8. String to Integer (atoi) - Solutions and Explanation

Problem Statement

The myAtoi(string s) function is designed to convert a string input into a 32-bit signed integer following specific parsing rules. The function ensures to handle spaces, optional sign symbols (+ or -), numerals, and ignores non-numerical characters after parsing any leading numbers. If a string does not start with an optional sign or numeral following optional leading spaces, the function returns zero. If the parsed integer exceeds the bounds of a 32-bit signed integer, it's clamped to the nearest limit, either the minimum or maximum allowable integer value of -2^31 and 2^31-1 respectively.

Examples

Example 1

Input:

s = "42"

Output:

Explanation:

The underlined characters are what is read in and the caret is the current reader position.
Step 1: "42" (no characters read because there is no leading whitespace)
^
Step 2: "42" (no characters read because there is neither a '-' nor '+')
^
Step 3: "42" ("42" is read in)
^

Example 2

Input:

s = " -042"

Output:

-42

Explanation:

Step 1: " -042" (leading whitespace is read and ignored)
^
Step 2: " -042" ('-' is read, so the result should be negative)
^
Step 3: " -042" ("042" is read in, leading zeros ignored in the result)
^

Example 3

Input:

s = "1337c0d3"

Output:

Explanation:

Step 1: "1337c0d3" (no characters read because there is no leading whitespace)
^
Step 2: "1337c0d3" (no characters read because there is neither a '-' nor '+')
^
Step 3: "1337c0d3" ("1337" is read in; reading stops because the next character is a non-digit)
^

Example 4

Input:

s = "0-1"

Output:

Explanation:

Step 1: "0-1" (no characters read because there is no leading whitespace)
^
Step 2: "0-1" (no characters read because there is neither a '-' nor '+')
^
Step 3: "0-1" ("0" is read in; reading stops because the next character is a non-digit)
^

Example 5

Input:

s = "words and 987"

Output:

Explanation:

Reading stops at the first non-digit character 'w'.

Constraints

0 <= s.length <= 200
s consists of English letters (lower-case and upper-case), digits (0-9), ' ', '+', '-', and '.'.

Approach and Intuition

The process for converting the string to an integer can be broken down into a structured approach considering both the examples and constraints provided:

Handling Whitespaces and Initial Parsing Position:
- Begin by ignoring any leading white spaces in the string until the first non-space character is encountered. This ensures that strings with leading spaces are handled correctly without altering the resultant number.
Determining Sign of the Resulting Integer:
- Immediately after the leading spaces, check for the presence of + or - to decide the sign of the resulting integer. If neither is present, the number is assumed to be positive.
Reading and Converting Numerals:
- Post sign detection, begin converting the subsequent characters as part of the number until a non-digit character is found. This conversion halts when characters outside the 0-9 range appear, marking the end of the integer part in the input string.
Handling Non-Digit Characters:
- Characters that are non-digits (including alphabets and special characters other than the sign symbols) after the first encountered number sequence are ignored. This implies that the parsing and conversion process is only interested in the longest leading sequence of digits that possibly follows a sign symbol.
Clamping to 32-bit Integer Range:
- After parsing the digits, the resultant integer is then checked against the 32-bit signed integer boundaries. If the number exceeds these limits, it is clamped to either -2^31 or 2^31 - 1 based on whether it's underflowing or overflowing, respectively.

Example-Based Explanation:

Example 1 ("42"):
- Directly reads digits and returns 42. No sign or leading zero interference.
Example 2 (" -042"):
- Handles the negative sign and leading zero, correctly discarding the zero and converting the result to -42.
Example 3 ("1337c0d3"):
- Stops reading further upon encountering 'c', a non-digit character, returning the parsed number 1337.
Example 4 ("0-1"):
- Reads the zero, then stops at the hyphen which is interpreted as a non-digit in this context, resulting in 0.
Example 5 ("words and 987"):
- Discards all characters up to the digits, but since no digits are leading, returns 0.

This approach and intuitive breakdown allow the myAtoi(string s) to be efficiently implemented while respecting the format and peculiarities of different string inputs as specified in the constraints.

