Luogu P2308_Interval dp_Output Path and Intermediate Process

#include <cstdio>
#include <cstring>

using namespace std;

const int maxn = 25;

int n, dp[maxn][maxn], gap[maxn][maxn];//g is the breakpoint position
int ll[maxn], rr[maxn];//Number of left/right parentheses of the number at this position
int a[maxn], sum[maxn];//Number, prefix sum

void dfs2(int x, int y);
void dfs1(int x, int y);

intmain()
{
    scanf("%d", &n);
    int i, j, len, l, r, k;
    sum[0] = 0;
    memset(dp, 0x3f, sizeof(dp));
    for(i = 1; i <= n; ++i)
    {
        scanf("%d", &a[i]);
        sum[i] = sum[i-1]+a[i];
        dp[i][i] = 0; // keep in mind
    }
    for (len = 2; len <= n; ++ len)
        for(l = 1; l+len-1 <= n; ++l)
    {
        r = l + len - 1;
        for(k = l; k < r; ++k)
        {
            int tmp = dp[l][k]+dp[k+1][r]+sum[r]-sum[l-1];
            if(tmp <= dp[l][r])
            {//Here is <=, not <, as far as possible to add parentheses, because n-1 parentheses need to be filled
                dp[l][r] = tmp;
                gap[l][r] = k;
            }
        }
    }
    dfs1(1, n);//Seek ll[] and rr[]
    for(i = 1; i <= n; ++i)
    {
        for(j = 1; j <= ll[i]; ++j) printf("(");
        printf("%d", a[i]);
        if(!rr[i] && i != n) printf("+");
        for(j = 1; j <= rr[i]; ++j) printf(")");
        if(rr[i] && i != n) printf("+");
    }
    printf("\n%d\n", dp[1][n]);
    dfs2(1, n);
    return 0;
}

void dfs1(int x, int y)
{
    if(x == y) return;
    ++ll[x],++rr[y];
    dfs1(x, gap[x][y]);
    dfs1(gap[x][y]+1, y);
}

void dfs2(int x, int y)
{
    if(x == y) return;
    dfs2(x, gap[x][y]);
    dfs2(gap[x][y]+1, y);
    printf("%d ", sum[y]-sum[x-1]);
}