Codeforces777C Alyona and Spreadsheet 2017-05-04 17:46 103人阅读 评论(0) 收藏

C. Alyona and Spreadsheet

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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".

Example

input

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

output

Yes
No
Yes
Yes
Yes
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.

——————————————————————————————————————

题目的意思是给出有个矩阵，给出k组查询，询问每一列中是否存在第l行到第r行满足非递减的序列。

思路：从最后一行开始到第一行dp记录每一个能最大到达的列，再把一行的最大值取出来，查询是只要比较l行的最大值和r的关系即可

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>
using namespace std;
#define inf 0x3f3f3f3f

vector<int>v[100005];
vector<int>mp[100005];
int ans[100005];

int main()
{
    int n,m,k,l,r,x;
    while(~scanf("%d%d",&n,&m))
    {

        for(int i=1; i<=n; i++)
            for(int j=0; j<m; j++)
            {
                scanf("%d",&x);
                mp[i].push_back(x);
            }
            memset(ans,-1, sizeof ans);
        for(int i=0; i<m; i++)
        {
            v[n].push_back(n);
        }
        ans[n]=n;
        for(int i=n-1; i>=1; i--)
        {
            for(int j=0; j<m; j++)
            {
                if(mp[i][j]>mp[i+1][j])
                    v[i].push_back(i);
                else
                    v[i].push_back(v[i+1][j]);
                    ans[i]=max(ans[i],v[i][j]);
            }

        }

        scanf("%d",&k);
        for(int i=0; i<k; i++)
        {
            scanf("%d%d",&l,&r);

            if(ans[l]<r)
                printf("No\n");
            else
                printf("Yes\n");
        }
    }
    return 0;
}