Solutions

C++
Java
C
JavaScript
Python

                            cpp
                            
                        
enum Status { S0, S1, S2, SD };

class Converter {
    Status currentStatus;
    int total, multiplier;

    void switchToS1(char& symbol) {
        multiplier = (symbol == '-') ? -1 : 1;
        currentStatus = S1;
    }

    void switchToS2(int num) {
        currentStatus = S2;
        addNumber(num);
    }

    void switchToSD() {
        currentStatus = SD;
    }

    void addNumber(int& num) {
        if ((total > INT_MAX / 10) || (total == INT_MAX / 10 && num > INT_MAX % 10)) {
            if (multiplier == 1) {
                total = INT_MAX;
            } else {
                total = INT_MIN;
                multiplier = 1;
            }
            switchToSD();
        } else {
            total = total * 10 + num;
        }
    }

public:
    Converter() {
        currentStatus = S0;
        total = 0;
        multiplier = 1;
    }

    void process(char& c) {
        if (currentStatus == S0) {
            if (c == ' ') {
                return;
            } else if (c == '+' || c == '-') {
                switchToS1(c);
            } else if (isdigit(c)) {
                switchToS2(c - '0');
            } else {
                switchToSD();
            }
        } else if (currentStatus == S1 || currentStatus == S2) {
            if (isdigit(c)) {
                switchToS2(c - '0');
            } else {
                switchToSD();
            }
        }
    }

    int retrieveInteger() {
        return multiplier * total;
    }

    Status getStatus() {
        return currentStatus;
    }
};

class Solution {
public:
    int myAtoi(string str) {
        Converter conv;

        for (int i = 0; i < str.size() && conv.getStatus() != SD; ++i) {
            conv.process(str[i]);
        }

        return conv.retrieveInteger();
    }
};

This solution provides an implementation for converting a string to an integer, mimicking the functionality commonly known as atoi. The primary goal is to parse the string, interpret the numerical value correctly, and handle potential integer overflows and invalid input gracefully, ensuring industry-standard behavior.

Approach:

The Converter class manages the conversion process using a finite state machine approach.
Different states (S0, S1, S2, SD) represent different parts of the parsing process:
- S0: Starting state, looking for the first non-whitespace character.
- S1: Sign character identified (+ or -).
- S2: Numeric digits being processed.
- SD: Discontinue parsing due to invalid input or end of numeric sequence.
Transitions between states occur when encountering different types of characters in the input string: space, digit, sign, or other characters.
The Converter class provides methods:
- switchToS1(char&): Transition to the state for handling signs.
- switchToS2(int): Transition to the state for numerical digits.
- switchToSD(): Transition to the discontinuation state.
- addNumber(int&): Adds a digit to the total while checking for overflow.
The Solution class uses Converter within myAtoi method:
- Iterates over input characters, processing each with the Converter.
- Stops if the discontinuation state (SD) is reached.
- Returns the computed integer.

Special Considerations:

Overflow and underflow conditions are explicitly handled. When detected, the number is capped at INT_MAX or INT_MIN accordingly.
Only leading whitespace is ignored. Characters following a valid number sequence or invalid symbol discontinue further processing.
The final value is adjusted according to any initial sign parsed.

Usage:

Instantiate Solution and use myAtoi method passing the string to convert.
The method returns the integer value as parsed according to the rules outlined, or zero if the input does not start with a sequence interpretable as an integer.

This careful consideration to detail ensures that the conversion aligns with expectations for robust applications parsing numerical inputs from varied sources.

                            java
                            
                        
enum Status {
    q0,
    q1,
    q2,
    qd
}

class ParseStateMachine {
    private Status currentStatus;
    private int numericResult, multiplier;

    public ParseStateMachine() {
        currentStatus = Status.q0;
        numericResult = 0;
        multiplier = 1;
    }

    private void switchToQ1(char ch) {
        multiplier = (ch == '-') ? -1 : 1;
        currentStatus = Status.q1;
    }

    private void switchToQ2(int num) {
        currentStatus = Status.q2;
        updateResult(num);
    }

    private void switchToQd() {
        currentStatus = Status.qd;
    }

    private void updateResult(int num) {
        if (
            (numericResult > Integer.MAX_VALUE / 10) ||
            (numericResult == Integer.MAX_VALUE / 10 && num > Integer.MAX_VALUE % 10)
        ) {
            if (multiplier == 1) {
                numericResult = Integer.MAX_VALUE;
            } else {
                numericResult = Integer.MIN_VALUE;
                multiplier = 1;
            }

