Pierre is recently obsessed with an online game. To encourage users to log in, this game will give users a continuous login reward. The mechanism of continuous login reward is as follows: If you have not logged in on a certain day, the reward of that day is 0, otherwise the reward is the previous day's plus 1.
On the other hand, Pierre is very fond of the number N. He wants to get exactly N points reward with the least possible interruption of continuous login.
Input
There are multiple test cases. The first line of input is an integer T indicates the number of test cases. For each test case:
There is one integer N (1 <= N <= 123456789).
Output
For each test case, output the days of continuous login, separated by a space.
This problem is special judged so any correct answer will be accepted.
Sample Input
4 20 19 6 9
Sample Output
4 4 3 4 2 3 2 3
Hint
20 = (1 + 2 + 3 + 4) + (1 + 2 + 3 + 4)
19 = (1 + 2 + 3) + (1 + 2 + 3 + 4) + (1 + 2)
6 = (1 + 2 + 3)
9 = (1 + 2) + (1 + 2 + 3)
Some problem has a simple, fast and correct solution.
1 #include<iostream> 2 #include<stdio.h> 3 #include<cstring> 4 #include<cstdlib> 5 #include<algorithm> 6 #include<queue> 7 8 int val[16001]; 9 bool hash[16002]; 10 struct node 11 { 12 int val; 13 int i; 14 struct node *next; 15 }f[16002]; 16 17 void Insert(int x,int i) 18 { 19 int k; 20 node *p; 21 k=x%16001; 22 p=&f[k]; 23 while(p!=NULL && p->val!=x) 24 { 25 p=p->next; 26 } 27 if(p==NULL) 28 { 29 p=(struct node*)malloc(sizeof(struct node)); 30 p->val=x; 31 p->i=i; 32 p->next=f[k].next; 33 f[k].next=p; 34 } 35 } 36 bool found(int x,int &i) 37 { 38 int k; 39 node *p; 40 k=x%16001; 41 p=&f[k]; 42 while(p!=NULL && p->val!=x) 43 { 44 p=p->next; 45 } 46 if(p==NULL) return false; 47 if(p->val==x) 48 { 49 i=p->i; 50 return true; 51 } 52 return false; 53 } 54 void prepare() 55 { 56 int i; 57 val[0]=0; 58 for(i=0;i<=16000;i++) 59 { 60 f[i].val=0; 61 f[i].i=0; 62 f[i].next=NULL; 63 } 64 for(i=1;i<=16000;i++) 65 { 66 val[i]=val[i-1]+i; 67 Insert(val[i],i); 68 } 69 } 70 void solve(int n) 71 { 72 int i,wz,k,j,s; 73 //one 74 if(found(n,wz)==true) 75 { 76 printf("%d ",wz); 77 return; 78 } 79 for(i=16000;;i--) 80 { 81 if(val[i]<n) 82 { 83 s=i; 84 break; 85 } 86 } 87 for(i=1;i<=s;i++) 88 { 89 k=n-val[i]; 90 if(found(k,wz)==true) 91 { 92 printf("%d %d ",i,wz); 93 return; 94 } 95 } 96 for(i=1;i<=s;i++) 97 { 98 for(j=s;j>=1;j--) 99 { 100 k=n-val[i]-val[j]; 101 if(k<0)continue; 102 if(found(k,wz)==true) 103 { 104 printf("%d %d %d ",i,j,wz); 105 return; 106 } 107 } 108 } 109 } 110 int main() 111 { 112 int T,n; 113 prepare(); 114 scanf("%d",&T); 115 while(T--) 116 { 117 scanf("%d",&n); 118 solve(n); 119 } 120 return 0; 121 }