luoguP2329 [SCOI2005]栅栏

Posted 2020-12-01 lylyl

首先我们可以看出一个性质:取小的一定不比取大的劣.显然嘛

于是我们将约翰所需的木板从小到大排序,原材料也按从小到大排序,然后二分一个(mid)表示约翰取几个木板,用搜索(check)一下即可.

几个剪枝:

• 一.我们可以定义一个全局变量(Waste)表示割下木板后总共浪费的原材料长度.

  ( herefore) 如果(Waste+sum_{i=1}^{mid}b_i>sum),直接退出,返回(0).

• 二.对于两个长度相等的所需木板,我们可以记一个(last)表示之前的所需木板找到了第(last)个,( herefore)直接从(last)开始找即可.

• 三.我们在二分前可以先将总和大于(sum)的删去,即(while (s[r] > sum)--r;)

#include<bits/stdc++.h>
#define il inline
#define rg register
#define gi read<int>
using namespace std;
template<class TT>
il TT read() {
    TT o = 0,fl = 1; char ch = getchar();
    while (!isdigit(ch) && ch != '-') ch = getchar();
    if (ch == '-') fl = -1, ch = getchar();
    while (isdigit(ch)) o = o * 10 + ch - '0', ch = getchar();
    return fl * o;
}
int n, m, sum, l, r, mid, t, ans, a[55], b[1005], c[55], s[1005];
bool check(int x, int last) {
    if (!x) return true;
    if (sum < t + s[mid]) return false;
    for (int i = last; i <= m; ++i) {
        if (c[i] >= b[x]) {
            c[i] -= b[x];
            if (c[i] < b[1]) t += c[i];
            if (b[x] == b[x - 1]) {
                if (check(x - 1, last)) return true;
            }
            else if (check(x - 1, 1)) return true;
            if (c[i] < b[1]) t -= c[i];
            c[i] += b[x];
        }
    }
    return false;
}
int main() {
    m = gi();
    for (int i = 1; i <= m; ++i)
        a[i] = gi(), sum += a[i];
    sort(a + 1, a + m + 1);
    n = gi();
    for (int i = 1; i <= n; ++i) b[i] = gi();
    sort(b + 1, b + n + 1);
    for (int i = 1; i <= n; ++i) s[i] = s[i - 1] + b[i];
    l = 1, r = n;
    while (s[r] > sum) --r;
    while (l <= r) {
        for (int i = 1; i <= m; ++i) c[i] = a[i];
        mid = l + r >> 1, t = 0;
        if (check(mid, 1)) ans = mid, l = mid + 1;
        else r = mid - 1;
    }
    printf("%d
", ans);
    return 0;
}