Alyona and Spreadsheet (Codeforces 777C)
Tags: Implement, two pointers

During the lesson small girl Alyona works with one famous spreadsheet computer program and learns how to edit tables.Now she has a table filled with integers. The table consists of n rows and m columns. By ai, j we will denote the integer located at the i-th row and the j-th column. We say that the table is sorted in non-decreasing order in the column j if ai, j ≤ ai + 1, j for all i from 1 to n - 1.Teacher gave Alyona k tasks. For each of the tasks two integers l and r are given and Alyona has to answer the following question: if one keeps the rows from l to r inclusive and deletes all others, will the table be sorted in non-decreasing order in at least one column? Formally, does there exist such j that ai, j ≤ ai + 1, j for all i from l to r - 1 inclusive.Alyona is too small to deal with this task and asks you to help!

Input: The first line of the input contains two positive integers n and m (1 ≤ n·m ≤ 100 000) — the number of rows and the number of columns in the table respectively. Note that your are given a constraint that bound the product of these two integers, i.e. the number of elements in the table.Each of the following n lines contains m integers. The j-th integers in the i of these lines stands for ai, j (1 ≤ ai, j ≤ 109).The next line of the input contains an integer k (1 ≤ k ≤ 100 000) — the number of task that teacher gave to Alyona.The i-th of the next k lines contains two integers li and ri (1 ≤ li ≤ ri ≤ n).

Output: Print "Yes" to the i-th line of the output if the table consisting of rows from li to ri inclusive is sorted in non-decreasing order in at least one column. Otherwise, print "No".

Note: In the sample, the whole table is not sorted in any column. However, rows 1–3 are sorted in column 1, while rows 4–5 are sorted in column 3.

Sample Inputs:
5 4
1 2 3 5
3 1 3 2
4 5 2 3
5 5 3 2
4 4 3 4
6
1 1
2 5
4 5
3 5
1 3
1 5

Sample Outputs:
Yes
No
Yes
Yes
Yes
No

Solution (Python):
import sys
import os
from io import BytesIO, IOBase
BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = 'x' in file.mode or 'r' not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            (self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b'\n') + (not b)
            ptr = self.buffer.tell()
            (self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            (self.buffer.truncate(0), self.buffer.seek(0))

class IOWrapper(IOBase):

    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode('ascii'))
        self.read = lambda : self.buffer.read().decode('ascii')
        self.readline = lambda : self.buffer.readline().decode('ascii')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')

def I():
    return input()

def II():
    return int(input())

def MII():
    return map(int, input().split())

def LI():
    return list(input().split())

def LII():
    return list(map(int, input().split()))

def GMI():
    return map(lambda x: int(x) - 1, input().split())
from bisect import *
from heapq import *
from collections import *
from functools import *
from itertools import *
from time import *
from random import *
from math import log, gcd, sqrt, ceil
''
from types import GeneratorType

def bootstrap(f, stack=[]):

    def wrappedfunc(*args, **kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to = stack[-1].send(to)
            return to
    return wrappedfunc

def solve():
    (n, m) = MII()
    pre_line = [2000000000.0] * m
    dp = [n] * n
    last_idx = [0] * m
    for i in range(n):
        cur_line = LII()
        for j in range(m):
            if cur_line[j] < pre_line[j]:
                last_idx[j] = i
            dp[i] = min(last_idx[j], dp[i])
        pre_line = cur_line
    for i in range(II()):
        (L, R) = MII()
        print('Yes' if L - 1 >= dp[R - 1] else 'No')
for x in range(1):
    solve()

Solution (Python):
import sys
import os
from io import BytesIO, IOBase
BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = 'x' in file.mode or 'r' not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            (self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b'\n') + (not b)
            ptr = self.buffer.tell()
            (self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            (self.buffer.truncate(0), self.buffer.seek(0))

class IOWrapper(IOBase):

    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode('ascii'))
        self.read = lambda : self.buffer.read().decode('ascii')
        self.readline = lambda : self.buffer.readline().decode('ascii')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')

def I():
    return input()

def II():
    return int(input())

def MII():
    return map(int, input().split())

def LI():
    return list(input().split())

def LII():
    return list(map(int, input().split()))

def GMI():
    return map(lambda x: int(x) - 1, input().split())
from bisect import *
from heapq import *
from collections import *
from functools import *
from itertools import *
from time import *
from random import *
from math import log, gcd, sqrt, ceil
''
from types import GeneratorType

def bootstrap(f, stack=[]):

    def wrappedfunc(*args, **kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to = stack[-1].send(to)
            return to
    return wrappedfunc

def solve():
    (n, m) = MII()
    pre_line = [2000000000.0] * m
    dp = [0] * m
    res = [0] * n
    for i in range(n):
        cur_line = LII()
        for j in range(m):
            if cur_line[j] >= pre_line[j]:
                dp[j] += 1
            else:
                dp[j] = 0
        res[i] = max(dp)
        pre_line = cur_line
    for i in range(II()):
        (L, R) = MII()
        print('Yes' if R - L <= res[R - 1] else 'No')
for x in range(1):
    solve()

Solution (Python):
import sys
import os
from io import BytesIO, IOBase
BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = 'x' in file.mode or 'r' not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            (self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b'\n') + (not b)
            ptr = self.buffer.tell()
            (self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            (self.buffer.truncate(0), self.buffer.seek(0))

class IOWrapper(IOBase):

    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode('ascii'))
        self.read = lambda : self.buffer.read().decode('ascii')
        self.readline = lambda : self.buffer.readline().decode('ascii')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')

def I():
    return input()

def II():
    return int(input())

def MII():
    return map(int, input().split())

def LI():
    return list(input().split())

def LII():
    return list(map(int, input().split()))

def GMI():
    return map(lambda x: int(x) - 1, input().split())
from bisect import *
from heapq import *
from collections import *
from functools import *
from itertools import *
from time import *
from random import *
from math import log, gcd, sqrt, ceil
''
from types import GeneratorType

def bootstrap(f, stack=[]):

    def wrappedfunc(*args, **kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to = stack[-1].send(to)
            return to
    return wrappedfunc

def solve():
    (n, m) = MII()
    v = [LII() for _ in range(n)]
    ml = [[i] * m for i in range(n)]
    for i in range(m):
        (pre, idx) = (int(2000000000.0), -1)
        for j in range(n):
            if v[j][i] >= pre:
                (pre, ml[j][i]) = (v[j][i], idx)
            else:
                (pre, idx) = (v[j][i], j)
    for i in range(n):
        for j in range(m):
            ml[i][0] = min(ml[i][0], ml[i][j])
    for i in range(II()):
        (L, R) = MII()
        print('Yes' if L - 1 >= ml[R - 1][0] else 'No')
for x in range(1):
    solve()