Egypt score (Vijos 1308)

Describe

In ancient Egypt, people used unit fractions and (like 1/a, A is the natural number) to represent all rational numbers. such as: 2/3=1/2+1/6, but do not allow 2/3=1/3+1/3, because addend have the same. For a fraction A/b, there are many ways to express it, but which is best? First of all, addend less than addend more good, second, add a number of the same, the smallest score bigger the better.

Example: 19/45=1/3 + 1/12 + 1/180
19/45=1/3 + 1/15 + 1/45
19/45=1/3 + 1/18 + 1/30,
19/45=1/4 + 1/6 + 1/180
19/45=1/5 + 1/6 + 1/18.
The best is the last one, because 1/18 is bigger than 1/180,1/45,1/30,1/180.

Give a B (0<a<b<1000), the best expression of programming calculation.

Input: a B
Output: Several numbers, from childhood to large permutations, in turn, the denominator of the unit fraction.

Example 1 Sample Input 1

19 45

Sample Output 1

5 6 18

Limit

Each test point 1s

(from https://vijos.org/p/1308)

This problem is obviously using search

(1) Deep Search, do not know the depth

(2) wide search, the amount of data stored may be too large

(3) Iterative deepening, pruning time should be able to

Then use the iteration to deepen

But there are some questions:

(1) Where to start enumerating the denominator

The lowest value of the previous denominator +1 for the countdown of the remaining fractions

The second one is well understood, as for the first one:

Assuming that A/b is left in front of you, using [b/a] as the denominator, the new score may be a little larger than the original score.

So you can do the starting condition.

(2) End for (max depth-current depth + 1) * (b/a) rounding

Code:

1 /**2 *vijos.org &codevs.cn3 *problem#1308 problem#12884 *accepted Accepted5 *time:528ms 741ms6 *memort:564k 256k7  */8#include <iostream>9#include <cstdio>Ten#include <cstring> One #defineint long Long A #definell Long Long - #define_max (A, B) (a>b)? (a):(B) - using namespacestd; the /** - * Defining Fractional classes -  */ -typedefBOOLBoolean; +typedefclassmyclass{ -      Public: +         ints; A         intm; atMyClass (): s (0), M (0){} -MyClass (intSintm): s (s), M (m) {} - #undefInt -MyClassoperator-(MyClass another) { - MyClass result; -             intG=getcommon ( This-m,another.s); inresult.m= This->m*another.m/G; -result.s= This->s*another.m/g- This->m/g*Another.s; to             intg1=Getcommon (RESULT.M,RESULT.S); +Result.m/=G1; -Result.s/=G1; the             returnresult; *         } $ Boolean empty () {Panax Notoginseng             return(m==0); -         } theBooleanoperator<(MyClass another) { +             if(Another.empty ())return true; A             if( This->empty ())return false; the             if( This-&GT;S==ANOTHER.S)return  This->m>another.m; +             return( This->s*1.0/ This-&GT;M) < (another.s*1.0/another.m); -         } $Booleanoperator< (Doubleanother) { $             if( This->empty ())return false; -             return( This->s*1.0/ This-&GT;M) <another; -         } theInlineintGetrint () { - //if (s==0) return-1;Wuyi             return(int)( This->m/ This-s); the         } - Boolean isworkable () { Wu             if( This->empty ())return false; -             return(m%s==0);  About         } $         void operator<< (IStream &inch){ -             inch>>s>>m; -         } -     Private: A         intGetcommon (ll a,ll b) { +             if(b==0)returnA; the             returnGetcommon (b,a%b); -         } $ }myclass; the MyClass Maxx; the intresults[ the]; the intlist[ the]; the intFound =0; -  in /** the * Iterative Deepening the  */ About voidSearchintDepthlimit,intNow,myclass FS) { the     if(fs<0)return ; the     if(Now>depthlimit)return ; the     if(Fs.isworkable () && (fs.m>list[now-1]) && (found==0|| maxx<FS)) { +maxx=FS; -results[depthlimit]=fs.m/FS.S; thememcpy (Results,list,sizeof(int)*depthlimit);BayiFound=Depthlimit; the         return ; the     } -      for(intI=_max (Fs.getrint (), list[now-1]+1); I<= (depthlimit-now+1) *fs.getrint (); i++){ -list[now]=i; theSearch (depthlimit,now+1, Fs-myclass (1, i)); the     } the }  the intMain () { - MyClass Q; theq<<cin; the //cout<<q.getrint (); the     intI=1;94list[0]=1; the      while(found==0){ theSearch (I,1, q); thei++;98     } About      for(intI=1; i<=found;i++){ -printf"%d", Results[i]);101     }102}

Iterative Deepening

Egypt score (Vijos 1308)