【DP】uva1354

#include<iostream>
#include<algorithm>
#include<string>
#include<sstream>
#include<set>
#include<vector>
#include<stack>
#include<map>
#include<queue>
#include<cassert>
#include<cstdlib>
#include<cstdio>
#include<ctime>
#include<cmath>
#include<cstring>
#include<functional>
using namespace std;
#define INF 0x3f3f3f3f
#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))
using namespace std;
const int N = 6;
const int MAXN = (1 << N);
int t, n, i, j, vis[MAXN];
double w
, sumw[MAXN], r;
struct Node {
double l, r;
Node() {}
Node(double ll, double rr) { l = ll; r = rr; }
};
vector<Node> node[MAXN];

int bitcount(int x) {
if (x == 0) return 0;
return bitcount(x / 2) + (x & 1);
}

void dfs(int s) {
if (vis[s]) return;
vis[s] = 1;
if (bitcount(s) == 1) {
node[s].push_back(Node(0, 0));
return;
}
for (int l = (s - 1)&s; l > 0; l = (l - 1)&s) {
int r = s^l;
dfs(l); dfs(r);
for (int i = 0; i < node[l].size(); i++) {
for (int j = 0; j < node[r].size(); j++) {
double ll = min(-sumw[r] / (sumw[l] + sumw[r]) + node[l][i].l, sumw[l] / (sumw[l] + sumw[r]) + node[r][j].l);
double rr = max(sumw[l] / (sumw[l] + sumw[r]) + node[r][j].r, -sumw[r] / (sumw[l] + sumw[r]) + node[l][i].r);
node[s].push_back(Node(ll, rr));
}
}
}
}

void solve() {
double ans = -1;
int s = (1 << n) - 1;
dfs(s);
for (int i = 0; i < node[s].size(); i++) {
if (node[s][i].r - node[s][i].l < r) {
if (node[s][i].r - node[s][i].l > ans)
ans = node[s][i].r - node[s][i].l;
}
}
if (ans == -1) printf("-1\n");
else printf("%.10lf\n", ans);
}

int main() {
scanf("%d", &t);
while (t--) {
memset(vis, 0, sizeof(vis));
memset(node, 0, sizeof(node));
scanf("%lf%d", &r, &n);
for (i = 0; i < n; i++)
scanf("%lf", &w[i]);
for (i = 0; i < (1 << n); i++) {
sumw[i] = 0;
for (j = 0; j < n; j++) {
if (i&(1 << j))
sumw[i] += w[j];
}
}
solve();
}
return 0;
}