Add PrefixToInfix.java new algorithm (#5552)

* Add `PrefixToInfix.java` new algorithm

* Update directory

* Fix clang error

* Update directory

* Fix comment

* Add suggested changes

---------

Co-authored-by: Hardvan <Hardvan@users.noreply.github.com>
Co-authored-by: Alex Klymenko <alexanderklmn@gmail.com>

DIRECTORY.md

@@ -552,6 +552,7 @@
             * [NextGreaterElement](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/stacks/NextGreaterElement.java)
             * [NextSmallerElement](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/stacks/NextSmallerElement.java)
             * [PostfixToInfix](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/stacks/PostfixToInfix.java)
+            * [PrefixToInfix](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/stacks/PrefixToInfix.java)
             * [StackPostfixNotation](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/stacks/StackPostfixNotation.java)
           * strings
             * [AhoCorasick](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/strings/AhoCorasick.java)
@@ -984,6 +985,7 @@
             * [NextGreaterElementTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/stacks/NextGreaterElementTest.java)
             * [NextSmallerElementTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/stacks/NextSmallerElementTest.java)
             * [PostfixToInfixTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/stacks/PostfixToInfixTest.java)
+            * [PrefixToInfixTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/stacks/PrefixToInfixTest.java)
             * [StackPostfixNotationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/stacks/StackPostfixNotationTest.java)
           * strings
             * [AhoCorasickTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/strings/AhoCorasickTest.java)

src/main/java/com/thealgorithms/stacks/PrefixToInfix.java

@@ -0,0 +1,69 @@
+package com.thealgorithms.stacks;
+
+import java.util.Stack;
+
+/**
+ * Converts a prefix expression to an infix expression using a stack.
+ *
+ * The input prefix expression should consist of
+ * valid operands (letters or digits) and operators (+, -, *, /, ^).
+ * Parentheses are not required in the prefix string.
+ */
+public final class PrefixToInfix {
+    private PrefixToInfix() {
+    }
+
+    /**
+     * Determines if a given character is a valid arithmetic operator.
+     *
+     * @param token the character to check
+     * @return true if the character is an operator, false otherwise
+     */
+    public static boolean isOperator(char token) {
+        return token == '+' || token == '-' || token == '/' || token == '*' || token == '^';
+    }
+
+    /**
+     * Converts a valid prefix expression to an infix expression.
+     *
+     * @param prefix the prefix expression to convert
+     * @return the equivalent infix expression
+     * @throws NullPointerException     if the prefix expression is null
+     */
+    public static String getPrefixToInfix(String prefix) {
+        if (prefix == null) {
+            throw new NullPointerException("Null prefix expression");
+        }
+        if (prefix.isEmpty()) {
+            return "";
+        }
+
+        Stack<String> stack = new Stack<>();
+
+        // Iterate over the prefix expression from right to left
+        for (int i = prefix.length() - 1; i >= 0; i--) {
+            char token = prefix.charAt(i);
+
+            if (isOperator(token)) {
+                // Pop two operands from stack
+                String operandA = stack.pop();
+                String operandB = stack.pop();
+
+                // Form the infix expression with parentheses
+                String infix = "(" + operandA + token + operandB + ")";
+
+                // Push the resulting infix expression back onto the stack
+                stack.push(infix);
+            } else {
+                // Push operand onto stack
+                stack.push(Character.toString(token));
+            }
+        }
+
+        if (stack.size() != 1) {
+            throw new ArithmeticException("Malformed prefix expression");
+        }
+
+        return stack.pop(); // final element on the stack is the full infix expression
+    }
+}

src/test/java/com/thealgorithms/stacks/PrefixToInfixTest.java

@@ -0,0 +1,44 @@
+package com.thealgorithms.stacks;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.util.stream.Stream;
+import org.junit.jupiter.api.Test;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.Arguments;
+import org.junit.jupiter.params.provider.MethodSource;
+
+class PrefixToInfixTest {
+
+    @ParameterizedTest
+    @MethodSource("provideValidPrefixToInfixTestCases")
+    void testValidPrefixToInfixConversion(String prefix, String expectedInfix) {
+        assertEquals(expectedInfix, PrefixToInfix.getPrefixToInfix(prefix));
+    }
+
+    static Stream<Arguments> provideValidPrefixToInfixTestCases() {
+        return Stream.of(Arguments.of("A", "A"), // Single operand
+            Arguments.of("+AB", "(A+B)"), // Addition
+            Arguments.of("*+ABC", "((A+B)*C)"), // Addition and multiplication
+            Arguments.of("-+A*BCD", "((A+(B*C))-D)"), // Mixed operators
+            Arguments.of("/-A*BC+DE", "((A-(B*C))/(D+E))"), // Mixed operators
+            Arguments.of("^+AB*CD", "((A+B)^(C*D))") // Mixed operators
+        );
+    }
+
+    @Test
+    void testEmptyPrefixExpression() {
+        assertEquals("", PrefixToInfix.getPrefixToInfix(""));
+    }
+
+    @Test
+    void testNullPrefixExpression() {
+        assertThrows(NullPointerException.class, () -> PrefixToInfix.getPrefixToInfix(null));
+    }
+
+    @Test
+    void testMalformedPrefixExpression() {
+        assertThrows(ArithmeticException.class, () -> PrefixToInfix.getPrefixToInfix("+ABC"));
+    }
+}