1268 和为K的组合 Meet in mid二分思路

http://www.51nod.com/onlineJudge/questionCode.html#!problemId=1268&judgeId=193772

给出n = 20个数，问其是否有和为k的情况

分两段，用O(2^(n / 2))复杂度维护出每一段的所有情况。

然后枚举第一段，二分判断第二段是否也有k - first

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <assert.h>
#define IOS ios::sync_with_stdio(false)
using namespace std;
#define inf (0x3f3f3f3f)
typedef long long int LL;


#include <iostream>
#include <sstream>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <string>
#include <bitset>
map<int, bool>dp1;
set<int>dp2;
void work() {
    int n, k;
    scanf("%d%d", &n, &k);
    dp1[0] = true;
    dp2.insert(0);
    for (int i = 1; i <= n / 2; ++i) {
        int x;
        scanf("%d", &x);
        map<int, bool> :: iterator it = dp1.end();
        it--;
        while (true) {
            dp1[it->first + x] = true;
            if (it == dp1.begin()) break;
            it--;
        }
    }
    for (int i = n / 2 + 1; i <= n; ++i) {
        int x;
        scanf("%d", &x);
        set<int> :: iterator it = dp2.end();
        it--;
        while (true) {
            dp2.insert(*it + x);
            if (it == dp2.begin()) break;
            it--;
        }
    }
    for (map<int, bool> :: iterator it = dp1.begin(); it != dp1.end(); ++it) {
        if (dp2.count(k - it->first)) {
            cout << "Yes" << endl;
            return;
        }
    }
    cout << "No" << endl;
    return;
}

int main() {
#ifdef local
    freopen("data.txt", "r", stdin);
//    freopen("data.txt", "w", stdout);
#endif
    work();
    return 0;
}