Your Question:

There are n machines placed in a line in a manufacturing unit. Their arrangement is represented as a binary string, machines, of length n, where a machine is running if the character is ' 1 ' and is not running if it is ' 0 '. In one operation, the state of a machine can be flipped, i.e., ' 1 ' is changed to ' 0 ' or vice versa, and the operation can be applied any number of times. An arrangement is valid if no running machine has a non-running machine to its immediate right, i.e., the final arrangement ches not contain "10" as a substring. Find the minimum number of operations required to form a valid arrangement. Example

Step By Step Answers with Explanation

To find the minimum number of operations required to form a valid arrangement of machines, where no running machine has a non-running machine to its immediate right (i.e., no "10" substring), we can follow these steps:

1. Initialize a variable operations to keep track of the number of operations required, initially set to 0.

5. Continue this process until you have checked all machines in the string.

6. Finally, the value of operations will represent the minimum number of operations required to form a valid arrangement.

2. • At position 0, we have "10". Increment operations by 1 and change the string to "1101001".

   • At position 2, we have "10". Increment operations by 1 and change the string to "1111001".

In this example, it took 4 operations to achieve a valid arrangement of machines. You can apply this algorithm to any binary string representing the arrangement of machines to find the minimum number of operations needed.