From 6f46fe956145953597cbde4c05ccbf723ce3090d Mon Sep 17 00:00:00 2001
From: ardallie <ardallie@outlook.com>
Date: Wed, 18 Aug 2021 00:18:55 +0100
Subject: [PATCH 1/3] Calculator

---
 src/hard/Calculator.java | 259 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 259 insertions(+)
 create mode 100644 src/hard/Calculator.java

diff --git a/src/hard/Calculator.java b/src/hard/Calculator.java
new file mode 100644
index 0000000..35831de
--- /dev/null
+++ b/src/hard/Calculator.java
@@ -0,0 +1,259 @@
+package hard;
+
+import java.util.ArrayList;
+import java.util.Dictionary;
+import java.util.Hashtable;
+import java.util.Stack;
+import java.util.regex.Matcher;
+import java.util.regex.Pattern;
+
+/**
+ * Have the function Calculator(str) take the str parameter being passed
+ * and evaluate the mathematical expression within in.
+ * For example, if str were "2+(3-1)*3" the output should be 8.
+ * Another example: if str were "(2-0)(6/2)" the output should be 6.
+ * There can be parenthesis within the string, so you must evaluate it
+ * properly according to the rules of arithmetic.
+ * The string will contain the operators: +, -, /, *, (, and ).
+ * If you have a string like this: #/#*# or #+#(#)/#,
+ * then evaluate from left to right. So divide then multiply,
+ * and for the second one multiply, divide, then add.
+ * The evaluations will be such that there will not be any decimal operations,
+ * so you do not need to account for rounding and whatnot.
+ */
+class Calculator {
+
+  // evaluate the Postfix expression
+  private static final Stack<String> stack = new Stack<>();
+
+  /**
+   * Cleaning, parsing and splitting the input string into the array of tokens
+   * 1. convert to lowercase
+   * 2. replace (a)(b) with (a) * (b)
+   * 3. replace a(b) with a * (b)
+   * 4. split two bundled characters (but only when the second character is not a digit)
+   * 5. split bundled command/operator and a digit. Excl. minus to keep negative numbers intact.
+   * 6. remove multiple spaces
+   * 7. trim (remove leading and trailing spaces)
+   * 8. split to array of strings
+   *
+   * @param input input string
+   * @return array of strings with parsed operators and operands
+   */
+  private static String[] parseConsoleInput(String input) {
+    return input
+        .toLowerCase()
+        .replaceAll("(\\)\\()", ") * (")
+        .replaceAll("([0-9])(?=[(])", "$1 *")
+        .replaceAll("([\\p{P}\\p{S}a-z0-9])(?=[\\p{P}\\p{S}a-z])", "$1 ")
+        .replaceAll("([^0-9])(?=[0-9])", "$1 ")
+        .replaceAll(" +", " ")
+        .trim()
+        .split(" ");
+  }
+
+  /**
+   * Prints out a message to the console if the user input is invalid.
+   *
+   * @param op single element of the input string
+   */
+  private static void printInputError(String op) {
+    System.out.println("Unrecognised operator or operand: \"" + op + "\".");
+  }
+
+  /**
+   * Reduces two operands to a single result
+   * by performing an arithmetical operation.
+   *
+   * @param a        operand A
+   * @param b        operand B
+   * @param operator denotes operation type (addition, substraction, division etc.)
+   * @return result of the arithmetical operation
+   * @throws ArithmeticException if divisor is 0
+   */
+  public static long reduceOperands(long a, long b, String operator) {
+    switch (operator) {
+      case "+":
+        return a + b;
+      case "-":
+        return a - b;
+      case "*":
+        return a * b;
+      case "/":
+        if (b == 0) {
+          System.out.println("Divide by 0.");
+          throw new ArithmeticException();
+        }
+        return a / b;
+      default:
+        return 0;
+    }
+  }
+
+  /**
+   * Checks if the token is an operand (0-9).
+   *
+   * @param op a single token from the input string
+   * @return true if the token is an operand, false if not
+   */
+  private static boolean isOperand(String op) {
+    Pattern pattern = Pattern.compile("^[\\d]|^-[\\d]");
+    Matcher matcher = pattern.matcher(op);
+    return matcher.find();
+  }
+
+  /**
+   * Checks if the token is an operator + - * / : ^ ( ) etc.
+   *
+   * @param op a single token from the input string
+   * @return true if the token is an operator, false if not
+   */
+  private static boolean isOperator(String op) {
