Build Lowest Number by Removing n digits from a given number

4

Given a string ‘str’ of digits and an integer ‘n’, build the lowest possible number by removing ‘n’ digits from the string and not changing the order of input digits.

Examples:

Input: str = "4325043", n = 3
Output: "2043"

Input: str = "765028321", n = 5
Output: "0221"

Input: str = "121198", n = 2
Output: "1118" 

The idea is based on the fact that a character among first (n+1) characters must be there in resultant number. So we pick the smallest of first (n+1) digits and put it in result, and recur for remaining characters. Below is complete algorithm.

Initialize result as empty string
     res = ""
buildLowestNumber(str, n, res)
1) If n == 0, then there is nothing to remove.
   Append the whole 'str' to 'res' and return

2) Let 'len' be length of 'str'. If 'len' is smaller or equal 
   to n, then everything can be removed
   Append nothing to 'res' and return

3) Find the smallest character among first (n+1) characters
   of 'str'.  Let the index of smallest character be minIndex.
   Append 'str[minIndex]' to 'res' and recur for substring after
   minIndex and for n = n-minIndex

     buildLowestNumber(str[minIndex+1..len-1], n-minIndex).

Below is C++ implementation of above algorithm.

// C++ program to build the smallest number by removing n digits from
// a given number
#include<iostream>
using namespace std;

// A recursive function that removes 'n' characters from 'str'
// to store the smallest possible number in 'res'
void buildLowestNumberRec(string str, int n, string &res)
{
    // If there are 0 characters to remove from str,
    // append everything to result
    if (n == 0)
    {
        res.append(str);
        return;
    }

    int len = str.length();

    // If there are more characters to remove than string
    // length, then append nothing to result
    if (len <= n)
        return;

    // Find the smallest character among first (n+1) characters
    // of str.
    int minIndex = 0;
    for (int i = 1; i<=n ; i++)
        if (str[i] < str[minIndex])
            minIndex = i;

    // Append the smallest character to result
    res.push_back(str[minIndex]);

    // substring starting from minIndex+1 to str.length() - 1.
    string new_str = str.substr(minIndex+1, len-minIndex);

    // Recur for the above substring and n equals to n-minIndex
    buildLowestNumberRec(new_str, n-minIndex, res);
}

// A wrapper over buildLowestNumberRec()
string buildLowestNumber(string str, int n)
{
    string res = "";

    // Note that result is passed by reference
    buildLowestNumberRec(str, n, res);

    return res;
}

// Driver program to test above function
int main()
{
    string str = "121198";
    int n = 2;
    cout << buildLowestNumber(str, n);
    return 0;
}

Output:

1118

Below is an optimised code in C++ contributed by Gaurav Mamgain

// C++ program to build the smallest number by removing
// n digits from a given number
#include<bits/stdc++.h>
using namespace std;

void insertInNonDecOrder(deque<char> &dq, char ch)
{
    // if container is empty , insert the current digit
    if (dq.empty())
        dq.push_back(ch);

    else
    {
        char temp = dq.back();

        // Keep removing digits larger than current digit
        // from the back side of deque
        while( temp > ch && !dq.empty())
        {
            dq.pop_back();
            if (!dq.empty())
                temp = dq.back();
        }
        dq.push_back(ch); // insert the current digit
    }
    return;
}

string buildLowestNumber(string str, int n)
{
    int len = str.length();

    // deleting n digits means we need to print k digits
    int k = len - n;

    deque<char> dq;
    string res = "";

    // leaving rightmost k-1 digits we need to choose
    // minimum digit from rest of the string and print it
    int i;
    for (i=0; i<=len-k; i++)

        // insert new digit from the back side in
        // appropriate position and/ keep removing
        // digits larger than current digit
        insertInNonDecOrder(dq, str[i]);

    // Now the minimum digit is at front of deque
    while (i < len)
    {
        // keep the minimum digit in output string
        res += dq.front();

        // remove minimum digit
        dq.pop_front();

        // Again insert new digit from the back
        // side in appropriate position and keep
        // removing digits larger than current digit
        insertInNonDecOrder(dq, str[i]);
        i++;
    }

    // Now only one element will be there in the deque
    res += dq.front();
    dq.pop_front();
    return res;
}

// Driver program to test above function
int main()
{
    string str = "765028321";
    int n = 5;
    cout << buildLowestNumber(str, n)<< endl;
    return 0;
}
// This code is contributed by Gaurav Mamgain

Output:

0221

Time Complexity: O(n)
Space Complexity: O(n)

This article is contributed by Pallav Gurha. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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