USACO 3.4.4 rockers & 4.1.1 nuggets 解题报告

rockers是USACO一道很经典的动态规划，这个题其实是可以优化状态的。将状态表示中的一部分记录到状态的最优解中，从而实现将空间和空间都降一维的目的。

nuggets这个题判别几个特殊情况后就是个裸的背包了。

这两题都不难，均为1A。

rockers:

/*
TASK:rockers
LANG:C++
*/
#include <iostream>
#include <fstream>
#include <climits>
using namespace std;

int a[21];
int f[21][21][21];
int n, t, m;

void init()
{
    scanf("%d%d%d", &n, &t, &m);
    for (int i = 1; i <= n; i++)
        scanf("%d", &a[i]);
}

void solve()
{
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++)
            for (int k = 0; k <= t; k++)
                if (k < a[i])
                    f[i][j][k] = max(f[i - 1][j][k], f[i][j - 1][t]);
                else
                    f[i][j][k] = max(f[i - 1][j][k - a[i]], f[i - 1][j - 1][t]) + 1;
}

void print()
{
    printf("%d\n", f[n][m][t]);
}

int main()
{
    freopen("rockers.in", "r", stdin);
    freopen("rockers.out", "w", stdout);

    init();
    solve();
    print();

    return 0;
}

nuggets:

/*
TASK:nuggets
LANG:C++
*/
#include <iostream>
#include <fstream>
#include <algorithm>
using namespace std;

int a[11];
bool f[100000];
int n, m;
bool flag;

int gcd(int x, int y)
{
    if (0 == y) return x;
    return gcd(y, x % y);
}

void init()
{
    scanf("%d", &n);
    for (int i = 0; i < n; i++)
    {
        scanf("%d", &a[i]);
        if (1 == a[i])
        {
            flag = 1; return;
        }
    }
    if (n == 1) {flag = 1; return;}
    sort(a, a + n);
}

void solve()
{
    if (flag) return;
    int tmp = a[0];
    for (int i = 1; i < n; i++)
        tmp = gcd(tmp, a[i]);
    if (tmp != 1) {flag = 1; return;}
    m = a[n - 1] * a[n - 2] / gcd(a[n - 1], a[n - 2]);

    f[0] = 1;
    for (int i = 0; i < n; i++)
        for (int j = a[i]; j <= m; j++)
            if (f[j - a[i]]) f[j] = 1;
}

void print()
{
    if (flag) printf("0\n");
    for (int i = m; i > 0; i--)
        if (!f[i])
        {
            printf("%d\n", i);
            break;
        }
}

int main()
{
    freopen("nuggets.in", "r", stdin);
    freopen("nuggets.out", "w", stdout);

    init();
    solve();
    print();

    return 0;
}