Problem:
 Score : 400 points    Problem Statement You are given a sequence A_1, A_2, ..., A_N and an integer K .  Print the maximum possible length of a sequence B that satisfies the following conditions:   B is a (not necessarily continuous) subsequence of A .  For each pair of adjacents elements of B , the absolute difference of the elements is at most K .       Constraints  1 \leq N \leq 300,000  0 \leq A_i \leq 300,000  0 \leq K \leq 300,000  All values in input are integers.         Input Input is given from Standard Input in the following format:  N  K  A_1  A_2  :  A_N       Output Print the answer.        Sample Input 1 10 3
1
5
4
3
8
6
9
7
2
4      Sample Output 1 7  For example, B = (1, 4, 3, 6, 9, 7, 4) satisfies the conditions.   It is a subsequence of A = (1, 5, 4, 3, 8, 6, 9, 7, 2, 4) .  All of the absolute differences between two adjacent elements ( |1-4|, |4-3|, |3-6|, |6-9|, |9-7|, |7-4| ) are at most K = 3 .

Solution (Python):
class SegmentTree:
    def __init__(self, data, default=0, func=max):
        """initialize the segment tree with data"""
        self._default = default
        self._func = func
        self._len = len(data)
        self._size = _size = 1 << (self._len - 1).bit_length()

        self.data = [default] * (2 * _size)
        self.data[_size:_size + self._len] = data
        for i in reversed(range(_size)):
            self.data[i] = func(self.data[i + i], self.data[i + i + 1])

    def __delitem__(self, idx):
        self[idx] = self._default

    def __getitem__(self, idx):
        return self.data[idx + self._size]

    def __setitem__(self, idx, value):
        idx += self._size
        self.data[idx] = value
        idx >>= 1
        while idx:
            self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
            idx >>= 1

    def __len__(self):
        return self._len

    def query(self, start, stop):
        """func of data[start, stop)"""
        start += self._size
        stop += self._size

        res_left = res_right = self._default
        while start < stop:
            if start & 1:
                res_left = self._func(res_left, self.data[start])
                start += 1
            if stop & 1:
                stop -= 1
                res_right = self._func(self.data[stop], res_right)
            start >>= 1
            stop >>= 1

        return self._func(res_left, res_right)

    def __repr__(self):
        return "SegmentTree({0})".format(self.data)
    
import sys
input = sys.stdin.readline

n, k = map(int, input().split())
seg = SegmentTree([0] * (1 << 20))
for _ in range(n):
    v = int(input())
    most = seg.query(max(0, v - k), v + k + 1)
    seg[v] = most + 1
print(seg.query(0, 1 << 20))

Solution (Python):
n, k = map(int, input().split())
l = []
for i in range(n):
    l.append(int(input()))

root = [1]*n

for i in range(n)[-2::-1]:
    num = 0
    for j in range(i + 1, i + 200):
        if j >= n:
            break
        if abs(l[i] - l[j]) <= k:
            num = max(num, root[j])
    root[i] += num

print(max(root))

Solution (Python):
import sys

input_methods=['clipboard','file','key']
using_method=1
input_method=input_methods[using_method]

tin=lambda : map(int, input().split())
lin=lambda : list(tin())
mod=1000000007




isTest=False

def pa(v):
	if isTest:
		print(v)
		
def input_clipboard():
	import clipboard
	input_text=clipboard.get()
	input_l=input_text.splitlines()
	for l in input_l:
		yield l


if sys.platform =='ios':
	if input_method==input_methods[0]:
		ic=input_clipboard()
		input = lambda : ic.__next__()
	elif input_method==input_methods[1]:
		sys.stdin=open('inputFile.txt')
	else:
		pass
	isTest=True
else:
	pass
	


def segfunc(x,y):
   return min(x,y)

def init(init_val):
    
    for i in range(n):
        seg[i+num-1]=init_val[i]    
    
    for i in range(num-2,-1,-1) :
        seg[i]=segfunc(seg[2*i+1],seg[2*i+2]) 
    
def update(k,x):
    k += num-1
    seg[k] = x
    while k:
        k = (k-1)//2
        seg[k] = segfunc(seg[k*2+1],seg[k*2+2])
    
