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.



Sample input:
10 3
1
5
4
3
8
6
9
7
2
4


Sample output:
7

Submission status: Runtime Error

Solution code:
# TODO: 更新ルールの異なる複数のセグ木を作ったときに正しく動くか検証
# TODO: 引数の順番間違えたりすると黙って落ちるのを何とかする

# 注: PyPy で普通に書いた方が速い


code_segtree = r"""
#define PY_SSIZE_T_CLEAN
#include <Python.h>
#include "structmember.h"

// >>> AtCoder >>>

#ifndef ATCODER_SEGTREE_HPP
#define ATCODER_SEGTREE_HPP 1

#include <algorithm>
#ifndef ATCODER_INTERNAL_BITOP_HPP
#define ATCODER_INTERNAL_BITOP_HPP 1

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

}  // namespace atcoder

#endif  // ATCODER_INTERNAL_BITOP_HPP
#include <cassert>
#include <vector>

namespace atcoder {

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
  public:
    segtree() : segtree(0) {}
    segtree(int n) : segtree(std::vector<S>(n, e())) {}
    segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

}  // namespace atcoder

#endif  // ATCODER_SEGTREE_HPP

// <<< AtCoder <<<

using namespace std;
using namespace atcoder;
#define PARSE_ARGS(types, ...) if(!PyArg_ParseTuple(args, types, __VA_ARGS__)) return NULL

struct AutoDecrefPtr{
    PyObject* p;
    AutoDecrefPtr(PyObject* _p) : p(_p) {};
    AutoDecrefPtr(const AutoDecrefPtr& rhs) : p(rhs.p) { Py_INCREF(p); };
    ~AutoDecrefPtr(){ Py_DECREF(p); }
    AutoDecrefPtr &operator=(const AutoDecrefPtr& rhs){
        Py_DECREF(p);
        p = rhs.p;
        Py_INCREF(p);
        return *this;
    }
};

static PyObject* segtree_op_py;
static AutoDecrefPtr segtree_op(AutoDecrefPtr a, AutoDecrefPtr b){
    auto tmp = PyObject_CallFunctionObjArgs(segtree_op_py, a.p, b.p, NULL);
    return AutoDecrefPtr(tmp);
}
static PyObject* segtree_e_py;
static AutoDecrefPtr segtree_e(){
    Py_INCREF(segtree_e_py);
    return AutoDecrefPtr(segtree_e_py);
}
static PyObject* segtree_f_py;
static bool segtree_f(AutoDecrefPtr x){
    PyObject* pyfunc_res = PyObject_CallFunctionObjArgs(segtree_f_py, x.p, NULL);
    int res = PyObject_IsTrue(pyfunc_res);
    if(res == -1) PyErr_Format(PyExc_ValueError, "error in SegTree f");
    return (bool)res;
}
struct SegTree{
    PyObject_HEAD
    segtree<AutoDecrefPtr, segtree_op, segtree_e>* seg;
    PyObject* op;
    PyObject* e;
    int n;
};

extern PyTypeObject SegTreeType;