            switchToQd();
        } else {
            numericResult = numericResult * 10 + num;
        }
    }

    public void updateStatus(char ch) {
        if (currentStatus == Status.q0) {
            if (ch == ' ') {
                return;
            } else if (ch == '-' || ch == '+') {
                switchToQ1(ch);
            } else if (Character.isDigit(ch)) {
                switchToQ2(ch - '0');
            } else {
                switchToQd();
            }
        } else if (currentStatus == Status.q1 || currentStatus == Status.q2) {
            if (Character.isDigit(ch)) {
                switchToQ2(ch - '0');
            } else {
                switchToQd();
            }
        }
    }

    public int getResult() {
        return multiplier * numericResult;
    }

    public Status getStatus() {
        return currentStatus;
    }
}

class Solution {
    public int myAtoi(String str) {
        ParseStateMachine machine = new ParseStateMachine();

        for (int i = 0; i < str.length() && machine.getStatus() != Status.qd; ++i) {
            machine.updateStatus(str.charAt(i));
        }

        return machine.getResult();
    }
}

In the given Java solution, you'll find an implementation for converting a string to an integer, which is similar to the atoi function in C. The code utilizes a finite state machine (FSM) approach, represented by the ParseStateMachine class and an enum Status to manage different states (q0, q1, q2, qd) involved in the parsing process.

The state q0 is the initial state where the machine checks for whitespace, a sign character ('+' or '-'), or a digit.
In state q1, the machine has recognized a sign and looks out for digits.
q2 represents the state of processing digits; the result is formed here.
Lastly, qd indicates that parsing is complete, which can be due to the end of the numeric portion of the string or encountering an invalid character.

The main methods within the ParseStateMachine handle transitions between these states:

switchToQ1 is called upon encountering a sign to set the number's sign (multiplier).
switchToQ2 updates the numeric result as digits are processed.
switchToQd indicates that parsing should cease.
updateResult carefully manages the accumulation of the final number to handle potential overflow scenarios, fixing the output to Integer.MAX_VALUE or Integer.MIN_VALUE as necessary.

The state machine is driven by updateStatus, which reacts according to the current character being processed and the current state. For example, spaces in the initial state (q0) do not change the state, while encountering a non-digit in the q2 state ends parsing.

In the Solution class, myAtoi method utilizes this state machine to interpret the string. It iterates over the input string, updating the state via ParseStateMachine until the string is fully processed or the qd state is reached.

The final result is fetched by calling getResult on the state machine instance, ensuring the outcome respects the parsed integer's sign and magnitude, with appropriate limits respected as per integer boundaries in Java.

                            c
                            
                        
// Define states of the automaton.
typedef enum { start, sign_state, number_state, dead_state } ParseState;

// Structure for state machine to process numerical strings.
typedef struct {
    ParseState current;
    int value;
    int multiplier;
} Parser;

// Initialize state machine values.
void initializeParser(Parser *p) {
    p->current = start;
    p->value = 0;
    p->multiplier = 1;
}

// Handle transition to state managing the sign.
void processSign(Parser *p, char c) {
    p->multiplier = (c == '-') ? -1 : 1;
    p->current = sign_state;
}

// Handle transition to state managing the numerical values.
void processNumber(Parser *p, int num) {
    p->current = number_state;
    if ((p->value > INT_MAX / 10) ||
        (p->value == INT_MAX / 10 && num > INT_MAX % 10)) {
        if (p->multiplier == 1) {
            p->value = INT_MAX;
        } else {
            p->value = INT_MIN;
            p->multiplier = 1;
        }
        p->current = dead_state;
    } else {
        p->value = p->value * 10 + num;
    }
}

// Transition to the state indicating no more valid input acceptance.
void processDeadState(Parser *p) { p->current = dead_state; }

// Determine the new state based on character input.
void changeState(Parser *p, char c) {
    if (p->current == start) {
        if (c == ' ') {
            return;
        } else if (c == '-' || c == '+') {
            processSign(p, c);
        } else if (isdigit(c)) {
            processNumber(p, c - '0');
        } else {
            processDeadState(p);
        }
    } else if (p->current == sign_state || p->current == number_state) {
        if (isdigit(c)) {
            processNumber(p, c - '0');
        } else {
            processDeadState(p);
        }
    }
}

