CodeForces 632 D Longest Subsequence(数論)
2062 ワード
題意:最長男シーケンスを求めてシーケンス中の数のlcmがmより小さいようにする
考え方:lcmは数の順序とは関係ないので,各数の出現回数を記録し,ふるい法のように各数の因子がいくつあるかを探せばよい.
Description
You are given array a with n elements and the number m. Consider some subsequence of a and the value of least common multiple (LCM) of its elements. Denote LCM as l. Find any longest subsequence of a with the value l ≤ m.
A subsequence of a is an array we can get by erasing some elements of a. It is allowed to erase zero or all elements.
The LCM of an empty array equals 1.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 106) — the size of the array a and the parameter from the problem statement.
The second line contains n integers ai (1 ≤ ai ≤ 109) — the elements of a.
Output
In the first line print two integers l and kmax (1 ≤ l ≤ m, 0 ≤ kmax ≤ n) — the value of LCM and the number of elements in optimal subsequence.
In the second line print kmax integers — the positions of the elements from the optimal subsequence in the ascending order.
Note that you can find and print any subsequence with the maximum length.
Sample Input
Input
Output
Input
Output
考え方:lcmは数の順序とは関係ないので,各数の出現回数を記録し,ふるい法のように各数の因子がいくつあるかを探せばよい.
#include<bits/stdc++.h>
using namespace std;
const int maxn = 1e6+5;
int cnt[maxn];
int dp[maxn];
int a[maxn];
int main()
{
int n,m;
scanf("%d%d",&n,&m);
for(int i=1;i<=n;i++)
{
scanf("%d",&a[i]);
if(a[i]<=m)cnt[a[i]]++;
}
for(int i=m;i;i--)
for(int j=i;j<=m;j+=i)
dp[j]+=cnt[i];
long long ans1=-1,ans2=-1;
for(int i=1;i<=m;i++)
if(dp[i]>ans1)
ans1=dp[i],ans2=i;
cout<<ans2<<" "<<ans1<<endl;
for(int i=1;i<=n;i++)
if(ans2%a[i]==0)
cout<<i<<" ";
cout<<endl;
}Description
You are given array a with n elements and the number m. Consider some subsequence of a and the value of least common multiple (LCM) of its elements. Denote LCM as l. Find any longest subsequence of a with the value l ≤ m.
A subsequence of a is an array we can get by erasing some elements of a. It is allowed to erase zero or all elements.
The LCM of an empty array equals 1.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 106) — the size of the array a and the parameter from the problem statement.
The second line contains n integers ai (1 ≤ ai ≤ 109) — the elements of a.
Output
In the first line print two integers l and kmax (1 ≤ l ≤ m, 0 ≤ kmax ≤ n) — the value of LCM and the number of elements in optimal subsequence.
In the second line print kmax integers — the positions of the elements from the optimal subsequence in the ascending order.
Note that you can find and print any subsequence with the maximum length.
Sample Input
Input
7 8
6 2 9 2 7 2 3
Output
6 5
1 2 4 6 7
Input
6 4
2 2 2 3 3 3
Output
2 3
1 2 3