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Pattern RepresentationMax Score: 100Given a pattern consisting only of 'I' and 'S', where I represents descending and S represents ascending, you need to display a sequence of numbers describing the ascending or descending order. Each character should be represented by 2 digits (between 1-9) - denoting the character's ascending or descending nature. The second character in the pattern takes the last digit from the first character to build the sequence. The third character in the pattern takes the last digit from the second character to build the sequence and so on. The sequence cannot have repeated digits. Find the smallest such sequence which represents the given pattern.Input FormatThe first line of input contains T - the number of test cases. It is followed by T lines, each containing a pattern, consisting only of 'S' and 'I'.Output FormatFor each test case, print the smallest sequence which represents the given pattern, separated by a newline.Constraints1 <= T <= 5001 <= len(str) <= 8ExampleInput4SISISIISSOutput1221132432145ExplanationExample 1:The given pattern has a single character 'S', which denotes ascending nature. There are multiple ways to represent it - 12, 47, 28, 34 etc. However, "12" is the smallest of them.Example 2:The given pattern has a single character 'I', which denotes descending nature. There are multiple ways to represent it - 21, 41, 75, 96 etc. However, "21" is the smallest of them.Example 3:The given pattern has 3 characters 'S' (ascending), 'I' (descending) and 'S' (ascending). There are multiple ways to represent it - 1324, 1634, 1435, 4812, 3748 etc. However, "1324" is the smallest of them.

Question

Pattern RepresentationMax Score: 100Given a pattern consisting only of 'I' and 'S', where I represents descending and S represents ascending, you need to display a sequence of numbers describing the ascending or descending order. Each character should be represented by 2 digits (between 1-9) - denoting the character's ascending or descending nature. The second character in the pattern takes the last digit from the first character to build the sequence. The third character in the pattern takes the last digit from the second character to build the sequence and so on. The sequence cannot have repeated digits. Find the smallest such sequence which represents the given pattern.Input FormatThe first line of input contains T - the number of test cases. It is followed by T lines, each containing a pattern, consisting only of 'S' and 'I'.Output FormatFor each test case, print the smallest sequence which represents the given pattern, separated by a newline.Constraints1 <= T <= 5001 <= len(str) <= 8ExampleInput4SISISIISSOutput1221132432145ExplanationExample 1:The given pattern has a single character 'S', which denotes ascending nature. There are multiple ways to represent it - 12, 47, 28, 34 etc. However, "12" is the smallest of them.Example 2:The given pattern has a single character 'I', which denotes descending nature. There are multiple ways to represent it - 21, 41, 75, 96 etc. However, "21" is the smallest of them.Example 3:The given pattern has 3 characters 'S' (ascending), 'I' (descending) and 'S' (ascending). There are multiple ways to represent it - 1324, 1634, 1435, 4812, 3748 etc. However, "1324" is the smallest of them.

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Solution 1

The problem is asking to generate the smallest sequence of numbers that represents a given pattern of 'S' and 'I'. 'S' represents ascending order and 'I' represents descending order. Each character in the pattern should be represented by two digits, and the sequence cannot have repeated digits.

Here are the steps to solve this problem:

  1. Initialize an empty list to store the sequence of numbers.
  2. Iterate over the pattern from left to right.
  3. For each character in the pattern, check if it is 'S' or 'I'.
  4. If the character is 'S', append the smallest available number to the sequence and remove it from the available numbers.
  5. If the character is 'I', append the largest available number to the sequence and remove it from the available numbers.
  6. Continue this process until all characters in the pattern have been processed.
  7. The resulting sequence of numbers is the smallest sequence that represents the given pattern.

For example, if the pattern is 'SISIS', the smallest sequence that represents this pattern is '13254'.

This is because:

  • For the first 'S', we append the smallest available number (1) to the sequence.
  • For the second 'I', we append the largest available number (3) to the sequence.
  • For the third 'S', we append the smallest available number (2) to the sequence.
  • For the fourth 'I', we append the largest available number (5) to the sequence.
  • For the fifth 'S', we append the smallest available number (4) to the sequence.

So, the smallest sequence that represents the pattern 'SISIS' is '13254'.

This problem has been solved

Solution 2

The problem is asking to generate the smallest sequence of numbers that represents a given pattern of 'S' and 'I'. 'S' represents ascending order and 'I' represents descending order. Each character in the pattern should be represented by two digits, and the sequence cannot have repeated digits.

Here is a step-by-step solution:

  1. Initialize an empty list to store the sequence of numbers.
  2. Iterate over the pattern from left to right.
  3. For each character in the pattern, check if it is 'S' or 'I'.
  4. If the character is 'S', append the smallest available number to the sequence and remove it from the available numbers.
  5. If the character is 'I', append the largest available number to the sequence and remove it from the available numbers.
  6. Continue this process until all characters in the pattern have been processed.
  7. The resulting sequence of numbers is the smallest sequence that represents the given pattern.

This solution works because appending the smallest available number for 'S' and the largest available number for 'I' ensures that the sequence is as small as possible while still representing the given pattern.

This problem has been solved

Solution 3

The problem is asking to generate the smallest sequence of numbers that represents a given pattern of 'S' and 'I'. 'S' represents ascending order and 'I' represents descending order. Each character in the pattern should be represented by two digits, and the sequence cannot have repeated digits.

Here are the steps to solve this problem:

  1. Initialize an empty list to store the sequence of numbers.
  2. Iterate over the pattern from left to right.
  3. For each character in the pattern, check if it is 'S' or 'I'.
  4. If the character is 'S', append the smallest available number to the sequence and remove it from the list of available numbers.
  5. If the character is 'I', append the largest available number to the sequence and remove it from the list of available numbers.
  6. Continue this process until all characters in the pattern have been processed.
  7. The resulting sequence of numbers is the smallest sequence that represents the given pattern.

This algorithm ensures that the sequence of numbers is as small as possible, as it always uses the smallest available number for 'S' and the largest available number for 'I'. It also ensures that the sequence does not have repeated digits, as each number is removed from the list of available numbers after it is used.

This problem has been solved

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