Hdu 5312 Sequence (mathematical deduction + linear probing (two-digit addition))

problem Description

Today, Soda have learned a sequence whose n-th (n≥1 is 3n (n−1) +1ifas the sum of some items of that sequence. If possible, what is the minimum items needed?  1+1+1=7+7+7 +1.

Input

There is multiple test cases. The first line of input contains an integer T (1≤t≤104case: there's a Lin E containing an integer m (1≤m≤109).

Output

case, output−1if as the sum of some items of that sequence, otherwise output t He minimum items needed.

Sample Input

Ten 1 2 3 4 5 6 7 8  A Ten

Sample Output

1 2 3 4 5 6 1 2 4 4

Source Bestcoder 1st Anniversary ($)

For this kind of question, first of all, we should study the formula given, and start from here is the right path.

Analysis Formula3N(N−1)+1, if you give a number n, suppose you want K3N(N−1)+1 add up to get N, i.e. 3n (n-1) k+k=n, noting < Span id= "mathjax-span-16" class= "Mi" > < Span id= "mathjax-span-21" class= "mn" >3n (n-1) k is a multiple of 6, then the smallest k satisfying (n-k)%6==0 is asked. There is also to notice that 1, 2 to be special, that is, K to enumerate from 3

1#include <iostream>2#include <cstdio>3#include <cstring>4#include <algorithm>5#include <queue>6#include <cmath>7#include <stdlib.h>8#include <map>9 using namespacestd;Ten #defineN 20000 One intNum[n]; A intN; - voidinit () { -      for(intI=1; i<n;i++){ thenum[i]=3*i* (I-1)+1; -     } - } - BOOLCheck1 () { +      for(intI=1; i<n;i++){ -         if(num[i]==N) +           return true; A     } at     return false; - } - BOOLCheck2 () { -     inti=m-1; -      for(intI=1; i<n;i++){ -          while(Num[i]+num[j]>n && j>0) j--; in         if(Num[i]+num[j]==n && j>0){ -             return true; to         } +     } -     return false; the } * intMain () $ {Panax Notoginseng init (); -     intT; thescanf"%d",&t); +      while(t--){ A          thescanf"%d",&n); +         if(Check1 ()) { -printf"1\n"); $         } $         Else if(Check2 ()) { -printf"2\n"); -         } the         Else{ -              for(intI=3;i<Ten; i++){Wuyi                 if((n-i)%6==0){ theprintf"%d\n", i); -                      Break; Wu                 } -             } About         } $     } -     return 0; -}

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Hdu 5312 Sequence (mathematical deduction + linear probing (two-digit addition))