static void SegTree_dealloc(SegTree* self){
    delete self->seg;
    Py_DECREF(self->op);
    Py_DECREF(self->e);
    Py_TYPE(self)->tp_free((PyObject*)self);
}
static PyObject* SegTree_new(PyTypeObject* type, PyObject* args, PyObject* kwds){
    SegTree* self;
    self = (SegTree*)type->tp_alloc(type, 0);
    return (PyObject*)self;
}
static inline void set_op_e(SegTree* self){
    segtree_op_py = self->op;
    segtree_e_py = self->e;
}
static int SegTree_init(SegTree* self, PyObject* args){
    if(Py_SIZE(args) != 3){
        self->op = Py_None;  // 何か入れておかないとヤバいことになる
        Py_INCREF(Py_None);
        self->e = Py_None;
        Py_INCREF(Py_None);
        PyErr_Format(PyExc_TypeError, "SegTree constructor expected 3 arguments (op, e, n), got %d", Py_SIZE(args));
        return -1;
    }
    PyObject* arg;
    if(!PyArg_ParseTuple(args, "OOO", &self->op, &self->e, &arg)) return -1;
    Py_INCREF(self->op);
    Py_INCREF(self->e);
    set_op_e(self);
    if(PyLong_Check(arg)){
        int n = (int)PyLong_AsLong(arg);
        if(PyErr_Occurred()) return -1;
        if(n < 0 || n > (int)1e8) {
            PyErr_Format(PyExc_ValueError, "constraint error in SegTree constructor (got %d)", n);
            return -1;
        }
        self->seg = new segtree<AutoDecrefPtr, segtree_op, segtree_e>(n);
        self->n = n;
    }else{
        PyObject *iterator = PyObject_GetIter(arg);
        if(iterator==NULL) return -1;
        PyObject *item;
        vector<AutoDecrefPtr> vec;
        if(Py_TYPE(arg)->tp_as_sequence != NULL) vec.reserve((int)Py_SIZE(arg));
        while(item = PyIter_Next(iterator)) {
            vec.push_back(item);
        }
        Py_DECREF(iterator);
        if (PyErr_Occurred()) return -1;
        self->seg = new segtree<AutoDecrefPtr, segtree_op, segtree_e>(vec);
        self->n = (int)vec.size();
    }
    return 0;
}
static PyObject* SegTree_set(SegTree* self, PyObject* args){
    long p;
    PyObject* x;
    PARSE_ARGS("lO", &p, &x);
    if(p < 0 || p >= self->n){
        PyErr_Format(PyExc_IndexError, "SegTree set index out of range (size=%d, index=%d)", self->n, p);
        return (PyObject*)NULL;
    }
    Py_INCREF(x);
    set_op_e(self);
    self->seg->set((int)p, AutoDecrefPtr(x));
    Py_RETURN_NONE;
}
static PyObject* SegTree_get(SegTree* self, PyObject* args){
    long p;
    PARSE_ARGS("l", &p);
    if(p < 0 || p >= self->n){
        PyErr_Format(PyExc_IndexError, "SegTree get index out of range (size=%d, index=%d)", self->n, p);
        return (PyObject*)NULL;
    }
    PyObject* res = self->seg->get((int)p).p;
    return Py_BuildValue("O", res);
}
static PyObject* SegTree_prod(SegTree* self, PyObject* args){
    long l, r;
    PARSE_ARGS("ll", &l, &r);
    set_op_e(self);
    auto res = self->seg->prod((int)l, (int)r).p;
    return Py_BuildValue("O", res);
}
static PyObject* SegTree_all_prod(SegTree* self, PyObject* args){
    PyObject* res = self->seg->all_prod().p;
    return Py_BuildValue("O", res);
}
static PyObject* SegTree_max_right(SegTree* self, PyObject* args){
    long l;
    PARSE_ARGS("lO", &l, &segtree_f_py);
    if(l < 0 || l > self->n){
        PyErr_Format(PyExc_IndexError, "SegTree max_right index out of range (size=%d, l=%d)", self->n, l);
        return (PyObject*)NULL;
    }
    set_op_e(self);
    int res = self->seg->max_right<segtree_f>((int)l);
    return Py_BuildValue("l", res);
}
static PyObject* SegTree_min_left(SegTree* self, PyObject* args){
    long r;
    PARSE_ARGS("lO", &r, &segtree_f_py);
    if(r < 0 || r > self->n){
        PyErr_Format(PyExc_IndexError, "SegTree max_right index out of range (size=%d, r=%d)", self->n, r);
        return (PyObject*)NULL;
    }
    set_op_e(self);
    int res = self->seg->min_left<segtree_f>((int)r);
    return Py_BuildValue("l", res);
}
static PyObject* SegTree_to_list(SegTree* self){
    PyObject* list = PyList_New(self->n);
    for(int i=0; i<self->n; i++){
        PyObject* val = self->seg->get(i).p;
        Py_INCREF(val);
        PyList_SET_ITEM(list, i, val);
    }
    return list;
}
static PyObject* SegTree_repr(PyObject* self){
    PyObject* list = SegTree_to_list((SegTree*)self);
    PyObject* res = PyUnicode_FromFormat("SegTree(%R)", list);
    Py_ReprLeave(self);
    Py_DECREF(list);
    return res;
}