def query(p,q):
    if q<=p:
        return ide_ele
    p += num-1
    q += num-2
    res=ide_ele
    while q-p>1:
        if p&1 == 0:
            res = segfunc(res,seg[p])
        if q&1 == 1:
            res = segfunc(res,seg[q])
            q -= 1
        p = p//2
        q = (q-1)//2
    if p == q:
        res = segfunc(res,seg[p])
    else:
        res = segfunc(segfunc(res,seg[p]),seg[q])
    return res


ide_ele = 0






n, k = tin()

v_max = 300000
mmv = [0] * (v_max+1)
num=2**(v_max-1).bit_length()
seg = [ide_ele]*2*num


for value_i in range(n):
	value_i=int(input())
	r = query(max(value_i-k,0), min(value_i+1+k,v_max+1))
	update(value_i, r-1)
v = -query(0, num)
print(v)

Solution (Python):
import sys
def input(): return sys.stdin.readline().rstrip()
from fractions import gcd
class seg():
    def __init__(self,init_val):
        self.n=len(init_val)
        self.ide_ele= 0 
        self.num=2**(self.n-1).bit_length() 
        self.seg=[self.ide_ele]*2*self.num
        for i in range(self.n):
            self.seg[i+self.num-1]=init_val[i]
        for i in range(self.num-2,-1,-1):
            self.seg[i]=self.seg_func(self.seg[2*i+1],self.seg[2*i+2])
    def seg_func(self,a,b):
        
        
        
        return max(a,b) 
        
    def update(self,k,x):
        k+=self.num-1
        self.seg[k]=x
        while k:
            k=(k-1)//2
            self.seg[k]=self.seg_func(self.seg[k*2+1],self.seg[k*2+2])
    def query(self,p,q): 
        if q<=p:return self.ide_ele
        p+=self.num-1
        q+=self.num-2
        self.res=self.ide_ele
        while q-p>1:
            if p&1==0:
                self.res=self.seg_func(self.res,self.seg[p])
            if q&1==1:
                self.res=self.seg_func(self.res,self.seg[q])
                q-=1
            p=p//2
            q=(q-1)//2
        if p==q:self.res=self.seg_func(self.res,self.seg[p])
        else:self.res=self.seg_func(self.seg_func(self.res,self.seg[p]),self.seg[q])
        return self.res

def main():
    n, k = map(int,input().split())
    A = [int(input())for _ in range(n)]
    max_a = max(A)
    A_len = [0] * (max_a + 1) 
    SEG = seg(A_len)
    for a in A:
        SEG.update(a, SEG.query(max(a - k, 0), min(a + k, max_a) + 1) + 1)
    print(SEG.query(0, max_a + 1))

if __name__=='__main__':
    main()

Solution (Python):
import math
from functools import reduce
from collections import deque
import sys
sys.setrecursionlimit(10**7)

def input():
    return sys.stdin.readline().strip()


def get_nums_l():
    return [ int(s) for s in input().split(" ")]


def get_all_int():
    return map(int, open(0).read().split())

def log(*args):
    print("DEBUG:", *args, file=sys.stderr)

class SegmentTree2:
    
    
    
    def __init__(self, size, f=lambda x,y : x+y, default=0):
        self.size = 2**(size-1).bit_length() 
        self.default = default
        self.dat = [default]*(self.size*2) 
        self.f = f

    def update(self, i, x):
        i += self.size
        self.dat[i] = x
        while i > 0:
            i >>= 1
            self.dat[i] = self.f(self.dat[i*2], self.dat[i*2+1])

    def query(self, l, r):
        l += self.size
        r += self.size
        lres, rres = self.default, self.default
        while l < r:
            if l & 1:
                lres = self.f(lres, self.dat[l])
                l += 1

            if r & 1:
                r -= 1
                rres = self.f(self.dat[r], rres) 
            l >>= 1
            r >>= 1
        res = self.f(lres, rres)
        return res

class segtree:
    def __init__(self, n,operator,identity):
        nb = bin(n)[2:]
        bc = sum([int(digit) for digit in nb])
        if bc == 1:
            self.num_end_leaves = 2**(len(nb)-1)
        else:
            self.num_end_leaves = 2**(len(nb))

        self.array = [identity for i in range(self.num_end_leaves * 2)]
        self.identity = identity
        self.operator =operator

    def update(self,x,val):
        actual_x = x+self.num_end_leaves
        self.array[actual_x] = val
        while actual_x > 0 :
            actual_x = actual_x//2
            self.array[actual_x] = self.operator(self.array[actual_x*2],self.array[actual_x*2+1])

