Problem description:

Given a non-negative integer num represented as a string, remove k digits from the number so that the new number is the smallest possible.

Note:
The length of num is less than 10002 and will be ≥ k.
The given num does not contain any leading zero.
Example 1:

Input: num = “1432219”, k = 3
Output: “1219”
Explanation: Remove the three digits 4, 3, and 2 to form the new number 1219 which is the smallest.
Example 2:

Input: num = “10200”, k = 1
Output: “200”
Explanation: Remove the leading 1 and the number is 200. Note that the output must not contain leading zeroes.
Example 3:

Input: num = “10”, k = 2
Output: “0”
Explanation: Remove all the digits from the number and it is left with nothing which is 0.

Solution:

Question to ask:

  1. what to output if there’s no digits left?
  2. Are there any character other than digits?
  3. Output type

Use a string as a stack, push_back every digit that is smaller than res.back().

example:
num: “12311421”
k: 3

1
12
123
11
111
1114
1112
11121

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class Solution {
public:
    string removeKdigits(string num, int k) {
        string res= "";
        int n= num.length(), keep= n-k;
        for(char c: num){
            while(k && res.size() && res.back()> c){
                //if 1st digit is greater than second digit, it will get remove too
                res.pop_back();
                --k;
            }
            res.push_back(c);
        }
        res.resize(keep); //if only 1 digit and remove 1 digit, then resize res to 0
        while(!res.empty() && res[0] == '0') res.erase(res.begin());
        return res.empty()? "0": res;
    }
};

time complexity: $O(n)$
space complexity: $O(n)$
reference:
https://goo.gl/8fQRQR
http://www.cnblogs.com/grandyang/p/5883736.html