在用string写题的时候，写了下面代码，调试时报错

#define _CRT_SECURE_NO_WARNINGS
#include<iostream>
#include<cmath>
#include<ctime>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<queue>
#include<cstdlib>
#pragma warning(suppress : 4996)
using namespace std;
string num[31];
int n;
string a(string n)
{
	string ans = "\0";
	int len = n.length();
	int lena = 1;
	int k = 1;
	for (int i = 1; i <= len; i++)
	{
		if (n[i] != n[i + 1])
		{
			ans[lena++] = k + 48;
			ans[lena++] = n[i];
			k = 1;
		}
		else
		{
			k++;
		}
	}
	return ans;
}
int main()
{
	cin >> n;
	num[1] = "1";
	for (int i = 2; i <= n; i++)
	{
		num[i] = a(num[i - 1]);
	}
	cout << num[n];
	return 0;
}

运行到if (n[i] != n[i + 1])时报的错，怀疑是string类型用错了