Minimize Result by Adding Parentheses to Expression

Minimize Result by Adding Parentheses to Expression

What is this problem about?

The "Minimize Result by Adding Parentheses to Expression" interview question challenges you to take a given string expression, which typically consists of two positive integers separated by a plus sign (e.g., "247+38"), and strategically add a single pair of parentheses to minimize the overall result. The parentheses must enclose a sub-expression, meaning they must be placed around a part of the original expression, transforming it into multiplication. For example, in "247+38", if you place parentheses like "2(4+7)38", it might become "2 * (4+7) * 38". The problem effectively asks you to explore all valid placements of parentheses that introduce multiplication and find the one that yields the smallest numerical outcome.

Why is this asked in interviews?

This type of enumeration and string manipulation problem is frequently posed in interviews by companies like Snap and Pinterest because it assesses a candidate's ability to systematically explore a solution space. It's not just about parsing strings; it's about understanding how to generate all valid permutations of parentheses placement and then evaluating each one. This "Minimize Result by Adding Parentheses to Expression" coding problem tests careful index manipulation, string slicing, and the conversion between string and numeric types. It also evaluates an interviewer's attention to detail and their capability to handle string-based problems, which are common in many software development roles.

Algorithmic pattern used

The primary algorithmic pattern to solve the "Minimize Result by Adding Parentheses to Expression" coding problem is Enumeration (or Brute Force search of a constrained space) combined with String Manipulation. Since the problem specifies adding a single pair of parentheses, the number of possible placements is relatively small. You can iterate through all possible starting positions for the left parenthesis and all possible ending positions for the right parenthesis. For each valid pair of positions, you construct the new expression, evaluate it, and keep track of the minimum result found so far. The string manipulation involves carefully splitting the original string into prefix, parenthesized part, and suffix, then converting these parts to numbers and performing the arithmetic operations (multiplication and addition).

Example explanation

Let's take the expression expression = "12+34". The plus sign is at index 2. The expression can be broken into num1 (before '+') and num2 (after '+'). Here, num1 = "12", num2 = "34".

We need to place parentheses ( ) around a sub-expression. The structure will always be prefix * (inner_sum) * suffix. The inner_sum is always formed from a part of num1, the +, and a part of num2. Let's consider possible placements:

1. Around "12+3": (12+3)4 -> (12+3)*4 (If we assume there's always a multiplication outside). This doesn't quite fit the pattern, let's re-evaluate the structure based on A(B+C)D. A is the part of num1 before '(' B is the part of num1 inside '(' C is the part of num2 inside ')' D is the part of num2 after ')'

   For "12+34": The '+' is at index sep_idx = 2. num1 = "12", num2 = "34".

   Iterate i from 0 to sep_idx - 1 (start of left parenthesis) Iterate j from sep_idx + 1 to len(expression) - 1 (end of right parenthesis)

   Case 1: (1+2)+34 is invalid (cannot enclose '+' by default if it means a single multiplication). The problem implies A * (B + C) * D.

   Let's find the + first: expression = "12+34", plus_idx = 2. left_num_str = "12", right_num_str = "34".

   Consider where the opening parenthesis ( can be placed:

   • Before '1': (12+34) -> 12+34 = 46. (No outer multiplication)
   • Before '2': 1(2+3)4 -> 1 * (2+3) * 4 = 1 * 5 * 4 = 20. This is valid.
   • After '1', before '+': 1(2+3)4 is not quite right. The rule is: prefix ( ... ) suffix.

   Let i be the index of the first digit inside the parentheses, and j be the index of the last digit inside the parentheses. expression = "12+34" plus_idx = 2

   Possible i values: 0, 1 Possible j values: 3, 4

   If i=0, j=4: (12+34). prefix = "", inner_exp = "12+34", suffix = "". Result: 12+34 = 46. If i=1, j=3: 1(2+3)4. prefix = "1", inner_exp = "2+3", suffix = "4". Result: int("1") * (int("2") + int("3")) * int("4") = 1 * 5 * 4 = 20. If i=0, j=3: (12+3)4. prefix = "", inner_exp = "12+3", suffix = "4". Result: (12+3) * int("4") = 15 * 4 = 60. If i=1, j=4: 1(2+34). prefix = "1", inner_exp = "2+34", suffix = "". Result: int("1") * (2+34) = 1 * 36 = 36.

   Minimum is 20.

Common mistakes candidates make

One frequent mistake in the "Minimize Result by Adding Parentheses to Expression" problem is incorrectly parsing the expression parts after adding parentheses. Candidates might miscalculate indices, leading to incorrect sub-strings for prefix, inner sum, and suffix. Another pitfall is not exploring all valid placements of parentheses, thus missing the optimal solution. Some might also forget to convert string parts to integers before performing arithmetic, or incorrectly handle cases where the prefix or suffix (or both) are empty strings, which should translate to a multiplication factor of 1 rather than 0. Edge cases with single-digit numbers or expressions where the + sign is at an extreme end also require careful handling.

Interview preparation tip

For "Minimize Result by Adding Parentheses to Expression" and similar string manipulation/enumeration problems, focus on precise index management and systematic iteration. Practice problems that involve splitting and joining strings, converting between string and number types, and evaluating expressions. Drawing out the structure of the string and identifying all valid (start, end) index pairs for the parentheses is crucial. Write down small examples and manually trace how each placement of parentheses affects the calculation. Ensure your logic correctly handles the conversion of empty prefix/suffix strings to multiplication factors of 1.