B. Bear and Blocks

本文介绍了一个迷宫逃脱问题的算法解决方案。小Vasya在一个由(n+1)个房间组成的迷宫中,需要从第一个房间到达最后一个房间。每个房间有两个单向门户,一个通往下一个房间,另一个通往编号小于等于当前房间的某个房间。通过设计动态规划算法,我们计算了最少的门户移动次数。

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One day, little Vasya found himself in a maze consisting of (n + 1) rooms, numbered from 1 to (n + 1). Initially, Vasya is at the first room and to get out of the maze, he needs to get to the (n + 1)-th one.

The maze is organized as follows. Each room of the maze has two one-way portals. Let's consider room number i (1 ≤ i ≤ n), someone can use the first portal to move from it to room number (i + 1), also someone can use the second portal to move from it to room number pi, where 1 ≤ pi ≤ i.

In order not to get lost, Vasya decided to act as follows.

  • Each time Vasya enters some room, he paints a cross on its ceiling. Initially, Vasya paints a cross at the ceiling of room 1.
  • Let's assume that Vasya is in room i and has already painted a cross on its ceiling. Then, if the ceiling now contains an odd number of crosses, Vasya uses the second portal (it leads to room pi), otherwise Vasya uses the first portal.

Help Vasya determine the number of times he needs to use portals to get to room (n + 1) in the end.

Input

The first line contains integer n (1 ≤ n ≤ 103) — the number of rooms. The second line contains n integers pi (1 ≤ pi ≤ i). Each pi denotes the number of the room, that someone can reach, if he will use the second portal in the i-th room.

Output

Print a single number — the number of portal moves the boy needs to go out of the maze. As the number can be rather large, print it modulo 1000000007 (109 + 7).

Examples

input

Copy

2
1 2

output

Copy

4

input

Copy

4
1 1 2 3

output

Copy

20

input

Copy

5
1 1 1 1 1

output

Copy

62

题意:

有n+1个房间,走到一个房间就要标记一次,偶数就跳到pi的房间,pi<=i;

奇数就直接到i+1的房间。

思路:

这道题开始想模拟,但发现不行,还有没注意pi<=i;

我们可以设计dp(i)为1到i的步数,如果我们现在在i房间,那么前面的房间标记的次数是偶数等价于0,那么此时的i是偶数次要先回到pi再由pi回到i(dp[i]-dp[pi]步)在从i到i+1(1步);

所以可得状态方程 dp[i+1]=dp[i]+dp[i]-dp[p[i]]+2;

2时i到p[i]要一步,到i+1要一步。

代码:

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#define LL long long

using namespace  std;
const int  maxn=1e5+10;
const int  mod=1000000007;
LL dp[maxn];
int a[maxn];

int main()
{
    int n;
    cin>>n;

    for(int i=1;i<=n;i++)
    {
        cin>>a[i];
    }
    dp[1]=0;
    for(int i=1;i<=n;i++)
    {
        dp[i+1]=(2*dp[i]%mod-dp[a[i]]%mod+2+mod)%mod;
    }
    cout<<dp[n+1]<<endl;
    return 0;
}

 

