基于自底向上的动态规划
1 #include <iostream>
2 #include <cstdio>
3 #include <algorithm>
4 #include <vector>
5 #include <cstring>
6 #include <string>
7
8 #define MAX 1000
9 using namespace std;
10
11
12 int a[MAX] = {0}, dp[MAX][MAX] = {0},path[MAX][MAX] = {0}, n;
13
14 void matrix_chain_order(){
15 for(int r = 2; r <= n; r ++ ){
16 for(int i = 1; i <= n-r; i ++){
17 int j = i+r-1;
18 dp[i][j] =dp[i][i]+dp[i+1][j]+a[i]*a[i+1]*a[j+1];
19 path[i][j] = i;
20 for(int k=i+1; k < j; k ++){
21 if( dp[i][j] > dp[i][k] + dp[k+1][j] + a[i]*a[k+1]*a[j+1] ){
22 dp[i][j] = dp[i][k] + dp[k+1][j] + a[i]*a[k+1]*a[j+1];
23 path[i][j] = k;
24 }
25 }
26 }
27 }
28 }
29
30 void print_optimal_parens(int i, int j){
31 if( i == j ) {cout<<'A'<<i;return;}
32 else{
33 cout<<"(";
34 print_optimal_parens(i,path[i][j]);
35 print_optimal_parens(path[i][j]+1,j);
36 cout<<")";
37 }
38 }
39
40
41 int main(){
42 int T;
43 cin >> T;
44 while(T--){
45 cin >> n ;
46 memset(a,0,sizeof(a));
47 for(int i = 1; i <= n; i ++ ) cin >>a[i];
48 memset(dp,0,sizeof(dp));
49 memset(path,0,sizeof(path));
50 matrix_chain_order();
51
52 cout<<"(";
53 print_optimal_parens(1,n-1);
54 cout<<")"<<endl;
55 }
56 return 0;
57 }
基于备忘录的自顶向下的动态规划
1 #include <iostream>
2 #include <cstdio>
3 #include <algorithm>
4 #include <vector>
5 #include <cstring>
6 #include <string>
7
8 #define MAX 1000
9 #define INF 1000000
10 using namespace std;
11
12
13 int a[MAX] = {0}, dp[MAX][MAX] = {0},path[MAX][MAX] = {0}, n;
14
15 int lookup_chain(int i,int j){
16 if(dp[i][j] < INF) return dp[i][j];
17 if(i == j ) return 0;
18 int u = lookup_chain(i,i)+lookup_chain(i+1,j) + a[i]*a[i+1]*a[j+1];
19 path[i][j] = i;
20 for(int k = i+1; k < j; k ++ ){
21 int t = lookup_chain(i,k)+lookup_chain(k+1,j)+a[i]*a[k+1]*a[j+1];
22 if(t < u){
23 u = t;
24 path[i][j] = k;
25 }
26 }
27 dp[i][j] = u;
28 return u;
29 }
30
31 void print_optimal_parens(int i, int j){
32 if( i == j ) {cout<<'A'<<i;return;}
33 else{
34 cout<<"(";
35 print_optimal_parens(i,path[i][j]);
36 print_optimal_parens(path[i][j]+1,j);
37 cout<<")";
38 }
39 }
40
41
42 int main(){
43 int T;
44 cin >> T;
45 while(T--){
46 cin >> n ;
47 memset(a,0,sizeof(a));
48 for(int i = 1; i <= n; i ++ ) cin >>a[i];
49 memset(dp,INF,sizeof(dp));
50 memset(path,0,sizeof(path));
51 lookup_chain(1,n);
52
53 cout<<"(";
54 print_optimal_parens(1,n-1);
55 cout<<")"<<endl;
56 }
57 return 0;
58 }
