spoj-SUBSUMS - Subset Sums

SUBSUMS - Subset Sums

Given a sequence of N (1 ≤ N ≤ 34) numbers S1, ..., SN (-20,000,000 ≤ Si ≤ 20,000,000), determine how many subsets of S (including the empty one) have a sum between A and B (-500,000,000 ≤ A ≤ B ≤ 500,000,000), inclusive.

Input

The first line of standard input contains the three integers N, A, and B. The following N lines contain S1 through SN, in order.

Output

Print a single integer to standard output representing the number of subsets satisfying the above property. Note that the answer may overflow a 32-bit integer.

Example

Input:

3 -1 2

1

-2

3

Output:

5

The following 5 subsets have a sum between -1 and 2:

0 = 0 (the empty subset)

1 = 1

1 + (-2) = -1

-2 + 3 = 1

1 + (-2) + 3 = 2

Submit solution!

思路：折半枚举+二分；

复杂度O（\(2^ \frac{n}{2}*log(2^ \frac{n}{2})\)）

#include<stdio.h>
#include<algorithm>
#include<iostream>
#include<queue>
#include<string.h>
#include<map>
typedef long long LL;
using namespace std;
int ans[50];
int aa[20],bb[20];
int a1[200000],a2[200000];
int low(int l,int r,int ask);
int high(int l,int r,int ask);
int main(void)
{
    int n,a,b;
    scanf("%d %d %d",&n,&a,&b);
    for(int i = 1; i <= n; i++)
    {
        scanf("%d",&ans[i]);
    }
    int cn = 0;
    for(int i = 1; i <= (n/2); i++)
    {
        aa[cn++] = ans[i];
    }
    cn  = 0;
    for(int i = n/2+1; i <= n; i++)
    {
        bb[cn++] = ans[i];
    }
    int x1 = n/2,x2 = n-x1;
    int cx1 = 0;
    for(int i = 0; i < (1<<x1); i++)
    {
        int sum = 0;
        for(int j = 0; j < x1; j++)
        {
            if(i&(1<<j))
                sum+= aa[j];
        }
        a1[cx1++] = sum;
    }
    int cx2 = 0;
    for(int i = 0; i < (1<<x2); i++)
    {
        int sum = 0;
        for(int j = 0; j < x2; j++)
        {
            if(i&(1<<j))
                sum += bb[j];
        }
        a2[cx2++] = sum;
    }
    sort(a1,a1+cx1);
    sort(a2,a2+cx2);
    LL acc = 0;
    for(int i = 0; i < cx1; i++)
    {
        int asl = a-a1[i];
        int asr = b-a1[i];
        int ll = low(0,cx2-1,asl);
        int rr = high(0,cx2-1,asr);
        if(rr >= ll&&ll!=-1&&rr!=-1)
        {
            acc += (LL)(rr-ll+1);
        }
    }
    printf("%lld\n",acc);
    return 0;
}
int low(int l,int r,int ask)
{
    int id = -1;
    while(l <= r)
    {
        int mid = (l+r)/2;
        if(a2[mid] >= ask)
        {
            id = mid;
            r = mid-1;
        }
        else l = mid+1;
    }
    return id;
}
int high(int l,int r,int ask)
{
    int id = -1;
    while(l <= r)
    {
        int mid = (l+r)/2;
        if(a2[mid] <= ask)
        {
            id = mid;
            l = mid+1;
        }
        else r = mid-1;
    }
    return id;
}