Number of Atoms

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class Solution:
    def countOfAtoms(self, formula: str) -> str:
        stack = []
        map = {}
        i, n = 0, len(formula)
        while i < n:
            c = formula[i]; i += 1
            if c == '(':
                stack.append(map)
                map = {}
            elif c == ')':
                val = 0
                while i < n and formula[i].isdigit():
                    val = val*10 + int(formula[i]); i += 1

                if val == 0: 
                    val = 1
                if stack:
                    temp = map
                    map = stack.pop()
                    for key in temp.keys():
                        map[key] = map.get(key, 0) + temp[key] * val
            else:
                start = i - 1
                while i < n and formula[i].islower():
                    i += 1
                s = formula[start:i]
                val = 0
                while i < n and formula[i].isdigit():
                    val = val*10 + int(formula[i]); i += 1
                if val == 0:
                    val = 1
                map[s] = map.get(s, 0) + val
        result = ''
        for key in sorted(map.keys()):
            result += key
            if map[key] > 1:
                result += str(map[key])
        return result

Problem Classification

The problem is a String Processing problem. The challenge involves parsing a string and making use of a data structure, making it a combination of String Processing and Data Structures.

‘What’ Components:

Input: The input is a string ‘formula’ that represents a chemical formula. The string has a certain format: it starts with an uppercase character (representing an atomic element), then it may contain zero or more lowercase letters (as part of the atomic element name), and may be followed by one or more digits (representing the count of the element). The string may also contain parentheses to encapsulate sub-formulas, which can also be followed by one or more digits (representing the count of the entire sub-formula).
Output: The output is a string, which contains the atomic elements in sorted order followed by their counts (only if the count is more than 1).
Constraints: The length of the formula is between 1 and 1000. The formula consists of English letters, digits, ‘(’, and ‘)’. The formula is always valid. All the values in the output fit in a 32-bit integer.

This is a Parsing problem. It involves reading a string in a certain format, interpreting its meaning, and then outputting a result based on that interpretation. In this case, the input string is a chemical formula, and the task is to parse this formula and count the number of each atomic element in it. It also includes elements of String Processing (understanding and manipulating a string in a certain way) and Data Structures (keeping track of counts of atomic elements).

Language Agnostic Coding Drills

Dissect the code and identify each distinct concept it contains.

Variable initialization: The code begins by initializing several variables, including a list stack, a dictionary map, and two integers i and n.
String parsing: The code then enters a while loop, where it reads and interprets each character in the string formula.
Control flow: The code uses if-elif-else statements to control the flow of the program based on the character currently being parsed.
Stack manipulation: The code uses a stack to handle nested parentheses in the formula.
Dictionary manipulation: The code uses a dictionary to keep track of the count of each atom.
String manipulation: The code constructs the output string based on the atom counts stored in the dictionary.

List out the coding concepts or drills in order of increasing difficulty.

Variable initialization: This is a fundamental concept in programming that involves assigning initial values to variables.
String parsing: This involves reading and interpreting a string character by character. It’s slightly more complex as it requires understanding of string indexing and iteration.
Control flow: This involves understanding the flow of a program. It’s essential for conditional execution of certain blocks of code.
Dictionary manipulation: This requires a good understanding of key-value pairs and how to add, remove, or update entries in a dictionary.
Stack manipulation: Stacks are a more advanced data structure that follow a “last in, first out” principle. Manipulating stacks requires understanding of stack operations such as push and pop.
String manipulation: Constructing a new string based on certain conditions can be tricky and requires good understanding of strings.

Problem-solving approach

Initialize variables: Begin by setting up a stack to keep track of atoms within parentheses, a dictionary to keep track of counts, and two integers to keep track of your position within the string and its length.
Parse the formula: Parse the formula string one character at a time. For each character, determine whether it’s an opening parentheses, closing parentheses, an uppercase letter (starting a new atom), a lowercase letter (continuing the current atom), or a digit (specifying the count of the current atom).
Handle parentheses: Use the stack to keep track of atom counts within parentheses. When you encounter an opening parentheses, push the current count dictionary onto the stack and start a new one. When you encounter a closing parentheses, multiply the counts in the current dictionary by the following number (if any), then merge it with the dictionary at the top of the stack.
Handle atoms: For each atom, update the count in the dictionary. If you encounter an uppercase letter, it means you’re starting a new atom. If it’s followed by lowercase letters, they are part of the same atom. If it’s followed by digits, they specify the count of the atom. If there are no digits following an atom, its count is 1.
Construct output string: Finally, construct the output string by iterating over the atom counts in the dictionary in sorted order. Append the atom name and its count (if greater than 1) to the output string.

This problem combines several fundamental coding concepts in a clever way to parse and interpret a chemical formula.

Targeted Drills in Python

Let’s illustrate each coding concept with a simple Python drill:

Variable Initialization:

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# Initializing variables
a = 0
b = "Hello"
c = []
d = {}

String Parsing:

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# Parsing a string
s = "Hello, World!"
for char in s:
    print(char)

Control Flow:

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# Using if-elif-else statements
num = 15
if num > 10:
    print("Greater than 10")
elif num < 10:
    print("Less than 10")
else:
    print("Equal to 10")

Dictionary Manipulation:

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# Manipulating a dictionary
dict = {'A': 1, 'B': 2}
dict['C'] = 3
print(dict.get('A'))
dict['A'] = 4
print(dict)

Stack Manipulation:

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# Using a stack
stack = []
stack.append('A')
stack.append('B')
print(stack.pop())
print(stack)

String Manipulation:

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# Constructing a string
s = ''
s += 'Hello'
s += ' World'
print(s)

Next, let’s identify problem-specific concepts:

Parsing a chemical formula: This involves recognizing uppercase letters as the start of a new atom, lowercase letters as the continuation of the current atom, digits as the count of the current atom, and parentheses as indicating a group of atoms.
Counting atoms: This involves updating a dictionary with the counts of each atom.

These concepts are essential for our problem because they allow us to interpret the given chemical formula and count the number of each atom.

Finally, to integrate these pieces together:

Start by initializing the necessary variables, including the stack and dictionary.
Enter a loop to parse the formula. Use if-elif-else statements to handle each type of character appropriately.
Inside the loop, use dictionary manipulation to update the counts of each atom and stack manipulation to handle parentheses.
After parsing the formula, use string manipulation to construct the output string.

Each of these steps builds on the previous ones, leading to the final solution.