+    Pattern pattern = Pattern.compile("^[+\\-*/^%]");
+    Matcher matcher = pattern.matcher(op);
+    return matcher.find();
+  }
+
+  /**
+   * Converts the Infix expression to Postfix.
+   *
+   * @param tokens expression tokens that are already parsed and split
+   */
+  private static String[] convertToPostfix(String[] tokens) {
+    Stack<String> infStack = new Stack<>();
+    String terminating = "#";
+    Dictionary<String, Integer> precedence = new Hashtable<>() {
+      {
+        put(terminating, 0);
+        put("(", 0);
+        put(")", 0);
+        put("+", 1);
+        put("-", 1);
+        put("*", 2);
+        put("/", 2);
+      }
+    };
+    ArrayList<String> output = new ArrayList<>();
+    infStack.push(terminating);
+    for (String token : tokens) {
+      // token is an operand, add to output and move on
+      if (isOperand(token)) {
+        output.add(token);
+        continue;
+      }
+      // left parenthesis, push it to stack and move on
+      if (token.equals("(")) {
+        infStack.push(token);
+        continue;
+      }
+      // right parenthesis, keep popping until the left parenthesis is found
+      if (token.equals(")")) {
+        while (true) {
+          String op = infStack.pop();
+          if (op.equals("(")) {
+            break;
+          } else {
+            output.add(op);
+          }
+        }
+        continue;
+      }
+      // token is an operator
+      if (isOperator(token)) {
+        int cmp1 = precedence.get(token);
+        while (true) {
+          int cmp2 = precedence.get(infStack.peek());
+          // operand has higher precedence than item on the top of stack
+          if (cmp1 > cmp2) {
+            infStack.push(token);
+            break;
+          } else {
+            output.add(infStack.pop());
+          }
+        }
+      }
+    }
+    // pop the remaining items until the terminating symbol is reached (complete)
+    while (!infStack.empty() && !infStack.peek().equals(terminating)) {
+      output.add(infStack.pop());
+    }
+    return output.toArray(new String[0]);
+  }
+
+  /**
+   * Takes two operands from stack and perform the operation with a provider operator.
+   *
+   * @param operator denotes operation type (addition, substraction, division etc.)
+   * @return result of the evaluation
+   */
+  private static String performArithOperation(String operator) {
+    if (stack.size() >= 2) {
+      // Safe to evaluate
+      String elementB = stack.pop();
+      String elementA = stack.pop();
+      long opB = Long.parseLong(elementB);
+      long opA = Long.parseLong(elementA);
+      long result = reduceOperands(opA, opB, operator);
+      return Long.toString(result);
+    } else {
+      // Stack underflow since at least one element is null
+      return null;
+    }
+  }
+
+  /**
+   * Computes the entire expression in Reverse Polish Notation.
+   *
+   * @param tokens expression tokens that are already parsed and split to Array of Strings
+   */
+  private static Long evaluateExpression(String[] tokens) {
+    for (String token : tokens) {
+      // token is an operand, push it to stack and move on
+      if (isOperand(token)) {
+        stack.push(token);
+        continue;
+      }
+      // token is an operator, evaluate
+      if (isOperator(token)) {
+        String result = performArithOperation(token);
+        if (result != null) {
+          stack.push(result);
+        }
+        continue;
+      }
+      // token is illegal
+      printInputError(token);
+    }
+    // all tokens have been processed
+    if (stack.isEmpty()) {
+      return null;
+    }
+    return Long.parseLong(stack.peek());
+  }
+
+
+  /**
+   * Calculate function.
+   *
+   * @param expression input to evaluate
+   * @return result of evaluation
+   */
+  public static String calculate(String expression) {
+    String[] tokens = parseConsoleInput(expression);
+    String[] postfix = convertToPostfix(tokens);
+    Long result = evaluateExpression(postfix);
+    return result == null ? "" : result.toString();
+  }
+
+  /**
+   * Entry point.
+   *
+   * @param args command line arguments
+   */
+  public static void main(String[] args) {
+    String expression = "8-7*(12+100/2)*9-2";
+    String result = calculate(expression);
+    System.out.println(result);
+  }
+
+}

