根据这个我们有如下递推关系：
int bracket(int i,int j){
if (i>j) return 0;
else if (i==j) return 1;
int answer = inf;
if ((s[i]=='('&&s[j]==')')||(s[i]=='['&&s[j]==']')) answer = min(answer,bracket(i+1,j-1));
else if (s[i]=='(' || s[i]=='[') answer = min(answer,bracket(i+1,j)+1);
else if (s[j]==')' || s[j]==']') answer = min(answer,bracket(i,j-1)+1);
for (int k=i;k<j;k++) answer = min(answer,bracket(i,k)+bracket(k+1,j));
return answer;
}
#include <iostream>
#include <string.h>
using namespace std;
#define MAX 0xffffff
int main(){
int dp[105][105];
char s[105];
while (cin>>s){
int n=strlen(s);
for (int i=0;i<n;i++){
dp[i][i-1]=0;
dp[i][i]=1;
}
for (int k=1;k<n;k++){ //表示i跟j之间的距离
for (int i=0;i<n-k;i++){
int j=i+k;
dp[i][j]=MAX;
if ((s[i]=='('&&s[j]==')')||(s[i]=='['&&s[j]==']')){
dp[i][j]=dp[i+1][j-1];
}
for (int p=i;p<j;p++){
if (dp[i][j]>dp[i][p]+dp[p+1][j]){
dp[i][j]=dp[i][p]+dp[p+1][j];
}
}
}
}
cout<<dp[0][n-1]<<endl;
}
return 0;
}
#include <iostream>
#include <string.h>
using namespace std;
#define inf 0xffffff
int dp[105][105];
int pos[105][105];
char s[105];
void show(int i,int j){
if (i>j)
return;
if (i==j){
if(s[i]=='('||s[i]==')')
cout<<"()";
else
cout<<"[]";
}
else{
if (pos[i][j]==-1){
cout<<s[i];
show(i+1,j-1);
cout<<s[j];
}
else{
show(i,pos[i][j]);
show(pos[i][j]+1,j);
}
}
}
int main(){
cin>>s;
int n=strlen(s);
for (int i=0;i<n;i++){
dp[i][i-1]=0;
dp[i][i]=1;
}
for (int k=1;k<n;k++){ //表示i跟j之间的距离
for (int i=0;i<n-k;i++){
int j=i+k;
dp[i][j]=inf;
if ((s[i]=='('&&s[j]==')')||(s[i]=='['&&s[j]==']')){
pos[i][j]=-1;
dp[i][j]=dp[i+1][j-1];
}
for (int p=i;p<j;p++){
if (dp[i][j]>dp[i][p]+dp[p+1][j]){
pos[i][j]=p;
dp[i][j]=dp[i][p]+dp[p+1][j];
}
}
}
}
show(0,n-1);
cout<<endl;
return 0;
}
原文地址：http://blog.csdn.net/codeforcer/article/details/41481041
