hdu 5900 QSC and Master 区间dp

题目链接

首先维护一个前缀和。 然后如果gcd(key[l], key[r]) != 1， 如果l == r-1， 那么dp[l][r] = val[l]+val[r]。 如果不相邻， 那么如果dp[l+1][r-1] 和pre[r-1][l]相等， 说明中间的那一段拿完了， 这种情况也可以将l和r取到。 剩下的就是普通的区间dp。

#include <iostream>
#include <vector>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <complex>
#include <cmath>
#include <map>
#include <set>
#include <string>
#include <queue>
#include <stack>
#include <bitset>
using namespace std;
#define pb(x) push_back(x)
#define ll long long
#define mk(x, y) make_pair(x, y)
#define lson l, m, rt<<1
#define mem(a) memset(a, 0, sizeof(a))
#define rson m+1, r, rt<<1|1
#define mem1(a) memset(a, -1, sizeof(a))
#define mem2(a) memset(a, 0x3f, sizeof(a))
#define rep(i, n, a) for(int i = a; i<n; i++)
#define fi first
#define se second
typedef complex <double> cmx;
typedef pair<int, int> pll;
const double PI = acos(-1.0);
const double eps = 1e-8;
const int mod = 1e9+7;
const int inf = 1061109567;
const int dir[][2] = { {-1, 0}, {1, 0}, {0, -1}, {0, 1} };
const int maxn = 305;
int key[maxn], val[maxn];
ll pre[maxn], dp[maxn][maxn];
ll dfs(int l, int r)
{
    if(~dp[l][r])
        return dp[l][r];
    if(l >= r)
        return dp[l][r] = 0;
    if(l == r - 1) {
        if(__gcd(key[l], key[r]) != 1) {
            return dp[l][r] = val[l] + val[r];
        }
        return dp[l][r] = 0;
    }
    dp[l][r] = 0;
    for(int i = l; i < r; i++) {
        dp[l][r] = max(dp[l][r], dfs(l, i) + dfs(i+1, r));
    }
    if(__gcd(key[l], key[r]) != 1 && r - l > 2 && dp[l+1][r-1] == pre[r-1]-pre[l]) {
        dp[l][r] = max(dp[l][r], pre[r] - pre[l-1]);
    }
    return dp[l][r];
}
int main()
{
    int t, n;
    cin>>t;
    while(t--) {
        cin>>n;
        mem1(dp);
        for(int i = 1; i <= n; i++) {
            scanf("%d", &key[i]);
        }
        for(int i = 1; i <= n; i++) {
            scanf("%d", &val[i]);
            pre[i] = pre[i-1] + val[i];
        }
        cout << dfs(1, n) << endl;
    }
    return 0;
}