From 282e696f4c5965c10bdf31b1280fa41e3180f2bf Mon Sep 17 00:00:00 2001
From: ardallie <ardallie@outlook.com>
Date: Wed, 18 Aug 2021 00:24:41 +0100
Subject: [PATCH 2/3] Reverse Polish Notation

---
 src/hard/ReversePolishNotation.java | 171 ++++++++++++++++++++++++++++
 1 file changed, 171 insertions(+)
 create mode 100644 src/hard/ReversePolishNotation.java

diff --git a/src/hard/ReversePolishNotation.java b/src/hard/ReversePolishNotation.java
new file mode 100644
index 0000000..9d25e16
--- /dev/null
+++ b/src/hard/ReversePolishNotation.java
@@ -0,0 +1,171 @@
+package hard;
+
+import java.util.Stack;
+import java.util.regex.Matcher;
+import java.util.regex.Pattern;
+
+/**
+ * Have the function ReversePolishNotation(str) read str which will be an arithmetic expression
+ * composed of only integers and the operators: +,-,* and /
+ * and the input expression will be in postfix notation (Reverse Polish notation),
+ * an example: (1 + 2) * 3 would be 1 2 + 3 * in postfix notation.
+ * Your program should determine the answer for the given postfix expression.
+ * For example: if str is 2 12 + 7 / then your program should output 2.
+ */
+class ReversePolishNotation {
+
+  private static final Stack<String> stack = new Stack<>();
+
+  /**
+   * Cleaning, parsing and splitting the input string into the array of tokens.
+   * 1. convert to lowercase
+   * 2. remove multiple spaces
+   * 3. split two bundled characters (but only when the second character is not a digit)
+   * 4. split bundled command/operator and a digit. Excl. minus to keep negative numbers intact.
+   * 5. trim (remove leading and trailing spaces)
+   * 6. split to array of strings
+   *
+   * @param input input string
+   * @return String array with parsed operators and operands
+   */
+  private static String[] parseConsoleInput(String input) {
+    return input
+        .toLowerCase()
+        .replaceAll(" +", " ")
+        .replaceAll("([\\p{P}\\p{S}a-z0-9])(?=[\\p{P}\\p{S}a-z])", "$1 ")
+        .replaceAll("([^- 0-9])(?=[0-9])", "$1 ")
+        .trim()
+        .split(" ");
+  }
+
+  /**
+   * Prints out a message to the console if the user input is invalid.
+   *
+   * @param op single element of the input string
+   */
+  private static void printInputError(String op) {
+    System.out.println("Unrecognised operator or operand: \"" + op + "\".");
+  }
+
+  /**
+   * Reduces two operands to a single result
+   * by performing an arithmetical operation.
+   *
+   * @param a        operand A
+   * @param b        operand B
+   * @param operator denotes operation type (addition, substraction, division etc.)
+   * @return result of the arithmetical operation
+   * @throws ArithmeticException if divisor is 0
+   */
+  public static long reduceOperands(long a, long b, String operator) {
+    switch (operator) {
+      case "+":
+        return a + b;
+      case "-":
+        return a - b;
+      case "*":
+        return a * b;
+      case "/":
+        if (b == 0) {
+          System.out.println("Divide by 0.");
+          throw new ArithmeticException();
+        }
+        return a / b;
+      default:
+        return 0;
+    }
+  }
+
+  /**
+   * Checks if the token is an operand (0-9).
+   *
+   * @param op a single token from the input string
+   * @return true if the token is an operand, false if not
+   */
+  private static boolean isOperand(String op) {
+    Pattern pattern = Pattern.compile("^[\\d]|^-[\\d]");
+    Matcher matcher = pattern.matcher(op);
+    return matcher.find();
+  }
+
+  /**
+   * Checks if the token is an operator + - * / : ^ ( ) etc.
+   *
+   * @param op a single token from the input string
+   * @return true if the token is an operator, false if not
+   */
+  private static boolean isOperator(String op) {
+    Pattern pattern = Pattern.compile("^[+\\-*/^%]");
+    Matcher matcher = pattern.matcher(op);
+    return matcher.find();
+  }
+
+  /**
+   * Takes two operands from stack and perform the operation with a provider operator.
+   *
+   * @param operator denotes operation type (addition, substraction, division etc.)
+   * @return result of the evaluation
+   */
+  private static String performArithOperation(String operator) {
+    if (stack.size() >= 2) {
+      // Safe to evaluate
+      String elementB = stack.pop();
+      String elementA = stack.pop();
+      long opB = Long.parseLong(elementB);
+      long opA = Long.parseLong(elementA);
+      long result = reduceOperands(opA, opB, operator);
+      return Long.toString(result);
+    } else {
+      // Stack underflow since at least one element is null
+      return null;
+    }
+  }
+
+  /**
+   * Computes the entire expression in Reverse Polish Notation.
+   *
+   * @param tokens expression tokens that are already parsed and split to Array of Strings
+   */
+  private static Long evaluateExpression(String[] tokens) {
+    for (String token : tokens) {
+      // token is an operand, push it to stack and move on
+      if (isOperand(token)) {
+        stack.push(token);
+        continue;
+      }
+      // token is an operator, evaluate
+      if (isOperator(token)) {
+        String result = performArithOperation(token);
+        if (result != null) {
+          stack.push(result);
+        }
+        continue;
+      }
+      // token is illegal
+      printInputError(token);
+    }
+    // all tokens have been processed
+    if (stack.isEmpty()) {
+      return null;
+    }
+    return Long.parseLong(stack.peek());
+  }
+
+  public static String reversePolishNotation(String expression) {
+    String[] tokens = parseConsoleInput(expression);
+    Long result = evaluateExpression(tokens);
+    return result == null ? "" : result.toString();
+  }
+
+  /**
+   * Entry point.
+   *
+   * @param args command line arguments
+   */
+  public static void main(String[] args) {
+    String expression = "1 1 + 1 + 1 +";
+    String result = reversePolishNotation(expression);
+    System.out.println(result);
+  }
+
+}

