一道挺有意思的题目,思路推荐上面的博客。
要在数组中找到一些数字,使得它们的和在范围 $[\frac{w}{2}, w]$ 内。首先把 $a_i > w$ 的数字去掉;如果某个数字就在给定的范围内,那么它就是一个解。接下来只需要考虑所有 $a_i < \frac{w}{2}$ 的数字,可以先排序,从小到大考虑累加,如果前缀和能到 $[\frac{w}{2}, w]$ 范围内,那么这个前缀就是一个解。
为什么这么做是对的呢?假设 $a_i + a_{i + 1} \lt \frac{w}{2}$,同时 $a_i + a_{i + 1} + a_{i + 2} > w$,可以得到 $a_{i + 2} > \frac{w}{2}$,这和 $a_{i+2} < \frac{w}{2}$ 矛盾。
// Date: Mon Dec 11 21:10:36 2023
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
using namespace std;
const int INF = 0x3f3f3f3f, MOD = 1e9 + 7;
const double eps = 1e-8;
const int dir[8][2] = {
{0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1},
};
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> VI;
typedef pair<int, int> PII;
const ull Pr = 131;
#define For(i, a, b) for (int i = int(a); i < int(b); ++i)
#define Rof(i, a, b) for (int i = int(b) - 1; i >= int(a); --i)
#define For1(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define Rof1(i, a, b) for (int i = int(b); i >= int(a); --i)
#define ForE(i, j) for (int i = h[j]; i != -1; i = ne[i])
#define f1 first
#define f2 second
#define pb push_back
#define has(a, x) (a.find(x) != a.end())
#define nonempty(a) (!a.empty())
#define all(a) (a).begin(), (a).end()
#define SZ(a) int((a).size())
#ifdef _DEBUG
#define debug1(x) cout << #x " = " << x << endl;
#define debug2(x, y) cout << #x " = " << x << " " #y " = " << y << endl;
#define debug3(x, y, z) \
cout << #x " = " << x << " " #y " = " << y << " " #z " = " << z << endl;
#else
#define debug1
#define debug2
#define debug3
#endif
const int N = 200010;
int t, n;
pair<ll, int> a[N], b[N];
ll w;
int main(void) {
#ifdef _DEBUG
freopen("1446a.in", "r", stdin);
#endif
std::ios::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
cin >> t;
while (t--) {
cin >> n >> w;
For1(i, 1, n) {
cin >> a[i].f1;
a[i].f2 = i;
}
int len = 0;
sort(a + 1, a + n + 1);
ll top = (w + 1) / 2;
VI res;
For1(i, 1, n) {
if (a[i].f1 > w)
continue;
if (a[i].f1 <= w && a[i].f1 >= top) {
res.pb(a[i].f2);
break;
}
b[++len] = a[i];
}
if (nonempty(res)) {
cout << SZ(res) << '\n';
for (auto x : res) {
cout << x << ' ';
}
cout << '\n';
continue;
}
bool flag = false;
ll sum = 0, right = -1;
For1(i, 1, len) {
sum += b[i].f1;
if (sum <= w && sum >= top) {
flag = true;
right = i;
break;
}
}
if (!flag)
cout << "-1\n";
else {
cout << right << '\n';
using PLI = pair<ll, int>;
sort(b + 1, b + right + 1,
[&](const PLI &x, const PLI &y) { return x.f2 < y.f2; });
For1(i, 1, right) { cout << b[i].f2 << ' '; }
cout << '\n';
}
}
return 0;
}