static PyMethodDef SegTree_methods[] = {
    {"set", (PyCFunction)SegTree_set, METH_VARARGS, "Set item"},
    {"get", (PyCFunction)SegTree_get, METH_VARARGS, "Get item"},
    {"prod", (PyCFunction)SegTree_prod, METH_VARARGS, "Get item"},
    {"all_prod", (PyCFunction)SegTree_all_prod, METH_VARARGS, "Get item"},
    {"max_right", (PyCFunction)SegTree_max_right, METH_VARARGS, "Binary search on segtree"},
    {"min_left", (PyCFunction)SegTree_min_left, METH_VARARGS, "Binary search on segtree"},
    {"to_list", (PyCFunction)SegTree_to_list, METH_VARARGS, "Convert to list"},
    {NULL}  /* Sentinel */
};
PyTypeObject SegTreeType = {
    PyObject_HEAD_INIT(NULL)
    "atcoder.SegTree",                  /*tp_name*/
    sizeof(SegTree),                    /*tp_basicsize*/
    0,                                  /*tp_itemsize*/
    (destructor)SegTree_dealloc,        /*tp_dealloc*/
    0,                                  /*tp_print*/
    0,                                  /*tp_getattr*/
    0,                                  /*tp_setattr*/
    0,                                  /*reserved*/
    SegTree_repr,                       /*tp_repr*/
    0,                                  /*tp_as_number*/
    0,                                  /*tp_as_sequence*/
    0,                                  /*tp_as_mapping*/
    0,                                  /*tp_hash*/
    0,                                  /*tp_call*/
    0,                                  /*tp_str*/
    0,                                  /*tp_getattro*/
    0,                                  /*tp_setattro*/
    0,                                  /*tp_as_buffer*/
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE, /*tp_flags*/
    0,                                  /*tp_doc*/
    0,                                  /*tp_traverse*/
    0,                                  /*tp_clear*/
    0,                                  /*tp_richcompare*/
    0,                                  /*tp_weaklistoffset*/
    0,                                  /*tp_iter*/
    0,                                  /*tp_iternext*/
    SegTree_methods,                    /*tp_methods*/
    0,                                  /*tp_members*/
    0,                                  /*tp_getset*/
    0,                                  /*tp_base*/
    0,                                  /*tp_dict*/
    0,                                  /*tp_descr_get*/
    0,                                  /*tp_descr_set*/
    0,                                  /*tp_dictoffset*/
    (initproc)SegTree_init,             /*tp_init*/
    0,                                  /*tp_alloc*/
    SegTree_new,                        /*tp_new*/
    0,                                  /*tp_free*/
    0,                                  /*tp_is_gc*/
    0,                                  /*tp_bases*/
    0,                                  /*tp_mro*/
    0,                                  /*tp_cache*/
    0,                                  /*tp_subclasses*/
    0,                                  /*tp_weaklist*/
    0,                                  /*tp_del*/
    0,                                  /*tp_version_tag*/
    0,                                  /*tp_finalize*/
};

static PyModuleDef atcodermodule = {
    PyModuleDef_HEAD_INIT,
    "atcoder",
    NULL,
    -1,
};

PyMODINIT_FUNC PyInit_atcoder(void)
{
    PyObject* m;
    if(PyType_Ready(&SegTreeType) < 0) return NULL;

    m = PyModule_Create(&atcodermodule);
    if(m == NULL) return NULL;

