >= now:
        now = robots[i][0] + robots[i][1]
    else:
        remove_num += 1
print(N - remove_num)

Submission status: Wrong Answer

Solution code:
N = int(input())
# X, L = [], []
A = []
for i in range(N):
    x, l = map(int, input().split())
    # X.append(x)
    # L.append(l)
    A.append((x - l, x + l))

A.sort()
ans = 0
x = -10e50
for i in range(N):
    l, r = A[i]
    if x <= l:
        ans += 1
        x = r

print(ans)


# 選べるロボットの中で最もX+Lが小さいもの

Submission status: Wrong Answer

Solution code:
N = int(input())
XL = []
for i in range(N):
    XL.append(list(map(int,input().split())))
XL.sort(key=lambda x:x[0])
ans = 0
left = XL[0][0]-XL[0][1]
right = XL[0][0]+XL[0][1]
for i in range(1,N):
    new_left = XL[i][0]-XL[i][1]
    new_right = XL[i][0]+XL[i][1]
    #if no overlap
    if new_left >= right:
        left = new_left
        right = new_right
    else:
        ans += 1
print(N-ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
robots = [list(map(int,input().split())) for i in range(N)]
coli = [0 for i in range(N)]

robots.sort(key=lambda x:x[0])

for i in range(N-1):
    #あたってるか判定
    #あたってたら右隣を1
    if coli[i] == 1:
        continue

    right_arm = robots[i][0] + robots[i][1]
    left_arm = robots[i+1][0] - robots[i+1][1]

    if right_arm > left_arm:
        coli[i+1] = 1

print(N-sum(coli))

Submission status: Wrong Answer

Solution code:
N=int(input())
xl=[list(map(int,input().split())) for _ in range(N)]
for i in range(N):
  x,l=xl[i]
  xl[i]=[x-l,x+l]
xl.sort()
a=0
r=xl[0][1]
for i in range(N-1):
  if r>xl[i+1][0]:
    a+=1
  else:
    r=xl[i+1][1]
    
xls=[[xl[i][1],xl[i][0]] for i in range(N)]
xls.sort(reverse=True)
b=0
l=xls[0][1]
for i in range(N-1):
  if l<xls[i+1][0]:
    b+=1
  else:
    l=xls[i+1][1]
    
print(N-min(a,b))

Submission status: Wrong Answer

Solution code:
N = int(input())
XL = sorted([list(map(int, input().split())) for _ in range(N)], key=lambda x:x[0])
last = XL[0]
cnt=1
for i in range(1, N):
    last_X, last_L = last
    c_X, c_L = XL[i]
    if last_X+last_L>c_X-c_L:
        continue
    else:
        last = XL[i]
        cnt+=1
print(cnt)

Submission status: Wrong Answer

Solution code:
from operator import itemgetter

n = int(input())
XL = sorted([list(map(int, input().split())) for _ in range(n)], key=itemgetter(0))
ans = len(XL)
i = 1
cnt = 0
while i != len(XL):
    if XL[i-1][0] + XL[i-1][1] > XL[i][0] - XL[i][1]:
        cnt += 1
        XL.pop(i)
    else:
        i += 1

print(ans - cnt)

Submission status: Wrong Answer

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
    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]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # 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]

    """ 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

    # H = r_int()
    # W = r_int()
    # N = r_int()
    # u = max(H, W)
    # t = N//u
    # if N%u != 0:
    #     t += 1
    # print(t)
    
    N = r_int()
    XL = [R() for _ in range(N)]
    XL.sort()
    tmp = -INF
    ans = N
    for x, l in XL:
        if x - (l-1) < tmp:
            ans -= 1
            tmp = min(tmp, x+(l-1))
        else:
            tmp = x+(l-1)
    print(ans)
    
    
                        
    
    # to finish code, use return instead of exit()
    # 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: Wrong Answer

Solution code:
n=int(input())
a=[]
c=0
d=[]
for i in range(n):
    b=list(map(int,input().split()))
    a.append([b[0]-b[1],1])
    a.append([b[0]+b[1],-1])
a=sorted(a,key=lambda x:(x[0],x[1]))
for i in range(n*2):
    c+=a[i][1]
    d.append(c)
print(n-max(d)+1)

Submission status: Wrong Answer

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

XL.sort(key=lambda x:(x[0],x[1]))
now=XL[0][0]+XL[0][1]
ans=0
for i in range(1,n):
  x,l=XL[i]
  if x<=now and x+l>now:
    ans+=1
  else:
    now=x+l
print(n-ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
Lpos = []
INF = 10 ** 9 + 7
for i in range(N):
    Lpos.append(list(map(int, input().split())))
Lpos.sort(key=lambda x: x[0])
Lpos.sort(key=lambda x: x[1])

endpos = -INF
cnt = 0
for i in range(N):
    if Lpos[i][0] > endpos:
        cnt += 1
        endpos = Lpos[i][0] + Lpos[i][1]
print(cnt)