zoukankan      html  css  js  c++  java
  • POJ:3977-Subset(双向搜索)

    Subset

    Time Limit: 30000MS Memory Limit: 65536K
    Total Submissions: 5961 Accepted: 1129

    Description

    Given a list of N integers with absolute values no larger than 1015, find a non empty subset of these numbers which minimizes the absolute value of the sum of its elements. In case there are multiple subsets, choose the one with fewer elements.

    Input

    The input contains multiple data sets, the first line of each data set contains N <= 35, the number of elements, the next line contains N numbers no larger than 1015 in absolute value and separated by a single space. The input is terminated with N = 0

    Output

    For each data set in the input print two integers, the minimum absolute sum and the number of elements in the optimal subset.

    Sample Input

    1
    10
    3
    20 100 -100
    0

    Sample Output

    10 1
    0 2


    解题心得:

    1. 就是一个双向搜索,要求的是选择出来的元素的总和的绝对值最小,按照双向搜索的思路去做就可以了。但是要注意的一点是在二分搜索最相近的答案的时候可能从这个数的lower_bound产生的结果,或者lower_bound的位置-1产生绝对值最小的答案。

    #include <algorithm>
    #include <cstring>
    #include <map>
    #include <stdio.h>
    using namespace std;
    typedef long long ll;
    const ll maxn = 45;
    const ll MAX = 1e15;
    
    map <ll,ll> M;
    pair <ll,ll> ans;
    ll n,num[maxn];
    
    ll Abs(ll x) {
        if(x < 0)
            return -x ;
        return x;
    }
    
    void init() {
        M.clear();
        ans = make_pair(MAX,MAX);
        for(int i=0;i<n;i++) scanf("%lld",&num[i]);
    }
    
    void get_sum(ll mid) {
        ll cnt,sum;
        for(ll i=1;i<(1<<mid);i++) {
            cnt = sum = 0;
            for(ll j=0;j<mid;j++) {
                if(1&(i>>j)) {
                    sum += num[j];
                    cnt++;
                }
            }
            ans = min(ans,make_pair(Abs(sum),cnt));
            if(M[sum]) {
                M[sum] = min(M[sum],cnt);
            } else
                M[sum] = cnt;
        }
    }
    
    void solve(ll mid) {
        map<ll,ll> :: iterator iter;
        for(ll i=1;i<(1<<(n-mid));i++) {
            ll sum,cnt;
            sum = cnt = 0;
            for(int j=0;j<(n-mid);j++) {
                if(1&(i>>j)) {
                    sum += num[mid+j];
                    cnt++;
                }
            }
            ans = min(ans,make_pair(Abs(sum),cnt));
    
            iter = M.lower_bound(-sum);
            if(iter != M.end()) {
                ans = min(ans,make_pair(Abs(iter->first+sum),cnt+iter->second));
            }
            if(iter != M.begin()) {
                iter--;
                ans = min(ans,make_pair(Abs(iter->first+sum),iter->second+cnt));
            }
        }
        printf("%lld %lld
    ",ans.first,ans.second);
    }
    
    int main() {
        while(scanf("%lld",&n) && n) {
            init();
            ll mid = n>>1;
            get_sum(mid);
            solve(mid);
        }
        return 0;
    }
  • 相关阅读:
    【无中生有】---4----数据库设计-3
    【无中生有】---2---数据库设计-1
    redis3.0的demo实验
    redis3.0的demo实验
    那些在学习iOS开发前就应该知道的事(part 1)
    模板文件中的插件嵌入点列表
    图像处理框架 Core Image 介绍
    sharepoint services
    DiscuzX2.5数据库字典 值得学习
    Sublime Text 使用技巧
  • 原文地址:https://www.cnblogs.com/GoldenFingers/p/9107101.html
Copyright © 2011-2022 走看看