    Py_INCREF(&SegTreeType);
    if (PyModule_AddObject(m, "SegTree", (PyObject*)&SegTreeType) < 0) {
        Py_DECREF(&SegTreeType);
        Py_DECREF(m);
        return NULL;
    }

    return m;
}
"""
code_setup = r"""
from distutils.core import setup, Extension
module = Extension(
    "atcoder",
    sources=["atcoder_library_wrapper.cpp"],
    extra_compile_args=["-O3", "-march=native", "-std=c++14"]
)
setup(
    name="atcoder-library",
    version="0.0.1",
    description="wrapper for atcoder library",
    ext_modules=[module]
)
"""

import os
import sys
if sys.argv[-1] == "ONLINE_JUDGE" or os.getcwd() != "/imojudge/sandbox":
    with open("atcoder_library_wrapper.cpp", "w") as f:
        f.write(code_segtree)
    with open("setup.py", "w") as f:
        f.write(code_setup)
    os.system(f"{sys.executable} setup.py build_ext --inplace")

from atcoder import SegTree


input = sys.stdin.buffer.readline
N, K = map(int, input().split())
A = [int(input()) for _ in range(N)]

op = lambda a, b: a if a > b else b
e = 0
seg = SegTree(op, e, 303030)
for a in A:
    seg.set(a, seg.prod(a-K, a+K+1) + 1)
ans = seg.all_prod()
print(ans)

Submission status: Runtime Error

Solution code:
import sys

def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c for j in range(b)] for i in range(a)]
def list3d(a, b, c, d): return [[[d for k in range(c)] for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e for l in range(d)] for k in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10**9)
INF = 10**19
MOD = 10**9 + 7
EPS = 10**-10

class SegTree:
    """
    セグメント木
    1.update: i番目の値をxに更新する
    2.query: 区間[l, r)の値を得る
    """

    def __init__(self, n, func, intv, A=[]):
        """
        :param n: 要素数(0-indexed)
        :param func: 値の操作に使う関数(min, max, add, gcdなど)
        :param intv: 要素の初期値(単位元)
        :param A: 初期化に使うリスト(オプション)
        """
        self.n = n
        self.func = func
        self.intv = intv
        # nより大きい2の冪数
        n2 = 1
        while n2 < n:
            n2 <<= 1
        self.n2 = n2
        self.tree = [self.intv] * (n2 << 1)
        # 初期化の値が決まっている場合
        if A:
            # 1段目(最下段)の初期化
            for i in range(n):
                self.tree[n2+i] = A[i]
            # 2段目以降の初期化
            for i in range(n2-1, -1, -1):
                self.tree[i] = self.func(self.tree[i*2], self.tree[i*2+1])

    def update(self, i, x):
        """
        i番目の値をxに更新
        :param i: index(0-indexed)
        :param x: update value
        """
        i += self.n2
        self.tree[i] = x
        while i > 0:
            i >>= 1
            self.tree[i] = self.func(self.tree[i*2], self.tree[i*2+1])

    def add(self, i, x):
        self.update(i, self.get(i) + x)

    def query(self, a, b):
        """
        [a, b)の値を得る
        :param a: index(0-indexed)
        :param b: index(0-indexed)
        """
        l = a + self.n2
        r = b + self.n2
        s = self.intv
        while l < r:
            if r & 1:
                r -= 1
                s = self.func(s, self.tree[r])
            if l & 1:
                s = self.func(s, self.tree[l])
                l += 1
            l >>= 1
            r >>= 1
        return s

    def get(self, i):
        """ 一点取得 """
        return self.tree[i+self.n2]

    def all(self):
        """ 全区間[0, n)の取得 """
        return self.tree[1]

    def bisearch_fore(self, l, r, x, func):
        """ 区間[l,r]で左から最初にxに対して比較の条件を満たすような値が出現する位置 """

        ok = r + 1
        ng = l - 1
        while ng+1 < ok:
            mid = (ok+ng) // 2
            if func(self.query(l, mid+1), x):
                ok = mid
            else:
                ng = mid
        if ok != r + 1:
            return ok
        else:
            return INF

    def bisearch_back(self, l, r, x, func):
        """ 区間[l,r]で右から最初にxに対して比較の条件を満たすような値が出現する位置 """

        ok = l - 1
        ng = r + 1
        while ok+1 < ng:
            mid = (ok+ng) // 2
            if func(self.query(mid, r+1), x):
                ok = mid
            else:
                ng = mid
        if ok != l - 1:
            return ok
        else:
            return -INF

    def print(self):
        for i in range(self.n):
            print(self.get(i), end=' ')
        print()