raise RuntimeError('Error(s) in loading state_dict for {}:\n\t{}'.format( RuntimeError: Error(s) in loading state_dict for PResNet: Missing key(s) in state_dict: "conv1.conv1_1.conv.weight", "conv1.conv1_1.norm.weight", "conv1.conv1_1.norm.bias", "conv1.conv1_1.norm.running_mean", "conv1.conv1_1.norm.running_var", "conv1.conv1_2.conv.weight", "conv1.conv1_2.norm.weight", "conv1.conv1_2.norm.bias", "conv1.conv1_2.norm.running_mean", "conv1.conv1_2.norm.running_var", "conv1.conv1_3.conv.weight", "conv1.conv1_3.norm.weight", "conv1.conv1_3.norm.bias", "conv1.conv1_3.norm.running_mean", "conv1.conv1_3.norm.running_var", "res_layers.0.blocks.0.branch2a.conv.weight", "res_layers.0.blocks.0.branch2a.norm.weight", "res_layers.0.blocks.0.branch2a.norm.bias", "res_layers.0.blocks.0.branch2a.norm.running_mean", "res_layers.0.blocks.0.branch2a.norm.running_var", "res_layers.0.blocks.0.branch2b.conv.weight", "res_layers.0.blocks.0.branch2b.norm.weight", "res_layers.0.blocks.0.branch2b.norm.bias", "res_layers.0.blocks.0.branch2b.norm.running_mean", "res_layers.0.blocks.0.branch2b.norm.running_var", "res_layers.0.blocks.0.branch2c.conv.weight", "res_layers.0.blocks.0.branch2c.norm.weight", "res_layers.0.blocks.0.branch2c.norm.bias", "res_layers.0.blocks.0.branch2c.norm.running_mean", "res_layers.0.blocks.0.branch2c.norm.running_var", "res_layers.0.blocks.0.short.conv.weight", "res_layers.0.blocks.0.short.norm.weight", "res_layers.0.blocks.0.short.norm.bias", "res_layers.0.blocks.0.short.norm.running_mean", "res_layers.0.blocks.0.short.norm.running_var", "res_layers.0.blocks.1.branch2a.conv.weight", "res_layers.0.blocks.1.branch2a.norm.weight", "res_layers.0.blocks.1.branch2a.norm.bias", "res_layers.0.blocks.1.branch2a.norm.running_mean", "res_layers.0.blocks.1.branch2a.norm.running_var", "res_layers.0.blocks.1.branch2b.conv.weight", "res_layers.0.blocks.1.branch2b.norm.weight", "res_layers.0.blocks.1.branch2b.norm.bias", "res_layers.0.blocks.1.branch2b.norm.running_mean", "res_layers.0.blocks.1.branch2b.norm.running_var", "res_layers.0.blocks.1.branch2c.conv.weight", "res_layers.0.blocks.1.branch2c.norm.weight", "res_layers.0.blocks.1.branch2c.norm.bias", "res_layers.0.blocks.1.branch2c.norm.running_mean", "res_layers.0.blocks.1.branch2c.norm.running_var", "res_layers.0.blocks.2.branch2a.conv.weight", "res_layers.0.blocks.2.branch2a.norm.weight", "res_layers.0.blocks.2.branch2a.norm.bias", "res_layers.0.blocks.2.branch2a.norm.running_mean", "res_layers.0.blocks.2.branch2a.norm.running_var", "res_layers.0.blocks.2.branch2b.conv.weight", "res_layers.0.blocks.2.branch2b.norm.weight", "res_layers.0.blocks.2.branch2b.norm.bias", "res_layers.0.blocks.2.branch2b.norm.running_mean", "res_layers.0.blocks.2.branch2b.norm.running_var", "res_layers.0.blocks.2.branch2c.conv.weight", "res_layers.0.blocks.2.branch2c.norm.weight", "res_layers.0.blocks.2.branch2c.norm.bias", "res_layers.0.blocks.2.branch2c.norm.running_mean", "res_layers.0.blocks.2.branch2c.norm.running_var", "res_layers.1.blocks.0.branch2a.conv.weight", "res_layers.1.blocks.0.branch2a.norm.weight", "res_layers.1.blocks.0.branch2a.norm.bias", "res_layers.1.blocks.0.branch2a.norm.running_mean", "res_layers.1.blocks.0.branch2a.norm.running_var", "res_layers.1.blocks.0.branch2b.conv.weight", "res_layers.1.blocks.0.branch2b.norm.weight", "res_layers.1.blocks.0.branch2b.norm.bias", "res_layers.1.blocks.0.branch2b.norm.running_mean", "res_layers.1.blocks.0.branch2b.norm.running_var", "res_layers.1.blocks.0.branch2c.conv.weight", "res_layers.1.blocks.0.branch2c.norm.weight", "res_layers.1.blocks.0.branch2c.norm.bias", "res_layers.1.blocks.0.branch2c.norm.running_mean", "res_layers.1.blocks.0.branch2c.norm.running_var", "res_layers.1.blocks.0.short.conv.conv.weight", "res_layers.1.blocks.0.short.conv.norm.weight", "res_layers.1.blocks.0.short.conv.norm.bias", "res_layers.1.blocks.0.short.conv.norm.running_mean", "res_layers.1.blocks.0.short.conv.norm.running_var", "res_layers.1.blocks.1.branch2a.conv.weight", "res_layers.1.blocks.1.branch2a.norm.weight", "res_layers.1.blocks.1.branch2a.norm.bias", "res_layers.1.blocks.1.branch2a.norm.running_mean", "res_layers.1.blocks.1.branch2a.norm.running_var", "res_layers.1.blocks.1.branch2b.conv.weight", "res_layers.1.blocks.1.branch2b.norm.weight", "res_layers.1.blocks.1.branch2b.norm.bias", "res_layers.1.blocks.1.branch2b.norm.running_mean", "res_layers.1.blocks.1.branch2b.norm.running_var", "res_layers.1.blocks.1.branch2c.conv.weight", "res_layers.1.blocks.1.branch2c.norm.weight", "res_layers.1.blocks.1.branch2c.norm.bias", "res_layers.1.blocks.1.branch2c.norm.running_mean", "res_layers.1.blocks.1.branch2c.norm.running_var", "res_layers.1.blocks.2.branch2a.conv.weight", "res_layers.1.blocks.2.branch2a.norm.weight", "res_layers.1.blocks.2.branch2a.norm.bias", "res_layers.1.blocks.2.branch2a.norm.running_mean", "res_layers.1.blocks.2.branch2a.norm.running_var", "res_layers.1.blocks.2.branch2b.conv.weight", "res_layers.1.blocks.2.branch2b.norm.weight", "res_layers.1.blocks.2.branch2b.norm.bias", "res_layers.1.blocks.2.branch2b.norm.running_mean", "res_layers.1.blocks.2.branch2b.norm.running_var", "res_layers.1.blocks.2.branch2c.conv.weight", "res_layers.1.blocks.2.branch2c.norm.weight", "res_layers.1.blocks.2.branch2c.norm.bias", "res_layers.1.blocks.2.branch2c.norm.running_mean", "res_layers.1.blocks.2.branch2c.norm.running_var", "res_layers.1.blocks.3.branch2a.conv.weight", "res_layers.1.blocks.3.branch2a.norm.weight", "res_layers.1.blocks.3.branch2a.norm.bias", "res_layers.1.blocks.3.branch2a.norm.running_mean", "res_layers.1.blocks.3.branch2a.norm.running_var", "res_layers.1.blocks.3.branch2b.conv.weight", "res_layers.1.blocks.3.branch2b.norm.weight", "res_layers.1.blocks.3.branch2b.norm.bias", "res_layers.1.blocks.3.branch2b.norm.running_mean", "res_layers.1.blocks.3.branch2b.norm.running_var", "res_layers.1.blocks.3.branch2c.conv.weight", "res_layers.1.blocks.3.branch2c.norm.weight", "res_layers.1.blocks.3.branch2c.norm.bias", "res_layers.1.blocks.3.branch2c.norm.running_mean", "res_layers.1.blocks.3.branch2c.norm.running_var", "res_layers.2.blocks.0.branch2a.conv.weight", "res_layers.2.blocks.0.branch2a.norm.weight", "res_layers.2.blocks.0.branch2a.norm.bias", "res_layers.2.blocks.0.branch2a.norm.running_mean", "res_layers.2.blocks.0.branch2a.norm.running_var", "res_layers.2.blocks.0.branch2b.conv.weight", "res_layers.2.blocks.0.branch2b.norm.weight", "res_layers.2.blocks.0.branch2b.norm.bias", "res_layers.2.blocks.0.branch2b.norm.running_mean", "res_layers.2.blocks.0.branch2b.norm.running_var", "res_layers.2.blocks.0