From fe1c8e2439efd34124fcb30091260d4aec8788a7 Mon Sep 17 00:00:00 2001
From: ardallie <ardallie@outlook.com>
Date: Wed, 18 Aug 2021 00:34:19 +0100
Subject: [PATCH 3/3] Roman Numeral Reduction

---
 src/hard/RomanNumReduction.java | 91 +++++++++++++++++++++++++++++++++
 1 file changed, 91 insertions(+)
 create mode 100644 src/hard/RomanNumReduction.java

diff --git a/src/hard/RomanNumReduction.java b/src/hard/RomanNumReduction.java
new file mode 100644
index 0000000..389ebef
--- /dev/null
+++ b/src/hard/RomanNumReduction.java
@@ -0,0 +1,91 @@
+package hard;
+
+import java.util.HashMap;
+
+/**
+ * Have the function RomanNumeralReduction(str) read str
+ * which will be a string of roman numerals in decreasing order.
+ * The numerals being used are: I for 1, V for 5, X for 10,
+ * L for 50, C for 100, D for 500 and M for 1000.
+ * Your program should return the same number given
+ * by str using a smaller set of roman numerals.
+ * For example: if str is "LLLXXXVVVV" this is 200, so your program should return CC
+ * because this is the shortest way to write 200 using the roman numeral system given above.
+ * If a string is given in its shortest form, just return that same string.
+ */
+public class RomanNumReduction {
+
+  private static final HashMap<String, Integer> romans = new HashMap<>() {
+    {
+      put("M", 1000);
+      put("D", 500);
+      put("C", 100);
+      put("L", 50);
+      put("X", 10);
+      put("V", 5);
+      put("I", 1);
+    }
+  };
+
+  private static final String[] orderedRomans = new String[]{"M", "D", "C", "L", "X", "V", "I"};
+
+  /**
+   * Calculate the sum for an expression.
+   *
+   * @param exp expression
+   * @return a sum
+   */
+  public static int sumRomans(String exp) {
+    int result = 0;
+    String[] tokens = exp.toUpperCase().split("");
+    for (String token : tokens) {
+      result += romans.get(token);
+    }
+    return result;
+  }
+
+  /**
+   * Reduce Roman numerals.
+   *
+   * @param sum a number
+   * @return a string of Roman numerals
+   */
+  public static String reduceRomans(int sum) {
+    StringBuilder output = new StringBuilder();
+    int remainder = sum;
+    for (String numeral : orderedRomans) {
+      Integer val = romans.get(numeral);
+      while (remainder / val >= 0 && remainder - val >= 0) {
+        output.append(numeral);
+        remainder -= val;
+      }
+    }
+    return output.toString();
+  }
+
+  /**
+   * Roman Numeral Reduction function.
+   *
+   * @param str input string
+   * @return result
+   */
+  public static String romanNumeralReduction(String str) {
+    int sum = sumRomans(str);
+    return reduceRomans(sum);
+  }
+
+  /**
+   * Entry point.
+   *
+   * @param args command line arguments
+   */
+  public static void main(String[] args) {
+    String result1 = romanNumeralReduction("XXXVVIIIIIIIIII");
+    System.out.println(result1);
+    String result2 = romanNumeralReduction("VVV");
+    System.out.println(result2);
+    String result3 = romanNumeralReduction("CCCCCIIIII");
+    System.out.println(result3);
+  }
+
+}

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