Count of Integers
<p>You are given two numeric strings <code>num1</code> and <code>num2</code> and two integers <code>max_sum</code> and <code>min_sum</code>. We denote an integer <code>x</code> to be <em>good</em> if:</p>

<ul>
	<li><code>num1 &lt;= x &lt;= num2</code></li>
	<li><code>min_sum &lt;= digit_sum(x) &lt;= max_sum</code>.</li>
</ul>

<p>Return <em>the number of good integers</em>. Since the answer may be large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>

<p>Note that <code>digit_sum(x)</code> denotes the sum of the digits of <code>x</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> num1 = &quot;1&quot;, num2 = &quot;12&quot;, <code>min_sum</code> = 1, max_sum = 8
<strong>Output:</strong> 11
<strong>Explanation:</strong> There are 11 integers whose sum of digits lies between 1 and 8 are 1,2,3,4,5,6,7,8,10,11, and 12. Thus, we return 11.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> num1 = &quot;1&quot;, num2 = &quot;5&quot;, <code>min_sum</code> = 1, max_sum = 5
<strong>Output:</strong> 5
<strong>Explanation:</strong> The 5 integers whose sum of digits lies between 1 and 5 are 1,2,3,4, and 5. Thus, we return 5.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num1 &lt;= num2 &lt;= 10<sup>22</sup></code></li>
	<li><code>1 &lt;= min_sum &lt;= max_sum &lt;= 400</code></li>
</ul>
Math; String; Dynamic Programming
class Solution {
public:
    int count(string num1, string num2, int min_sum, int max_sum) {
        const int mod = 1e9 + 7;
        int f[23][220];
        memset(f, -1, sizeof(f));
        string num = num2;

        function<int(int, int, bool)> dfs = [&](int pos, int s, bool limit) -> int {
            if (pos >= num.size()) {
                return s >= min_sum && s <= max_sum ? 1 : 0;
            }
            if (!limit && f[pos][s] != -1) {
                return f[pos][s];
            }
            int up = limit ? num[pos] - '0' : 9;
            int ans = 0;
            for (int i = 0; i <= up; ++i) {
                ans += dfs(pos + 1, s + i, limit && i == up);
                ans %= mod;
            }
            if (!limit) {
                f[pos][s] = ans;
            }
            return ans;
        };

        int a = dfs(0, 0, true);
        for (int i = num1.size() - 1; ~i; --i) {
            if (num1[i] == '0') {
                num1[i] = '9';
            } else {
                num1[i] -= 1;
                break;
            }
        }
        num = num1;
        memset(f, -1, sizeof(f));
        int b = dfs(0, 0, true);
        return (a - b + mod) % mod;
    }
};