Beautiful String

Posted: 3 Feb, 2021
Difficulty: Easy

PROBLEM STATEMENT

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Ninja has been given a binary string ‘STR’ containing either ‘0’ or ‘1’. A binary string is called beautiful if it contains alternating 0s and 1s.

For Example:‘0101’, ‘1010’, ‘101’, ‘010’ are beautiful strings.

He wants to make ‘STR’ beautiful by performing some operations on it. In one operation, Ninja can convert ‘0’ into ‘1’ or vice versa.

Your task is to determine the minimum number of operations Ninja should perform to make ‘STR’ beautiful.

For Example :

Minimum operations to make ‘STR’ ‘0010’ beautiful is ‘1’. In one operation, we can convert ‘0’ at index ‘0’ (0-based indexing) to ‘1’. The ‘STR’ now becomes ‘1010’ which is a beautiful string. 

Input Format :

The first line contains an integer 'T' which denotes the number of test cases or queries to be run. Then the test cases follow.

The only line of each test case contains a binary string 'STR'.

Output Format :

For each test case, print the minimum operations needed to make ‘STR’ beautiful.

Print the output of each test case in a separate line.

Note :

You are not required to print the expected output, it has already been taken care of. Just implement the given function.

Constraints :

1 <= T <= 100
2 <= |STR| <= 10^5
STR[i] = ‘1’ or ‘0’

Where '|STR|' denotes the length of ‘STR’.

Time Limit: 1 sec 
Approach 1

We observe that for any length of the given string ‘STR’, there are only two possible beautiful strings ie: one starting with ‘1’ and the other starting with ‘0’.

 

For example for ‘N’ = 4 , “1010” and “0101” are the only two possible beautiful strings.

Now, we just need to count the different values at the same index in a possible beautiful string and given ’STR’.

 

For example: If ‘STR’ = “1011”, there exist two beautiful strings of length 4 ie: “1010” and “0101”. The count of different values at same index in ‘STR’ and “1010” is 1 and ‘STR’ and “0101” is 3 respectively and 1 is the  minimum of these two so we need only ‘1’ operation to convert ‘1011’ to ‘1010’. 

 

Algorithm:

Initialize four variables ‘T1’ = 0, ‘T2’ = 0,’S1’ = 0’ and ‘S2’ = 1 where ‘T1’ denotes the difference between values at indices in ‘STR’ and the possible beautiful string starting with 0 and ‘T2’ denotes the difference between values at indices in ‘STR’ and the possible beautiful string starting with 1.‘S1’ and ‘S2’ denote the expected value at index ‘i’ in both of the possible beautiful strings 

 

Iterate the given string ‘STR’ and do the following:

  • If ‘STR[i]’ == 1
    • If ‘S1’ == 0’ then T1++.
    • Else T2++.
  • If ‘STR[i]’ == 0
    • If ‘S1’ == 1 then T1++.
    • Else T2++
  • If ‘S1’ == 0’ then make it 1 and vise versa do the same for ‘S2’.
  • Finally return the minimum of ‘T1’ and ‘T2’.
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