<p>Given string num representing a non-negative integer <code>num</code>, and an integer <code>k</code>, return <em>the smallest possible integer after removing</em> <code>k</code> <em>digits from</em> <code>num</code>.</p>

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

<pre>
<strong>Input:</strong> num = &quot;1432219&quot;, k = 3
<strong>Output:</strong> &quot;1219&quot;
<strong>Explanation:</strong> Remove the three digits 4, 3, and 2 to form the new number 1219 which is the smallest.
</pre>

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

<pre>
<strong>Input:</strong> num = &quot;10200&quot;, k = 1
<strong>Output:</strong> &quot;200&quot;
<strong>Explanation:</strong> Remove the leading 1 and the number is 200. Note that the output must not contain leading zeroes.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;10&quot;, k = 2
<strong>Output:</strong> &quot;0&quot;
<strong>Explanation:</strong> Remove all the digits from the number and it is left with nothing which is 0.
</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= num.length &lt;= 10<sup>5</sup></code></li>
	<li><code>num</code> consists of only digits.</li>
	<li><code>num</code> does not have any leading zeros except for the zero itself.</li>
</ul>

class Solution {
public:
    string removeKdigits(string num, int k) {
        // find nearest smallest element to right side
        int n = num.size();
        vector<int> arr(n,n);
        stack<int> st;
        for(int i = n-1;i>=0;i--){
            int el = num[i]-'0';
            if(st.size() != 0){
                while(st.size() && (int)(num[st.top()]-'0') >= el){
                    st.pop();
                }
                if(st.size()){
                    arr[i] = st.top();
                }
                
            }
            st.push(i);
        }
        string ans = "";
        int ind = 0;
        while(k>0 && ind<n){
           if(arr[ind]-ind<=k){
                k--;
            }else{
                ans += num[ind];
            }
            ind ++;
        }
        while(ind<n) ans += num[ind], ind++;
        // remove starting zero;
        string res = "";
        ind = 0;
        while(ans[ind]=='0') ind++;
        while(ind<ans.size()) res += ans[ind], ind++;
        if(res.size() == 0) res = "0";
        return res;
    }
};
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