【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 = 1; x = 0;
        char c = getchar();
        for (; !isdigit(c); c = getchar()) { if (c == '-') f = -f; }
        for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
        x *= f;
}
template <typename T> inline void write(T x) {
    if (x < 0) { putchar('-'); x = -x; }
    if (x > 9) write(x/10);
    putchar(x%10+'0');
}
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]-1);
                dfs(root[l][r]+1,r);    
        }
}

int main() {
        
        read(n);
        for (i = 0; i <= n; i++) {
                for (j = 0; j <= n; j++) {
                        f[i][j] = 1;
                }
        }
        for (i = 1; i <= n; i++) {
                read(d[i]);
                f[i][i] = d[i];
                root[i][i] = i;        
        }
        
        for (k = 2; k <= n; k++) {
                for (l = 1; l <= n - k + 1; l++) {
                        r = l + k - 1;
                        for (mid = l; mid <= r; mid++) {
                                if (f[l][mid-1] * f[mid+1][r] + d[mid] > f[l][r]) {
                                        f[l][r] = f[l][mid-1] * f[mid+1][r] + d[mid];
                                        root[l][r] = mid;
                                }
                        }
                }    
        }
        writeln(f[1][n]);
        write(root[1][n]);
        dfs(1,root[1][n]-1);
        dfs(root[1][n]+1,n);
        
        return 0;
    
}