N, K = MAP()
A = LIST(N)

M = max(A)
seg = SegTree(N+1, max, -INF, [0]*(N+1))

for a in A:
    res = seg.query(max(a-K, 0), min(a+K, N)+1) + 1
    seg.update(a, res)
ans = seg.all()
print(ans)

Submission status: Runtime Error

Solution code:
def dfs(i,ans):
  if i == n:
    return
  if len(ans) == 0:
    ans.append(a[i])
    dfs(i+1,ans)
  else:
    if abs(ans[-1]-a[i])<=k:
      ans.append(a[i])
    dfs(i+1,ans)

n,k = map(int,input().split())
ans = []
a = []
for i in range(n):
  a.append(int(input()))
#print(a)
mx = 0
for i in range(n):
  tmp = []
  dfs(i,tmp)
  mx = max(mx,len(tmp))
print(mx)

Submission status: Runtime Error

Solution code:
class segment_tree:
    __slots__ = ["op_M", "e_M","N","N0","dat"]
    def __init__(self, N, operator_M, e_M):
        self.op_M = operator_M
        self.e_M = e_M
        self.N = N
        self.N0 = 1<<(N-1).bit_length()
        self.dat = [self.e_M]*(2*self.N0)
    
    # 長さNの配列 initial で初期化
    def build(self, initial):
        assert self.N == len(initial)
        self.dat[self.N0:self.N0+len(initial)] = initial[:]
        for k in range(self.N0-1,0,-1):
            self.dat[k] = self.op_M(self.dat[2*k], self.dat[2*k+1])

    # a_k の値を x に更新
    def update(self,k,x):
        k += self.N0
        self.dat[k] = x
        k >>= 1
        while k:
            self.dat[k] = self.op_M(self.dat[2*k], self.dat[2*k+1])
            k >>= 1

    # 区間[L,R]をopでまとめる
    def query(self,L,R):
        L += self.N0; R += self.N0 + 1 
        sl = sr = self.e_M
        while L < R:
            if R & 1:
                R -= 1
                sr = self.op_M(self.dat[R],sr)
            if L & 1:
                sl = self.op_M(sl,self.dat[L])
                L += 1
            L >>= 1; R >>= 1
        return self.op_M(sl,sr)

    def get(self, k): #k番目の値を取得。query[k,k]と同じ
        return self.dat[k+self.N0]
    
    """
    f(x_l*...*x_{r-1}) が True になる最大の r 
    つまり TTTTFFFF となるとき、F となる最小の添え字
    存在しない場合 n が返る
    f(e_M) = True でないと壊れる
    """
    def max_right(self,l,f):
        if l == self.N: return self.N;
        l += self.N0
        sm = self.e_M
        while True:
            while l&1==0:
                l >>= 1
            
            if not f(self.op_M(sm,self.dat[l])):
                while l < self.N0:
                    l *= 2
                    if f(self.op_M(sm,self.dat[l])):
                        sm = self.op_M(sm,self.dat[l])
                        l += 1
                return l - self.N0

            sm = self.op_M(sm,self.dat[l])
            l += 1
            if (l & -l) == l: break
        
        return self.N

    """
    f(x_l*...*x_{r-1}) が True になる最小の l
    つまり FFFFTTTT となるとき、T となる最小の添え字
    存在しない場合 r が返る
    f(e_M) = True でないと壊れる
    """
    def min_left(self,r,f):
        if r == 0: return 0
        r += self.N0
        sm = self.e_M
        
