P3052 [USACO12MAR]Cows in a Skyscraper G

P3052 [USACO12MAR]Cows in a Skyscraper G

题意：给出n个物品，体积为w[i]，现把其分成若干组，要求每组总体积 ≤ W，问最小分组。(\(n ≤ 18\)​)

解题思路：数位DP，记录每一头牛放到哪一个电梯中，l数组表示剩余的体积，\(f[i]\)表示当状态下的最有放置，那么答案就是\(f[(1 << n) - 1]\)

解题代码：

#include <bits/stdc++.h>
#define pii pair<int,int>
#define endl '\n'
using namespace std;
#define int long long
const int maxn = 1e6 + 5;
const int MOD = 1e9 + 7;
int f[maxn];
int l[maxn];
int c[maxn];
signed main() {
	int n,w;
	cin >> n >> w;
	for(int i = 0;i<n;i++)cin >> c[i];
	int ri = (1 << n);
	memset(f,0x7f,sizeof f);
	f[0] = 1;
	l[0] = w;
	for(int i = 0;i < ri;i++){
		for(int j = 0;j < n;j++){
			if(i & (1 << j))continue;
			if(l[i] >= c[j]){
				if(f[i] <= f[i|(1 << j)]){
					f[i|(1 << j)] = f[i];
					l[i|(1 << j)] = max(l[i|(1 << j)],l[i] - c[j]);
				}
			}else{
				if(f[i] + 1 <= f[i|(1 << j)]){
					 f[i|(1 << j)] = f[i] + 1;
					 l[i|(1 << j)] = max(l[i|(1 << j)],w - c[j]);
				}
			}
		}
	}
	cout << f[ri - 1] << endl;
	system("pause");
	return 0;
}