.branch2c.conv.weight", "res_layers.2.blocks.0.branch2c.norm.weight", "res_layers.2.blocks.0.branch2c.norm.bias", "res_layers.2.blocks.0.branch2c.norm.running_mean", "res_layers.2.blocks.0.branch2c.norm.running_var", "res_layers.2.blocks.0.short.conv.conv.weight", "res_layers.2.blocks.0.short.conv.norm.weight", "res_layers.2.blocks.0.short.conv.norm.bias", "res_layers.2.blocks.0.short.conv.norm.running_mean", "res_layers.2.blocks.0.short.conv.norm.running_var", "res_layers.2.blocks.1.branch2a.conv.weight", "res_layers.2.blocks.1.branch2a.norm.weight", "res_layers.2.blocks.1.branch2a.norm.bias", "res_layers.2.blocks.1.branch2a.norm.running_mean", "res_layers.2.blocks.1.branch2a.norm.running_var", "res_layers.2.blocks.1.branch2b.conv.weight", "res_layers.2.blocks.1.branch2b.norm.weight", "res_layers.2.blocks.1.branch2b.norm.bias", "res_layers.2.blocks.1.branch2b.norm.running_mean", "res_layers.2.blocks.1.branch2b.norm.running_var", "res_layers.2.blocks.1.branch2c.conv.weight", "res_layers.2.blocks.1.branch2c.norm.weight", "res_layers.2.blocks.1.branch2c.norm.bias", "res_layers.2.blocks.1.branch2c.norm.running_mean", "res_layers.2.blocks.1.branch2c.norm.running_var", "res_layers.2.blocks.2.branch2a.conv.weight", "res_layers.2.blocks.2.branch2a.norm.weight", "res_layers.2.blocks.2.branch2a.norm.bias", "res_layers.2.blocks.2.branch2a.norm.running_mean", "res_layers.2.blocks.2.branch2a.norm.running_var", "res_layers.2.blocks.2.branch2b.conv.weight", "res_layers.2.blocks.2.branch2b.norm.weight", "res_layers.2.blocks.2.branch2b.norm.bias", "res_layers.2.blocks.2.branch2b.norm.running_mean", "res_layers.2.blocks.2.branch2b.norm.running_var", "res_layers.2.blocks.2.branch2c.conv.weight", "res_layers.2.blocks.2.branch2c.norm.weight", "res_layers.2.blocks.2.branch2c.norm.bias", "res_layers.2.blocks.2.branch2c.norm.running_mean", "res_layers.2.blocks.2.branch2c.norm.running_var", "res_layers.2.blocks.3.branch2a.conv.weight", "res_layers.2.blocks.3.branch2a.norm.weight", "res_layers.2.blocks.3.branch2a.norm.bias", "res_layers.2.blocks.3.branch2a.norm.running_mean", "res_layers.2.blocks.3.branch2a.norm.running_var", "res_layers.2.blocks.3.branch2b.conv.weight", "res_layers.2.blocks.3.branch2b.norm.weight", "res_layers.2.blocks.3.branch2b.norm.bias", "res_layers.2.blocks.3.branch2b.norm.running_mean", "res_layers.2.blocks.3.branch2b.norm.running_var", "res_layers.2.blocks.3.branch2c.conv.weight", "res_layers.2.blocks.3.branch2c.norm.weight", "res_layers.2.blocks.3.branch2c.norm.bias", "res_layers.2.blocks.3.branch2c.norm.running_mean", "res_layers.2.blocks.3.branch2c.norm.running_var", "res_layers.2.blocks.4.branch2a.conv.weight", "res_layers.2.blocks.4.branch2a.norm.weight", "res_layers.2.blocks.4.branch2a.norm.bias", "res_layers.2.blocks.4.branch2a.norm.running_mean", "res_layers.2.blocks.4.branch2a.norm.running_var", "res_layers.2.blocks.4.branch2b.conv.weight", "res_layers.2.blocks.4.branch2b.norm.weight", "res_layers.2.blocks.4.branch2b.norm.bias", "res_layers.2.blocks.4.branch2b.norm.running_mean", "res_layers.2.blocks.4.branch2b.norm.running_var", "res_layers.2.blocks.4.branch2c.conv.weight", "res_layers.2.blocks.4.branch2c.norm.weight", "res_layers.2.blocks.4.branch2c.norm.bias", "res_layers.2.blocks.4.branch2c.norm.running_mean", "res_layers.2.blocks.4.branch2c.norm.running_var", "res_layers.2.blocks.5.branch2a.conv.weight", "res_layers.2.blocks.5.branch2a.norm.weight", "res_layers.2.blocks.5.branch2a.norm.bias", "res_layers.2.blocks.5.branch2a.norm.running_mean", "res_layers.2.blocks.5.branch2a.norm.running_var", "res_layers.2.blocks.5.branch2b.conv.weight", "res_layers.2.blocks.5.branch2b.norm.weight", "res_layers.2.blocks.5.branch2b.norm.bias", "res_layers.2.blocks.5.branch2b.norm.running_mean", "res_layers.2.blocks.5.branch2b.norm.running_var", "res_layers.2.blocks.5.branch2c.conv.weight", "res_layers.2.blocks.5.branch2c.norm.weight", "res_layers.2.blocks.5.branch2c.norm.bias", "res_layers.2.blocks.5.branch2c.norm.running_mean", "res_layers.2.blocks.5.branch2c.norm.running_var", "res_layers.3.blocks.0.branch2a.conv.weight", "res_layers.3.blocks.0.branch2a.norm.weight", "res_layers.3.blocks.0.branch2a.norm.bias", "res_layers.3.blocks.0.branch2a.norm.running_mean", "res_layers.3.blocks.0.branch2a.norm.running_var", "res_layers.3.blocks.0.branch2b.conv.weight", "res_layers.3.blocks.0.branch2b.norm.weight", "res_layers.3.blocks.0.branch2b.norm.bias", "res_layers.3.blocks.0.branch2b.norm.running_mean", "res_layers.3.blocks.0.branch2b.norm.running_var", "res_layers.3.blocks.0.branch2c.conv.weight", "res_layers.3.blocks.0.branch2c.norm.weight", "res_layers.3.blocks.0.branch2c.norm.bias", "res_layers.3.blocks.0.branch2c.norm.running_mean", "res_layers.3.blocks.0.branch2c.norm.running_var", "res_layers.3.blocks.0.short.conv.conv.weight", "res_layers.3.blocks.0.short.conv.norm.weight", "res_layers.3.blocks.0.short.conv.norm.bias", "res_layers.3.blocks.0.short.conv.norm.running_mean", "res_layers.3.blocks.0.short.conv.norm.running_var", "res_layers.3.blocks.1.branch2a.conv.weight", "res_layers.3.blocks.1.branch2a.norm.weight", "res_layers.3.blocks.1.branch2a.norm.bias", "res_layers.3.blocks.1.branch2a.norm.running_mean", "res_layers.3.blocks.1.branch2a.norm.running_var", "res_layers.3.blocks.1.branch2b.conv.weight", "res_layers.3.blocks.1.branch2b.norm.weight", "res_layers.3.blocks.1.branch2b.norm.bias", "res_layers.3.blocks.1.branch2b.norm.running_mean", "res_layers.3.blocks.1.branch2b.norm.running_var", "res_layers.3.blocks.1.branch2c.conv.weight", "res_layers.3.blocks.1.branch2c.norm.weight", "res_layers.3.blocks.1.branch2c.norm.bias", "res_layers.3.blocks.1.branch2c.norm.running_mean", "res_layers.3.blocks.1.branch2c.norm.running_var", "res_layers.3.blocks.2.branch2a.conv.weight", "res_layers.3.blocks.2.branch2a.norm.weight", "res_layers.3.blocks.2.branch2a.norm.bias", "res_layers.3.blocks.2.branch2a.norm.running_mean", "res_layers.3.blocks.2.branch2a.norm.running_var", "res_layers.3.blocks.2.branch2b.conv.weight", "res_layers.3.blocks.2.branch2b.norm.weight", "res_layers.3.blocks.2.branch2b.norm.bias", "res_layers.3.blocks.2.branch2b.norm.running_mean", "res_layers.3.blocks.2.branch2b.norm.running_var", "res_layers.3.blocks.2.branch2c.conv.weight", "res_layers.3.blocks.2.branch2c.norm.weight", "res_layers.3.blocks.2.branch2c.norm.bias", "res_layers.3.blocks.2.branch2c.norm.running_mean", "res_layers.3.blocks.2.branch2c.norm.running_var". Unexpected key(s) in state_dict: "ema".跑rt-detr官方代码报错
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08-02
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