欧拉工程第38题：Pandigital multiples

题目链接：https://projecteuler.net/problem=38
一个数，分别与1-n相乘，n>1，并把n个结果链接起来，如果连接后的数字是9位数字且各位是在都在1-9，1-9中的每个数字也只能出现一次。求满足这个条件的最大链接数。
例如：
92 × 1 = 192
192 × 2 = 384
192 × 3 = 576
By concatenating each product we get the 1 to 9 pandigital, 192384576. We will call 192384576 the concatenated product of 192 and (1,2,3)

思路：
1.先考虑一个数是不是只包含1-9的数字
1.1 长度是9
1.2不能包含0
1.3不能有重复数字
2.这个数乘以1-n，结果链接后的值，长度大于9时候结束
3.如果确定上界？

num*1链接上num*2 是 一个1到9只出现一次的九位数 ，此时num最大就是上界。
显然num最大是4位数，最大的4位数是9999

感觉不能再缩小了，其实最大的数是：9327

Java程序：

package projecteuler31to40;

import java.util.Date;
import java.util.Set;
import java.util.TreeSet;

class level38{

    void solve(){
        int Max_Value=9999;
        int num=0;
        int max=0;
        for(int i=2;i<Max_Value;i++){
            int digitnum=Mulitnum(i);
            if(digitnum>max && JudgeNineDigit(digitnum) ){
                max=digitnum;
                num=i;
            }
        }
        System.out.println(max+","+num);
    }
    int Mulitnum(int num){
        String str=String.valueOf(num);
        for(int i=2;i<=9;i++){
            if(str.length()<9){
                int res=num*i;
                str=str.concat(String.valueOf(res));

            }
        }
        if(str.length()>9) return 0;
        return Integer.parseInt(str);
    }
    boolean JudgeNineDigit (int num){
        String str=String.valueOf(num);
        Set<Character> set=new TreeSet<Character>();
        if(str.length()!=9) return false;
        if(str.indexOf("0")>-1) return false;
        for(int i=0;i<9;i++){
            set.add(str.charAt(i));
        }
        if(set.size()==9) return true;
        return false;
    }

}
public class Problem38 {


    public static void main(String[] args){
        Date beginTime=new Date();
        new level38().solve();//932718654
        Date endTime=new Date();
        long Time=endTime.getTime()-beginTime.getTime();
        System.out.println("Time:"+Time/1000+"s"+Time%1000+"ms");
    }

}

结果：

932718654,9327
Time:0s69ms

Python代码

def mulitnum(num):
    p=str(num)
    for i in range(2,10):
        if len(p)<9:
            res=num*i
            p=p+str(res)
    if len(p)>9:
        return 0
    return p

from time import time
t0=time()
digits=set('123456789')
maxnum=0

for i in range(2,9999):
    product=str(mulitnum(i))
    if len(product)==9 and digits==set(product):
        if int(product)>maxnum:
            maxnum=int(product)

print maxnum
print("time is {0}".format(time() - t))   

结果：

>>> print maxnum
932718654
>>> 
>>> print("time is {0}".format(time() - t))   
time is 3.35899996758

Python Help Set

help(set)
Help on class set in module __builtin__:

class set(object)
 |  set() -> new empty set object
 |  set(iterable) -> new set object
 |  
 |  Build an unordered collection of unique elements.
 |  建立一个无须唯一的元素集合
 |  Methods defined here:
 |  方法：
 |  __and__(...) 
 |      x.__and__(y) <==> x&y
 |  
 |  __cmp__(...)
 |      x.__cmp__(y) <==> cmp(x,y)
 |  
 |  __contains__(...)
 |      x.__contains__(y) <==> y in x.
 |  
 |  __eq__(...)
 |      x.__eq__(y) <==> x==y
 |  
 |  __ge__(...)
 |      x.__ge__(y) <==> x>=y
 |  
 |  __getattribute__(...)
 |      x.__getattribute__('name') <==> x.name
 |  
 |  __gt__(...)
 |      x.__gt__(y) <==> x>y
 |  
 |  __iand__(...)
 |      x.__iand__(y) <==> x&=y
 |  
 |  __init__(...)
 |      x.__init__(...) initializes x; see help(type(x)) for signature
 |  
 |  __ior__(...)
 |      x.__ior__(y) <==> x|=y
 |  
 |  __isub__(...)
 |      x.__isub__(y) <==> x-=y
 |  
 |  __iter__(...)
 |      x.__iter__() <==> iter(x)
 |  
 |  __ixor__(...)
 |      x.__ixor__(y) <==> x^=y
 |  
 |  __le__(...)
 |      x.__le__(y) <==> x<=y
 |  
 |  __len__(...)
 |      x.__len__() <==> len(x)
 |  
 |  __lt__(...)
 |      x.__lt__(y) <==> x<y
 |  
 |  __ne__(...)
 |      x.__ne__(y) <==> x!=y
 |  
 |  __or__(...)
 |      x.__or__(y) <==> x|y
 |  
 |  __rand__(...)
 |      x.__rand__(y) <==> y&x
 |  
 |  __reduce__(...)
 |      Return state information for pickling.
 |  
 |  __repr__(...)
 |      x.__repr__() <==> repr(x)
 |  
 |  __ror__(...)
 |      x.__ror__(y) <==> y|x
 |  
 |  __rsub__(...)
 |      x.__rsub__(y) <==> y-x
 |  
 |  __rxor__(...)
 |      x.__rxor__(y) <==> y^x
 |  
 |  __sizeof__(...)
 |      S.__sizeof__() -> size of S in memory, in bytes
 |  
 |  __sub__(...)
 |      x.__sub__(y) <==> x-y
 |  
 |  __xor__(...)
 |      x.__xor__(y) <==> x^y
 |  
 |  add(...)
 |      Add an element to a set.
 |      
 |      This has no effect if the element is already present.
 |  
 |  clear(...)
 |      Remove all elements from this set.
 |  
 |  copy(...)
 |      Return a shallow copy of a set.
 |  
 |  difference(...)
 |      Return the difference of two or more sets as a new set.
 |      
 |      (i.e. all elements that are in this set but not the others.)
 |  
 |  difference_update(...)
 |      Remove all elements of another set from this set.
 |  
 |  discard(...)
 |      Remove an element from a set if it is a member.
 |      
 |      If the element is not a member, do nothing.
 |  
 |  intersection(...)
 |      Return the intersection of two or more sets as a new set.
 |      返回两个或更多的交集集作为一个新的集合。
 |      (i.e. elements that are common to all of the sets.)
 |  
 |  intersection_update(...)
 |      Update a set with the intersection of itself and another.
 |  
 |  isdisjoint(...)
 |      Return True if two sets have a null intersection.
 |  
 |  issubset(...)
 |      Report whether another set contains this set.
 |  
 |  issuperset(...)
 |      Report whether this set contains another set.
 |  
 |  pop(...)
 |      Remove and return an arbitrary set element.
 |      Raises KeyError if the set is empty.
 |  
 |  remove(...)
 |      Remove an element from a set; it must be a member.
 |      
 |      If the element is not a member, raise a KeyError.
 |  
 |  symmetric_difference(...)
 |      Return the symmetric difference of two sets as a new set.
 |      
 |      (i.e. all elements that are in exactly one of the sets.)
 |  
 |  symmetric_difference_update(...)
 |      Update a set with the symmetric difference of itself and another.
 |  
 |  union(...)
 |      Return the union of sets as a new set.
 |      
 |      (i.e. all elements that are in either set.)
 |  
 |  update(...)
 |      Update a set with the union of itself and others.
 |  
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |  
 |  __hash__ = None
 |  
 |  __new__ = <built-in method __new__ of type object>
 |      T.__new__(S, ...) -> a new object with type S, a subtype of T