Jon fought bravely to rescue the wildlings who were attacked by the white-walkers at Hardhome. On his arrival, Sam tells him that he wants to go to Oldtown to train at the Citadel to become a maester, so he can return and take the deceased Aemon's place as maester of Castle Black. Jon agrees to Sam's proposal and Sam sets off his journey to the Citadel. However becoming a trainee at the Citadel is not a cakewalk and hence the maesters at the Citadel gave Sam a problem to test his eligibility.
Initially Sam has a list with a single element n. Then he has to perform certain operations on this list. In each operation Sam must remove any element x, such that x > 1, from the list and insert at the same position , , sequentially. He must continue with these operations until all the elements in the list are either 0 or 1.
Now the masters want the total number of 1s in the range l to r (1-indexed). Sam wants to become a maester but unfortunately he cannot solve this problem. Can you help Sam to pass the eligibility test?
The first line contains three integers n, l, r (0 ≤ n < 250, 0 ≤ r - l ≤ 105, r ≥ 1, l ≥ 1) – initial element and the range lto r.
It is guaranteed that r is not greater than the length of the final list.
Output the total number of 1s in the range l to r in the final sequence.
7 2 5
4
10 3 10
5
Consider first example:
Elements on positions from 2-nd to 5-th in list is [1, 1, 1, 1]. The number of ones is 4.
For the second example:
Elements on positions from 3-rd to 10-th in list is [1, 1, 1, 0, 1, 0, 1, 0]. The number of ones is 5.
题意:将一个数列中大于1的数x,经过一个操作,在其位置上用 , , 代替x,直至将整个数列化作01序列。
也是悲剧,比赛时把n的规模看成了10^50,卡了好久。。。
直接用dfs会超时,因为n的规模是2^50。看题解,用了类似线段树的区间查询,二分区间查询。
#include<iostream> #include<cstdio> #include<cstring> using namespace std; #define LL long long LL getLen(LL num) { if(num==0) return 0; if(num==1) return 1; return getLen(num/2)*2+1; } int query(LL nu,LL L,LL R,LL l,LL r) { if(R<l||L>r||nu==0) return 0; if(nu==1) return 1; LL mid=l+getLen(nu/2); return query(nu/2,L,R,l,mid-1)+query(nu%2,L,R,mid,mid)+query(nu/2,L,R,mid+1,r); } int main() { //cout<<getLen(7)<<endl; LL n,l,r; scanf("%I64d%I64d%I64d",&n,&l,&r); LL len=getLen(n); //cout<<len<<endl; int res=query(n,l,r,1,len); printf("%d ",res); return 0; }