Quasi Binary---codeforces

发布时间 2023-04-23 15:02:46作者: 尼古丁不真

# Quasi Binary

## 题面翻译

**题目描述**

给出一个数n,你需要将n写成若干个数的和,其中每个数的十进制表示中仅包含0和1。

问最少需要多少个数

**输入输出格式**


输入格式:

一行 一个数 n(1≤n≤10^6)

输出格式:

最少的数的个数,并给出一种方案。

## 题目描述

A number is called quasibinary if its decimal representation contains only digits 0 or 1. For example, numbers 0, 1, 101, 110011 — are quasibinary and numbers 2, 12, 900 are not.

You are given a positive integer $ n $ . Represent it as a sum of minimum number of quasibinary numbers.

## 输入格式

The first line contains a single integer $ n $ ( $ 1<=n<=10^{6} $ ).

## 输出格式

In the first line print a single integer $ k $ — the minimum number of numbers in the representation of number $ n $ as a sum of quasibinary numbers.

In the second line print $ k $ numbers — the elements of the sum. All these numbers should be quasibinary according to the definition above, their sum should equal $ n $ . Do not have to print the leading zeroes in the numbers. The order of numbers doesn't matter. If there are multiple possible representations, you are allowed to print any of them.

## 样例 #1

### 样例输入 #1

```
9
```

### 样例输出 #1

```
9
1 1 1 1 1 1 1 1 1
```

## 样例 #2

### 样例输入 #2

```
32
```

### 样例输出 #2

```
3
10 11 11
```

#include<iostream>
#include<cstdio>
using namespace std;

int Ans,num[100];//其实这里定义10就够了,因为最多9个数就一定可以构成n

int main()
{
    int n,Res;
    scanf("%d",&n);
    for(int bit=1;bit<=n;bit*=10)//将每一个res对应的数值在每一次for循环中分配给res个num数组中的数,比如2,分配给num[1]1和num{2]1,
                      比如3,对应其实是30,那么就分配给num[1]10,num[2]10,num[3]10,综上看来,num[1]是最大的,num[res]
                      是最小的,所以倒序输出,就是num[ans] { Res
=(n/bit)%10;//每一位的数值 Ans=max(Ans,Res); for(int i=1;i<=Res;++i) num[i]+=bit; } printf("%d\n",Ans); for(;Ans;--Ans) printf("%d ",num[Ans]);//倒序输出,从小到大 putchar('\n'); return 0; }

一个数最少可以由它的数位中最大数的个数的01二位数组成。

 

心得:感觉这种思维题真的很难想,反正我是想不出哎