HDU 3516 Tree Construction
Long time no more a blog
CSP 2019 cool. .
The title looks like interval dp, can write
$ dp[i][j] = max{dp[i][k]+dp[k+1][r]+x_{k+1}-x_i+y_k-y_r} $
Is considered $ [i, j] $ this interval, wherein from $ [l, k], [k + 1, r] $ Both sections are well tree structure, the tree structure and probably
Play table found it to meet the quadrangle inequality.
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cstdio>
using namespace std;
#define MAXN 1016
int n;
int x[MAXN] , y[MAXN];
int dp[MAXN][MAXN] , mn[MAXN][MAXN];
int main() {
while( cin >> n ) {
for( int i = 1 ; i <= n ; ++ i ) scanf("%d%d",&x[i],&y[i]);
memset( dp , 0x3f , sizeof dp );
for( int i = 1 ; i <= n ; ++ i ) dp[i][i] = 0 , mn[i][i] = i;
for( int len = 2 ; len <= n ; ++ len ) {
for( int i = 1 ; i + len - 1 <= n ; ++ i ) {
int j = i + len - 1;
for( int k = mn[i][j - 1] ; k <= mn[i + 1][j] ; ++ k ) {
int t = dp[i][k] + dp[k + 1][j] + x[k+1] - x[i] + y[k] - y[j];
if( t < dp[i][j] )
mn[i][j] = k , dp[i][j] = t;
}
}
}
cout << dp[1][n] << endl;
}
}