【CodeForces】C. Drazil and Factorial

Problem here

Problem

Drazil is playing a math game with Varda.

Let’s define for positive integer x as a product of factorials of its digits. For example,

First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:

1. x doesn’t contain neither digit 0 nor digit 1.

2. =

Help friends find such number.

INPUT

The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.

The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.

OUTPUT

Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.

Sample

input

4
1234

output

33222

input

3
555

output

555

Solution

首先將2~9轉成這樣(0,1為空)：
2 -> 2 (2! = 2不能以其他方式組成)
3 -> 3 (3! = 6不能以其他方式組成)
4 -> 322 (4! = 24 可以用3! * 2! * 2! 組成)
5 -> 5 (5! = 120)
6 -> 53
7 -> 7
8 -> 7222
9 ->7332
證明參考這裡

#include <iostream>
#include <string>
#include <algorithm>
using namespace std;

string arr[] = {"0", "0", "2", "3", "322", "5", "53", "7", "7222", "7332"};

bool cmp(char &a, char &b){
    return a > b;
}

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

    string input;
    cin >> input;
    string result = "";
    for(int i = 0; i < input.length(); i++){
        if(input[i] != '0' && input[i] != '1'){
            result += arr[input[i]-'0'];
        }
    }
    sort(result.begin(), result.end(), cmp);
    cout << result << endl;

    return 0;
}