    def get(self,q_left,q_right,arr_ind=1,leaf_left=0,depth=0):
        """
        [q_left, q_right] (閉区間) の値を集計して返します。
        """

        width_of_floor = self.num_end_leaves//(2**depth)
        leaf_right = leaf_left+width_of_floor-1

        if leaf_left > q_right or leaf_right < q_left:
            return  self.identity

        elif leaf_left >= q_left and leaf_right <= q_right:
            return self.array[arr_ind]

        else:
            val_l = self.get(q_left,q_right,2*arr_ind,leaf_left,depth+1)
            val_r = self.get(q_left,q_right,2*arr_ind+1,leaf_left+width_of_floor//2,depth+1)
            return self.operator(val_l,val_r)

def main():
    INF = 999999999999999999999999
    MOD = 10**9+7

    n,k = get_nums_l()
    A = list(map(int, [input() for _ in range(n)]))


    
    sg = SegmentTree2(300001, max, 0)

    for i in range(0, n):
        a = A[i]
        l = max(0, a-k)
        r = min(300000, a+k)
        v = sg.query(l, r+1)
        sg.update(a, v+1)

    print(sg.query(0, 300001))

main()

Solution (Python):





import math
import fractions
import sys
import bisect
import heapq  
import collections
from collections import Counter
from collections import deque
import pprint
import itertools

sr = lambda: input()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

"""nを素因数分解"""
"""2以上の整数n => [[素因数, 指数], ...]の2次元リスト"""


def factorization(n):
    arr = []
    temp = n
    if n == 1:
        return arr

    for i in range(2, int(-(-n ** 0.5 // 1)) + 1):
        if temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append([i, cnt])

    if temp != 1:
        arr.append([temp, 1])

    if arr == []:
        arr.append([n, 1])

    return arr



def power(a, n, mod):
    x = 1
    while n:
        if n & 1:
            x *= a % mod
        n >>= 1
        a *= a % mod
    return x % mod



def kaijo(n, l, mod):
    if n == 0:
        return 1
    a = n
    tmp = n - 1
    while (tmp >= l):
        a = a * tmp % mod
        tmp -= 1
    return a


class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


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

inf = 10 ** 18
mod = 10 ** 9 + 7



class SegmentTree:
    
    
    
    def __init__(self, size, f=lambda x, y: x + y, default=0):
        self.size = 2 ** (size - 1).bit_length()  
        self.default = default
        self.dat = [default] * (self.size * 2)  
        self.f = f

    def update(self, i, x):
        i += self.size
        self.dat[i] = x
        while i > 0:
            i >>= 1
            self.dat[i] = self.f(self.dat[i * 2], self.dat[i * 2 + 1])

    def query(self, l, r):
        l += self.size
        r += self.size
        lres, rres = self.default, self.default
        while l < r:
            if l & 1:
                lres = self.f(lres, self.dat[l])
                l += 1

            if r & 1:
                r -= 1
                rres = self.f(self.dat[r], rres)  
            l >>= 1
            r >>= 1
        res = self.f(lres, rres)
        return res



n,k = lr()
a = [ir() for i in range(n)]

seg = SegmentTree(300001, max, 0)  
for num in a:
    max_k = seg.query(max(0,num-k), min(300001,num+k+1))
    seg.update(num, max_k+1)
print(seg.query(0, 300001))

Solution (Python):

def segfunc(x, y):
  return max(x,y)



ide_ele = 0


class SegTree:
  """
  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
    
    for i in range(n):
        self.tree[self.num + i] = init_val[i]
    
    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

def main():
  n,k = map(int, input().split())
  a = []
  for i in range(n):
    a.append(int(input()))

  array = [0] * (3 * (10 ** 5) + 1)
  seg = SegTree(array, segfunc, ide_ele)

  for i in range(len(a)):
    low = max(0, a[i] - k)
    high = min(a[i] + k + 1, 3 * (10 ** 5) + 1)
    tmp = seg.query(low, high) + 1
    
    seg.update(a[i], tmp)
    
  print(seg.query(0, 3 * (10 ** 5) + 1))
  
main()

Solution (Python):




def segfunc(x, y):
    return max(x,y)



ide_ele = 0


class SegTree:
    """
    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
        
        for i in range(n):
            self.tree[self.num + i] = init_val[i]
        