        while True:
            r -= 1
            while r > 1 and r&1:
                r >>= 1

            if not f(self.op_M(self.dat[r],sm)):
                while r < self.N0:
                    r = r*2 + 1
                    if f(self.op_M(self.dat[r],sm)):
                        sm = self.op_M(self.dat[r],sm)
                        r -= 1
                return r + 1 - self.N0

            sm = self.op_M(self.dat[r],sm)
            if (r & -r) == r: break

        return 0


###########################################################################
import sys
readline = sys.stdin.readline

n,k = map(int, readline().split())
#*a, = map(int, readline().split())

seg = segment_tree(n+1,max,0)
#seg.build(a)

for _ in range(n):
    a = int(readline())
    v = seg.query(max(0,a-k),min(n,a+k))
    seg.update(a,v+1)

print(seg.dat[1])

Submission status: Runtime Error

Solution code:
from sys import stdin, stdout
from collections import defaultdict
input = stdin.readline

class Graph: 
	
	def __init__(self,V): 
		self.V = V 
		self.adj = [[] for i in range(V)] 

	def DFSUtil(self, temp, v, visited): 

		visited[v] = True

		temp.append(v) 

		for i in self.adj[v]: 
			if visited[i] == False: 
				
				temp = self.DFSUtil(temp, i, visited) 
		return temp 

	def addEdge(self, v, w): 
		self.adj[v].append(w) 
		self.adj[w].append(v) 

	def connectedComponents(self): 
		visited = [] 
		cc = [] 
		for i in range(self.V): 
			visited.append(False) 
		for v in range(self.V): 
			if visited[v] == False: 
				temp = [] 
				cc.append(self.DFSUtil(temp, v, visited)) 
		return cc 

if __name__=="__main__": 
	n, m = map(int, input().split())
	g = Graph(n)
	for i in range(m):
		x, y = map(int, input().split())
		g.addEdge(x-1, y-1)
	print(len(g.connectedComponents())-1)

Submission status: Runtime Error

Solution code:
import sys


class SegTreeMax:
    """
    以下のクエリを処理する
    1.update:  i番目の値をxに更新する
    2.get_min: 区間[l, r)の最小値を得る
    """

    def __init__(self, n, INF):
        """
        :param n: 要素数
        :param INF: 初期値（入りうる要素より十分に大きな数）
        """
        n2 = 1 << (n - 1).bit_length()
        self.offset = n2
        self.tree = [INF] * (n2 << 1)
        self.INF = INF

    @classmethod
    def from_array(cls, arr, INF):
        ins = cls(len(arr), INF)
        ins.tree[ins.offset:ins.offset + len(arr)] = arr
        for i in range(ins.offset - 1, 0, -1):
            l = i << 1
            r = l + 1
            ins.tree[i] = max(ins.tree[l], ins.tree[r])
        return ins

    def update(self, i, x):
        """
        i番目の値をxに更新
        :param i: index(0-indexed)
        :param x: update value
        """
        i += self.offset
        self.tree[i] = x
        while i > 1:
            y = self.tree[i ^ 1]
            if y >= x:
                break
            i >>= 1
            self.tree[i] = x

    def get_max(self, a, b):
        """
        [a, b)の最大値を得る
        :param a: index(0-indexed)
        :param b: index(0-indexed)
        """
        result = self.INF

        l = a + self.offset
        r = b + self.offset
        while l < r:
            if r & 1:
                result = max(result, self.tree[r - 1])
            if l & 1:
                result = max(result, self.tree[l])
                l += 1
            l >>= 1
            r >>= 1

        return result


n, k, *aaa = map(int, sys.stdin.buffer.read().split())

sgt = SegTreeMax(300001, 0)
for a in aaa:
    nxt = sgt.get_max(max(0, a - k), min(a + k + 1, 3000001))
    sgt.update(a, nxt + 1)
print(sgt.get_max(0, 300001))

