题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=3450
Counting Sequences
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/65536 K (Java/Others)
Total Submission(s): 1815 Accepted Submission(s): 618
Problem Description
For a set of sequences of integers{a1,a2,a3,...an}, we define a sequence{ai1,ai2,ai3...aik}in which 1<=i1<i2<i3<...<ik<=n, as the sub-sequence of {a1,a2,a3,...an}. It is quite obvious that a sequence with the length n has 2^n sub-sequences.
And for a sub-sequence{ai1,ai2,ai3...aik},if it matches the following qualities: k >= 2, and the neighboring 2 elements have the difference not larger than d, it will be defined as a Perfect Sub-sequence. Now given an integer sequence, calculate the number
of its perfect sub-sequence.
Input
Multiple test cases The first line will contain 2 integers n, d(2<=n<=100000,1<=d=<=10000000) The second line n integers, representing the suquence
Output
The number of Perfect Sub-sequences mod 9901
Sample Input
4 2 1 3 7 5
Sample Output
4
Source
2010 ACM-ICPC Multi-University Training Contest(2)——Host
by BUPT
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题意:一个集合有n个数,然后要你找出所有的完美子序列对9901取模~
思路:很容易想到dp,我们可以用dp[i]表示以第i个数为结尾的完美子序列的个数,那么sum(总的完美子序列的个数)=dp[2]+dp[3]+dp[4]+.....dp[n];
然后接着想满足完美子序列的条件是什么? |x-a[i]|<=d 那么就有 a[i]-d <=x <=a[i]+d;
然后用树状数组动态维护即可~~~
#include <iostream> #include <stdio.h> #include <string> #include <string.h> #include <cstdio> #include <algorithm> #include <cmath> const int N=1e5+100; const int mod=9901; using namespace std; struct node { int v,id; }a[N]; bool cmp(node a,node b) { return a.v<b.v; } int n,d,c[N],b[N]; int lowbit(int x) { return x&(-x); } void update(int x,int d) { while(x<=n) { c[x]+=d; if(c[x]>mod)c[x]%=mod; x+=lowbit(x); } } int getsum(int x) { int ans=0; while(x>0) { ans+=c[x]; if(ans>mod)ans%=mod; x-=lowbit(x); } return ans; } int find(int x) { if(x>=a[n].v)return n; if(x<a[1].v)return 0; int l=1,r=n,ret=0; while(l<=r) { int mid=(l+r)/2; if(x>=a[mid].v) { ret=mid; l=mid+1; } else r=mid-1; } return ret; } int main() { while(scanf("%d%d",&n,&d)!=EOF) { memset(c,0,sizeof(c)); memset(b,0,sizeof(b)); for(int i=1;i<=n;i++) { scanf("%d",&a[i].v); a[i].id=i; } sort(a+1,a+1+n,cmp); for(int i=1;i<=n;i++)b[a[i].id]=i; int sum=0; for(int i=1;i<=n;i++) { int p=find(a[b[i]].v+d); int q=find(a[b[i]].v-d-1); int temp=getsum(p)-getsum(q); temp=(temp+mod)%mod; sum=(sum+temp)%mod; update(b[i],temp+1); } printf("%d\n",sum); } return 0; }