Key approach of the solution: Backtracking with Expression Evaluation
Define a recursive function that takes the index of the current digit, the current expression string, the current value of the expression, the last operand, and a list to store valid expressions.
If the index reaches the end of the string, check if the current value equals the target. If so, add the expression to the list.
Iterate over the remaining digits, extending the current operand by one digit at a time.
For each extended operand, recursively explore the three possibilities of adding '+', '-', or '*' between the current operand and the next.
Handle the '*' operator by reversing the effect of the last operand before multiplying.
Continue the recursion until all digits are processed.
Return the list of valid expressions.
Key approach of the solution: Iterative Depth-First Search