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Minimum Number of Flips

In this article, we are going to see how to solve the following flipping problem on forming a binary string? This problem has been featured in Goldman Sachs interview round.
Submitted by Radib Kar, on March 07, 2019

Problem statement:

Given a binary string (containing only 0s and 1s). We need to make this string a sequence of alternate characters (0 and 1) by flipping some of the bits, our goal is to minimize the number of bits to be flipped. Write a program to determine the minimum number of bits to reach the goal.

Examples:

    Input:
    0000 (binary string)
    Output: 
    2

    Input:
    110 (binary string)
    Output:
    1

Example explanations:

    Input:
    0000
    Output strings possible from the input string, 
    which satisfies the constraints:
    0101
    1010
    Both strings are valid and both require 2 bits to be flipped. 
    Thus minimum no of flipping needed is 2

    Input:
    110
    Output strings possible from the input string, 
    which satisfies the constraints:
    010
    101
    The first one needs only one flips
    While the second one need two flips
    Hence minimum flip required is 1

Solution:

Observation reveals that the converted string can be of two types:

  1. Starts with a 0
  2. Starts with a 1

What we need to do is to convert the input string into both of this two category. Calculate corresponding flips needed to convert. Return the minimum flips.

Pre-requisite:

Input string s

Algorithm:

1) Declare variables and initialize like below.

    flip0 = 0, flip1 = 0, flag0 = 0, flag1 = 1
    flip0=number of flips needed when converted string starts with 0
    flip1=number of flips needed when converted string starts with 1
    flag0=the current character value that should be at current string index,
    incase converted string starts from 0, value changes from 0 to 1,
    1 to 0 alternatively
    flag1 = the current character value that should be at current string index,
    incase converted string starts from 1,
    value changes from 0 to 1, 1 to 0 alternatively

2) Count number of flips needed for converting input string to the valid string starting with 0

    for i=0:s.length()-1
        iF (flag0 != s[i]-'0')
            flip0++;
        END IF
        flag0=1-flag0;
    END FOR

3) Count number of flips needed for converting input string to the valid string starting with 1

    for i=0:s.length()-1
        iF (flag1 != s[i]-'0')
            flip1++;
        END IF
        flag1=1-flag1;
    END FOR

4) return minimum of flip0 and flip1;


C++ implementation

#include <bits/stdc++.h>
using namespace std;

void print(vector<int> a,int n){
	for(int i=0;i<n;i++)
		cout<<a[i]<<" ";
	cout<<endl;
}

int minflip(string s)
{
	int flip0=0,flip1=0,flag0=0,flag1=1;
	
	//converting to string starting with 0
	for(int i=0;i<s.length();i++){
		if(flag0!=s[i]-'0')
			flip0++;
		flag0=1-flag0;
	}
	
	//converting to string starting with 1
	for(int i=0;i<s.length();i++){
		if(flag1!=s[i]-'0')
			flip1++;
		flag1=1-flag1;
	}
	
	return flip0>flip1?flip1:flip0; //returnig minimum
}

int main()
{
	string s;

	cout<<"Enter input string\n";
	cin>>s;

	cout<<"minimum no of flip required is: "<<minflip(s)<<endl;

	return 0;
}

Output

First run:
Enter input string
0000
minimum no of flip required is: 2

Second run:
Enter input string
110
minimum no of flip required is: 1





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