// Compute the final integer result considering the sign.
int computeResult(Parser *p) {
    return p->multiplier * p->value;
}

// Obtain the current state of the parser.
ParseState getCurrentState(Parser *p) { return p->current; }

// Convert string to integer using the state machine.
int stringToInt(char *str) {
    Parser parserEntity;
    initializeParser(&parserEntity);

    for (int i = 0; str[i] != '\0' && getCurrentState(&parserEntity) != dead_state; ++i) {
        changeState(&parserEntity, str[i]);
    }

    return computeResult(&parserEntity);
}

The solution implements a function to convert a string into an integer, mimicking the standard atoi function, by using a finite state machine approach, designed in C programming language. Here’s how the solution approaches the problem and what each part does:

Define a state machine using an enum for different parsing states which include initial, processing sign, processing number, and a dead state where no further input is processed.
Use a struct to encapsulate the parser's state, the currently computed value, and a multiplier to determine if the resulting number should be positive or negative.
Initialize the parser to set the starting state, initialize the computed value to zero, and set the multiplier default to handle positive numbers.
Implement functions to handle transitions between states:
- processSign adjusts the multiplier based on whether the input sign is positive or negative.
- processNumber calculates the numeric value from string characters ensuring it handles overflow by setting the value to INT_MAX or INT_MIN as necessary.
- processDeadState moves the parser to a dead state where no further processing occurs for invalid inputs.
- changeState determines the new state of the parser based on the current state and input character, managing transitions and processing of characters accordingly.
At the end of parsing:
- Compute the final integer result, taking into account the sign.
- The main function, stringToInt, iterates through each character of the input string, changing states and processing based on the character, until it reaches the string's end or transitions into the dead state.

This implementation robustly handles spaces, signs, and numbers, making it versatile for reading integers from various formatted strings safely with boundary checks for overflows.

                            js
                            
                        
class StringParser {
    #currentState;
    #computedValue;
    #valueSign;

    States;
    #MAX_INT;
    #MIN_INT;

    constructor() {
        this.States = { initial: 1, signDetected: 2, numberDetected: 3, deadState: 4 };
        this.#MAX_INT = Math.pow(2, 31) - 1;
        this.#MIN_INT = -Math.pow(2, 31);

        this.#currentState = this.States.initial;
        this.#computedValue = 0;
        this.#valueSign = 1;
    }

    toInitialSignState(symbol) {
        this.#valueSign = symbol == "-" ? -1 : 1;
        this.#currentState = this.States.signDetected;
    }

    toNumberState(number) {
        this.#currentState = this.States.numberDetected;
        this.addNumber(number);
    }

    toDeadState() {
        this.#currentState = this.States.deadState;
    }

    addNumber(number) {
        if (
            this.#computedValue > Math.floor(this.#MAX_INT / 10) ||
            (this.#computedValue == Math.floor(this.#MAX_INT / 10) &&
                number > this.#MAX_INT % 10)
        ) {
            if (this.#valueSign == 1) {
                this.#computedValue = this.#MAX_INT;
            } else {
                this.#computedValue = this.#MIN_INT;
                this.#valueSign = 1;
            }
            this.toDeadState();
        } else {
            this.#computedValue = this.#computedValue * 10 + number;
        }
    }

    transition(symbol) {
        if (this.#currentState == this.States.initial) {
            if (symbol == " ") {
                return;
            } else if (symbol == "-" || symbol == "+") {
                this.toInitialSignState(symbol);
            } else if (symbol >= "0" && symbol <= "9") {
                this.toNumberState(symbol - "0");
            } else {
                this.toDeadState();
            }
        } else if (
            this.#currentState == this.States.signDetected ||
            this.#currentState == this.States.numberDetected
        ) {
            if (symbol >= "0" && symbol <= "9") {
                this.toNumberState(symbol - "0");
            } else {
                this.toDeadState();
            }
        }
    }

    getComputedValue() {
        return this.#valueSign * this.#computedValue;
    }

    getCurrentState() {
        return this.#currentState;
    }
}

var myAtoi = function (str) {
    let parser = new StringParser();

    for (let index = 0; index < str.length && parser.getCurrentState() != parser.States.deadState; ++index) {
        parser.transition(str[index]);
    }

    return parser.getComputedValue();
};

The provided solution implements a string parser to convert a string containing numerical values into integers, mimicking the behavior of the atoi function in JavaScript. The parser is carefully designed to handle various edge cases found in the string such as spaces, plus and minus signs, and non-digit characters. This method ensures only valid number strings are converted to integers, while invalid characters transition the parser to a dead state, stopping further processing.

Here's the step-by-step breakdown on how the function works:

An instance of StringParser starts in the initial state and awaits characters to process.
Each character from the input string transitions the parser to different states (initial, signDetected, numberDetected, deadState):
- If encountering a space in the initial state, continue without changing the state.
- A '+' or '-' sign transitions the parser to signDetected establishing the number's sign.
- Numeric characters move the parser to numberDetected where the number is constructed.
- Any invalid character shifts the parser to the deadState, stopping further processing.
The number construction in numberDetected state properly handles large values by comparing against maximum and minimum int values, adjusting the computed value and transitioning to deadState if overflow/underflow is about to occur.
The final computed integer value respects the sign detected and is computed correctly within the range boundaries defined by 32-bit signed integer representation.

This robust implementation efficiently processes the string by adhering to complex state transition rules and safeguards against various invalid inputs, ensuring correct integer representation or early termination in cases where conversion is not applicable.

                            python
                            
                        
class Automaton:
    def __init__(self):
        self.states = {"start": 1, "signed": 2, "in_number": 3, "end": 4}
        self.MAX_INT, self.MIN_INT = 2147483647, -2147483648

        self.current_state = self.states["start"]
        self.total = 0
        self.sign = 1

    def transition_to_signed(self, character: chr) -> None:
        self.sign = -1 if character == "-" else 1
        self.current_state = self.states["signed"]

    def transition_to_in_number(self, value: int) -> None:
        self.current_state = self.states["in_number"]
        self.add_digit(value)

    def transition_to_end(self) -> None:
        self.current_state = self.states["end"]

    def add_digit(self, digit: int) -> None:
        if (self.total > self.MAX_INT // 10) or (self.total == self.MAX_INT // 10 and digit > self.MAX_INT % 10):
            if self.sign == 1:
                self.total = self.MAX_INT
            else:
                self.total = self.MIN_INT
            self.transition_to_end()
        else:
            self.total = (self.total * 10) + digit

    def proceed(self, character: chr) -> None:
        if self.current_state == self.states["start"]:
            if character == " ":
                return
            elif character == "-" or character == "+":
                self.transition_to_signed(character)
            elif character.isdigit():
                self.transition_to_in_number(int(character))
            else:
                self.transition_to_end()

        elif self.current_state in [self.states["signed"], self.states["in_number"]]:
            if character.isdigit():
                self.transition_to_in_number(int(character))
            else:
                self.transition_to_end()

    def compute_result(self) -> int:
        return self.sign * self.total

    def get_current_state(self) -> int:
        return self.current_state


class Solution:
    def string_to_integer(self, data: str) -> int:
        automaton = Automaton()

        for char in data:
            automaton.proceed(char)
            if automaton.get_current_state() == automaton.states["end"]:
                break

        return automaton.compute_result()

The provided Python code implements a function string_to_integer that converts a string into an integer, mimicking the atoi (ASCII to integer) function in the C programming language. The main components of this code are:

Automaton Class:
- Manages state transitions and numeric calculations based on current state and input character. States include "start", "signed", "in_number", and "end".
- The proceed method directs the state transition and processes the characters to form the integer. Space characters are ignored in the "start" state, while "+" or "-" initiate a signed number processing. Numeric characters cause a transition to or continuation of the "in_number" state.
- Overflow conditions are handled during the number formation. It ensures that the number does not exceed the bounds of a 32-bit signed integer.
Solution Class:
- Contains the string_to_integer function which utilizes the Automaton class to parse the input string.
- Iterates through each character of the input string, using the automatons proceed method to process and evaluate the character based on the current state of the automaton.

This implementation effectively captures and converts valid numeric strings while managing potential edge cases like space management, signs, and integer overflow. Full functionality is achieved through careful state management and character handling inside the Automaton class.

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String to Integer (atoi)

Problem Statement

Examples

Example 1

Example 2

Example 3

Example 4

Example 5

Constraints

Approach and Intuition

Example-Based Explanation:

Solutions

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