Submission status: Runtime Error

Solution code:
import sys


class SegTreeMax:
    """
    以下のクエリを処理する
    1.update:  i番目の値をxに更新する
    2.get_min: 区間[l, r)の最小値を得る
    """

    def __init__(self, n, INF):
        """
        :param n: 要素数
        :param INF: 初期値（入りうる要素より十分に大きな数）
        """
        n2 = 1 << (n - 1).bit_length()
        self.offset = n2
        self.tree = [INF] * (n2 << 1)
        self.INF = INF

    @classmethod
    def from_array(cls, arr, INF):
        ins = cls(len(arr), INF)
        ins.tree[ins.offset:ins.offset + len(arr)] = arr
        for i in range(ins.offset - 1, 0, -1):
            l = i << 1
            r = l + 1
            ins.tree[i] = max(ins.tree[l], ins.tree[r])
        return ins

    def update(self, i, x):
        """
        i番目の値をxに更新
        :param i: index(0-indexed)
        :param x: update value
        """
        i += self.offset
        self.tree[i] = x
        while i > 1:
            y = self.tree[i ^ 1]
            if y >= x:
                break
            i >>= 1
            self.tree[i] = x

    def get_max(self, a, b):
        """
        [a, b)の最大値を得る
        :param a: index(0-indexed)
        :param b: index(0-indexed)
        """
        result = self.INF

        l = a + self.offset
        r = b + self.offset
        while l < r:
            if r & 1:
                result = max(result, self.tree[r - 1])
            if l & 1:
                result = max(result, self.tree[l])
                l += 1
            l >>= 1
            r >>= 1

        return result


n, k, *aaa = map(int, sys.stdin.buffer.read().split())

sgt = SegTreeMax(300001, 0)
for a in aaa:
    nxt = sgt.get_max(a - k, a + k + 1)
    sgt.update(a, nxt + 1)
print(sgt.get_max(0, 300001))

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-
import sys
sys.setrecursionlimit(10**9)
INF=10**18
MOD=10**9+7
input=lambda: sys.stdin.readline().rstrip()
YesNo=lambda b: bool([print('Yes')] if b else print('No'))
YESNO=lambda b: bool([print('YES')] if b else print('NO'))
int1=lambda x:int(x)-1

N,K=map(int,input().split())
A=[int(input()) for i in range(N)]
class SegmentTree:
    def __init__(self,n,segfunc,ide_ele):
        self.segfunc=segfunc
        self.ide_ele=ide_ele
        self.num=2**(n-1).bit_length()
        self.dat=[ide_ele]*2*self.num
    
    def init(self,iter):
        for i in range(len(iter)):
            self.dat[i+self.num]=iter[i]
        for i in range(self.num-1,0,-1):
            self.dat[i]=self.segfunc(self.dat[i*2],self.dat[i*2+1])
    
    def update(self,k,x):
        k+=self.num
        self.dat[k]=x
        while k:
            k//=2
            self.dat[k]=self.segfunc(self.dat[k*2],self.dat[k*2+1])
    
    def query(self,p,q):
        if q<=p:
            return self.ide_ele
        p+=self.num
        q+=self.num-1
        res=self.ide_ele
        while q-p>1:
            if p&1==1:
                res=self.segfunc(res,self.dat[p])
            if q&1==0:
                res=self.segfunc(res,self.dat[q])
                q-=1
            p=(p+1)//2
            q=q//2
        if p==q:
            res=self.segfunc(res,self.dat[p])
        else:
            res=self.segfunc(self.segfunc(res,self.dat[p]),self.dat[q])
        return res

s=SegmentTree(N,lambda a,b: max(a,b),0)

s.update(A[0],1)
ans=1

for x in A[1:]:
    p=max(x-K,0)
    q=min(x+K+1,N)
    res=s.query(p,q)
    s.update(x,res+1)
    ans=max(ans,res+1)
print(ans)