        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 ※区間注意
        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

N, K = map(int, input().split())
A = [int(input()) for _ in range(N)]
seg = SegTree([0 for i in range(300050)], segfunc, ide_ele)

answer = 0
for i in range(N):
    
    under = max(0,A[i]-K)
    upper = min(300050,A[i]+K)
    now = seg.query(under, upper+1)
    seg.update(A[i], now+1)
    if answer < now+1:
        answer = now+1
print(answer)

Solution (Python):
import sys

sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7


class SegTree:
    """
    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(N)
    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
        
        for i in range(n):
            self.tree[self.num + i] = init_val[i]
        
        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, left, right):
        """
        [left, right)のsegfuncしたものを得る
        left: index(0-index)
        right: index(0-index)
        """
        res = self.ide_ele
        left += self.num
        right += self.num
        while left < right:
            if left & 1:
                res = self.segfunc(res, self.tree[left])
                left += 1
            if right & 1:
                res = self.segfunc(res, self.tree[right - 1])
            left >>= 1
            right >>= 1
        return res


def resolve():
    n, k = map(int, input().split())
    A = list(int(input()) for _ in range(n))
    MAX = max(A) + 1
    seg = SegTree([0 for _ in range(MAX)], lambda x, y: max(x, y), -f_inf)
    res = [0] * MAX
    for a in A:
        left = max(0, a - k)
        right = min(MAX + 1, a + k + 1)
        ma = seg.query(left, right)
        seg.update(a, ma + 1)
        res[a - 1] = ma + 1

    print(max(res))


if __name__ == '__main__':
    resolve()

Solution (Python):

from collections import defaultdict
from bisect import bisect

n, k = list(map(int, input().split()))
al = [0] * n
for i in range(n):
    al[i] = int(input())
max_al = max(al)
min_al = min(al)


N = max(al)+1
N0 = 2**(N-1).bit_length()
INF = 2**31-1
data = [INF]*(2*N0)



def update(k, x):
    k += N0-1
    data[k] = x
    while k >= 0:
        k = (k - 1) // 2
        data[k] = min(data[2*k+1], data[2*k+2])



def query(l, r):
    L = l + N0
    R = r + N0
    s = INF
    while L < R:
        if R & 1:
            R -= 1
            s = min(s, data[R-1])

        if L & 1:
            s = min(s, data[L-1])
            L += 1
        L >>= 1
        R >>= 1
    return s


for i in range(n):
    update(al[i], n)

for a in al:
    v = query(max(min_al, a-k), min(a+k, max_al)+1)
    update(a, n-((n-v)+1))
v = query(min_al, max_al+1)
print(n-v)

Solution (Python):
class SegmentTreeMAX():
    def __init__(self,A,n,ide_ele_max=-1):
        self.ide_ele_max = ide_ele_max
        self.num_max =2**(n-1).bit_length()
        self.seg_max=[ide_ele_max]*2*self.num_max
        
        for i in range(n):
            self.seg_max[i+self.num_max-1]=A[i]
        
        for i in range(self.num_max-2,-1,-1) :
            self.seg_max[i]=max(self.seg_max[2*i+1],self.seg_max[2*i+2])

    def update_max(self,k,x):
        k += self.num_max-1
        self.seg_max[k] = x
        while k:
            k = (k-1)//2
            self.seg_max[k] = max(self.seg_max[k*2+1],self.seg_max[k*2+2])

    def query_max(self,p,q):
        if q<=p:
            return self.ide_ele_max
        p += self.num_max-1
        q += self.num_max-2
        res=self.ide_ele_max
        while q-p>1:
            if p&1 == 0:
                res = max(res,self.seg_max[p])
            if q&1 == 1:
                res = max(res,self.seg_max[q])
                q -= 1
            p = p//2
            q = (q-1)//2
        if p == q:
            res = max(res,self.seg_max[p])
        else:
            res = max(max(res,self.seg_max[p]),self.seg_max[q])
        return res

N,K=list(map(int,input().split()))
T = [0]*(300001)
SegTree = SegmentTreeMAX(T,300001)
for i in range(N):
    A=int(input())
    X=SegTree.query_max(max(0,A-K),min(A+K,300000)+1)
    SegTree.update_max(A,X+1)
    T[A]=X+1
print(SegTree.query_max(0,300000+1))

