bracket sequence (interval dp)

bracket sequence (interval dp)

Enter a sequence consisting of "(", ")", "[", ")" whose length does not exceed 100. Please add as few brackets as possible to get a regular bracket sequence. If there are multiple solutions, output any sequence.

A bracket sequence is defined like this:

• An empty sequence is a bracketed sequence
• If S is a bracket sequence, then (S) and [S] are also regular bracket sequences
• If both A and B are regular bracket sequences, then AB is also a regular bracket sequence.

So, as long as a sequence of parentheses is not an empty sequence, we can certainly strip it from both ends, or divide it into two sequences of parentheses. Let \(f[i][j]\) mean that the string \(s[i][j]\) needs to add at least a few parentheses, then \(f[i][j]\) must be transferred to \ (f[i][k]+f[k][j]\) . If \(s[i]=s[j]\) , then you can also move to \(f[i+1][j-1]\) .

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

const int maxn=105;
int T, f[maxn][maxn], n;
char s[maxn];

//函数能使语义更清晰
bool match(int x, int y){ return s[y]-s[x]>0&&s[y]-s[x]<=2; }

void print(int l, int r){  //[l,r]
    if (l>r) return;
    if (l==r){
        if (s[l]=='('||s[l]==')') printf("()");
        else printf("[]"); return; }
    int ans=f[l][r];
    if (match(l, r)&&f[l+1][r-1]==ans){
        putchar(s[l]); print(l+1, r-1); putchar(s[r]);
        return; }
    for (int k=l; k<r; ++k)
        if (f[l][k]+f[k+1][r]==ans){
            print(l, k); print(k+1, r); return; }
}

int main(){
    scanf("%d", &T);
    while (T--){
        fgets(s, maxn, stdin);
        fgets(s, maxn, stdin);
        n=strlen(s)-1;
        for (int i=0; i<n; ++i) f[i+1][i]=0, f[i][i]=1;
        for (int i=n-2; i>=0; --i)
            for (int j=i+1; j<n; ++j){
                f[i][j]=n;
                if (match(i, j)) f[i][j]=f[i+1][j-1]; //[i,j]
                for (int k=i; k<j; ++k)
                    f[i][j]=min(f[i][j], f[i][k]+f[k+1][j]);
            }
        print(0, n-1); puts("");
    }
    return 0;  //忘记return 0了！！
}