POJ 1141 Brackets Sequence

思路：动态规划，dp[i][j]表示i到j之间最少需要添加的字符的个数，path[i][j]记录i到j之间添加字符个数为dp[i][j]时的分割位置，path[i][j]初始化为-1，就表示i到j之间没有分割位置。

状态转移方程：dp[i][j] = min(dp[i][j],dp[i][k-1]+dp[k+1][j-1]),其中str[k]必须要与str[j]匹配，k即为分割位置。

打印字符的时候用dfs。

#include<cstdio>
#include<string>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int MAXN = 111;
char s[MAXN];
int dp[MAXN][MAXN];
int path[MAXN][MAXN];
bool canMacth(char c1, char c2){
    return (c1 == '(' && c2 == ')') ||
           (c1 == '[' && c2 == ']');
}
void dfs(int n, int m){
    if(n > m) return;
    if(path[n][m] == -1){
        if(n == m){
            if(s[n] == '(' || s[n] == ')') printf("()");
            else printf("[]");
        }else{
            if(canMacth(s[n], s[m])){
                printf("%c", s[n]);
                dfs(n+1, m-1);
                printf("%c", s[m]);
            }else{
                if(s[m] == ')' || s[m] == ']'){
                    dfs(n, m-1);
                    printf("%c%c", s[m] == ')'?'(':'[', s[m]);
                }else{
                    dfs(n, m-1);
                    printf("%c%c", s[m], s[m] == '('?')':']');
                }
            }
        }
    }
    else{
        dfs(n, path[n][m]-1);
        printf("%c", s[path[n][m]]);
        dfs(path[n][m]+1, m-1);
        printf("%c", s[m]);
    }
}
int main(){
    while(gets(s) != NULL){
        int len = strlen(s);
        memset(path, -1, sizeof(path));
        for(int i = 0;i < MAXN;i ++) dp[i][i] = 1;
        for(int i = 1;i < len;i ++){
            for(int j = i-1;j >= 0;j --){
                path[j][i] = -1;
                dp[j][i] = dp[j][i-1]+1;
                for(int k = j;k < i;k ++){
                    if(canMacth(s[k], s[i])){
                        if(dp[j][i] > dp[j][k-1] + dp[k+1][i-1]){
                            dp[j][i] = dp[j][k-1] + dp[k+1][i-1];
                            path[j][i] = k;
                        }
                    }
                }
            }
        }
        dfs(0, len-1);
        printf("
");
    }
    return 0;
}