Solution (Python):

n,K=map(int,input().split())
A= [int(input()) for _ in range(n)]


def segfunc(x, y):
    return max(x,y)



ide_ele = -1


class SegTree:
    """
    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
        
        for i in range(n):
            self.tree[self.num + i] = init_val[i]
        
        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

maxa=max(A)
z= [0 for i in range(maxa)]
seg = SegTree(z, segfunc, ide_ele)

for i in range(n):
    mini = max(0,A[i]-K)
    maxi = min(maxa,A[i]+K)
    tmp=seg.query(mini,maxi+1)
    seg.update(A[i],tmp+1)

print(seg.query(0,maxa+1))

Solution (Python):
import sys
input = sys.stdin.buffer.readline

MOD = 10 ** 9 + 7
INF = 2 * 10**18

in_n = lambda: int(input())
in_nn = lambda: map(int, input().split())
in_s = lambda: input().rstrip().decode('utf-8')
in_map = lambda: [s == ord('.') for s in input() if s != ord('\n')]



class SegTree:

    def __init__(self, init_val, segfunc, ide_ele):

        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

        for i in range(n):
            self.tree[self.num + i] = init_val[i]

        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 += 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):

        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

    def get(self, k):
        k += self.num
        return self.tree[k]


def main():

    M = 3 * 10**5 + 10
    N, K = in_nn()
    A = [0] * N

    for i in range(N):
        A[i] = in_n()

    seg = SegTree([0] * M, segfunc=lambda a, b: max(a, b), ide_ele=0)

    for i in range(N):
        now = A[i]
        left = max(0, now - K)
        right = min(now + K + 1, M)
        u = seg.query(left, right)
        seg.update(now, u + 1)

    ans = seg.query(0, M)
    print(ans)


if __name__ == '__main__':
    main()

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

def segfunc(x, y):
    return max(x,y)



ide_ele =0


class SegTree:
    def __init__(self, init_val, segfunc, ide_ele):
        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
        
        for i in range(n):
            self.tree[self.num + i] = init_val[i]
        
        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 += 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):
        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
Ma=max(A)
Tree=[0]*(Ma+1)
seg = SegTree(Tree, segfunc, ide_ele)
ans=0
for i in range(N):
    a=A[i]
    l=max(0,a-K)
    r=min(a+K,Ma)
    Ans=seg.query(l,r+1)
    seg.update(a, Ans+1)
    ans=max(ans,Ans+1)
print(ans)

Solution (Python):
import sys
input=sys.stdin.readline
N,k=map(int,input().split())
n=300_003
def update(i,x):
	now=2**deep+i
	seg[now-1]=x
	while now>1:
		now//=2
		seg[now-1]=min(seg[now*2-1],seg[now*2])
def minimum(x,y):
	s=inf
	l=x+2**deep
	r=y+2**deep+1
	while l<r:
		if l%2==1:
			s=min(s,seg[l-1])
			l+=1
		if r%2==1:
			r-=1
			s=min(s,seg[r-1])
		l//=2
		r//=2
	return s
inf=0
deep=(n-1).bit_length()
seg=[inf]*(2**deep*2-1)
for i in range(N):
	a=int(input())
	x=max(a-k,0)
	y=min(a+k,n)
	update(a,minimum(x,y)-1)
print(-minimum(0,n-1))

Solution (Python):
N, K = map(int,input().split())
L = [int(input()) for _ in range(N)]
A = [[] for _ in range(N)]
tmp = 0
A[0].append(L[0])
for num in L[1:]:
  for i in reversed(range(0,tmp+1)):
    for a in A[i]:
      if abs(a-num) <= K:
        A[i+1].append(num)
        tmp = max(tmp,i+1)
        break
    else:
      continue
    break
  else:
    A[0].append(num)
print(tmp+1)

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

def segfunc(x, y):
    return max(x,y)



ide_ele =0


class SegTree:
    """
    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
        
        for i in range(n):
            self.tree[self.num + i] = init_val[i]
        
        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 += 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):
        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
Ma=max(A)
Tree=[0]*(Ma+1)
seg = SegTree(Tree, segfunc, ide_ele)
ans=0
for i in range(N):
    a=A[i]
    l=max(0,a-K)
    r=min(a+K,Ma)
    Ans=seg.query(l,r+1)
    seg.update(a, Ans+1)
    ans=max(ans,Ans+1)
print(ans)