wikioi 1251--括号

题目描述：给定n个变量，求乘积的表达式的个数。相邻元素相乘需要加*号。

思路：直接递归即可，ans[i][j] = ans[i][k]+ans[k+1][j]（i<=k<j）;对于单个字符而言，没有括号

#include<cstdio>
#include<cmath>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<vector>
#include<string>
using namespace std;


vector<string> ans[20][15];
string a[15];
int n;
void dfs(int l, int r)
{
    string s;
    if (ans[l][r].size())
        return;
    if (l == r)
        ans[l][r].push_back(a[l]);
    else
    {
        for (int i = l; i < r; i++)
        {
            dfs(l, i);
            dfs(i + 1, r);
            int m1 = ans[l][i].size(), m2 = ans[i+1][r].size();
            for (int j = 0; j < m1; j++)
            {
                for (int k = 0; k < m2; k++)
                {
                    if (l == i && i + 1 == r)
                        s = "(" + ans[l][i][j] + "*" + ans[i + 1][r][k] + ")";
                    else
                    {
                        s = "(" + ans[l][i][j] + ans[i+1][r][k] + ")";
                    }
                    ans[l][r].push_back(s);
                }
            }
        }
    }
}
int main()
{
    cin >> n;
    for (int i = 1; i <= n; i++)
        cin >> a[i];
    dfs(1, n);
    int m = ans[1][n].size();
    for (int i = 0; i < m; i++)
        cout << ans[1][n][i] << endl;
    return 0;
}