洛谷1040 加分二叉树

题目：加分二叉树

思路：DP。f[i][j]为中序遍历为a[1][j]的二叉树的最大分值。枚举根节点k，转移方程：f[i][j]=f[i][k-1]*f[k+1][j]+a[k]

代码：

#include <cstdio>#include <iostream>#include <algorithm>#include <stack>#include <queue>#include <deque>#include <set>#include <cstring>#include <map>using namespace std;#define ll long longint n;int a[50]= {0};ll f[50][50]= {0};int root[50][50]= {0};void dfs(int l,int r) {if(l>r) return ;int k=root[l][r];printf("%d ",k);dfs(l,k-1),dfs(k+1,r);}int main() {scanf("%d",&n);for(int i=1; i<=n; i++) {scanf("%d",&a[i]);}for(int i=1; i<=n; i++) {f[i][i]=a[i],f[i][i-1]=1;root[i][i]=i;}for(int i=n; i>=1; i--) {for(int j=i+1; j<=n; j++) {for(int k=i; k<=j; k++) {if(f[i][j]<f[i][k-1]*f[k+1][j]+a[k]) {f[i][j]=f[i][k-1]*f[k+1][j]+a[k];root[i][j]=k;}}}}printf("%d\n",f[1][n]);dfs(1,n);return 0;}