【NOIP 2003】 加分二叉树

【题目链接】

点击打开链接

【算法】

树形DP即可

【代码】

#include<bits/stdc++.h>
using namespace std;
#define MAXN 50

int i,j,k,n,l,r,mid;
int d[MAXN],f[MAXN][MAXN],root[MAXN][MAXN];

template <typename T> inline void read(T &x) {
        int f = ; x = ;
        char c = getchar();
        for (; !isdigit(c); c = getchar()) { if (c == '-') f = -f; }
        for (; isdigit(c); c = getchar()) x = (x << ) + (x << ) + c - '';
        x *= f;
}
template <typename T> inline void write(T x) {
    if (x < ) { putchar('-'); x = -x; }
    if (x > ) write(x/);
    putchar(x%+'');
}
template <typename T> inline void writeln(T x) {
    write(x);
    puts("");
}
inline void dfs(int l,int r) {
        if (l <= r) {
                putchar(' ');
                write(root[l][r]);
                dfs(l,root[l][r]-);
                dfs(root[l][r]+,r);
        }
}

int main() {

        read(n);
        for (i = ; i <= n; i++) {
                for (j = ; j <= n; j++) {
                        f[i][j] = ;
                }
        }
        for (i = ; i <= n; i++) {
                read(d[i]);
                f[i][i] = d[i];
                root[i][i] = i;
        }

        for (k = ; k <= n; k++) {
                for (l = ; l <= n - k + ; l++) {
                        r = l + k - ;
                        for (mid = l; mid <= r; mid++) {
                                if (f[l][mid-] * f[mid+][r] + d[mid] > f[l][r]) {
                                        f[l][r] = f[l][mid-] * f[mid+][r] + d[mid];
                                        root[l][r] = mid;
                                }
                        }
                }
        }
        writeln(f[][n]);
        write(root[][n]);
        dfs(,root[][n]-);
        dfs(root[][n]+,n);

        return ;

}