Merge pull request #18893 from nikhil1980/BAEL-8807

BAEL-8807: Check if a number can be written as a sum of two squares i…

Author: davidmartinezbarua

algorithms-modules/algorithms-numeric/src/main/java/com/baeldung/algorithms/sumoftwosquares/NumberAsSumOfTwoSquares.java

@@ -0,0 +1,59 @@
+package com.baeldung.algorithms.sumoftwosquares;
+
+import org.slf4j.Logger;
+import org.slf4j.LoggerFactory;
+
+public class NumberAsSumOfTwoSquares {
+
+    private static final Logger LOGGER = LoggerFactory.getLogger(NumberAsSumOfTwoSquares.class);
+
+    /**
+     * Checks if a non-negative integer n can be written as the
+     * sum of two squares i.e. (a^2 + b^2)
+     * This implementation is based on Fermat's theorem on sums of two squares.
+     *
+     * @param n The number to check (must be non-negative).
+     * @return true if n can be written as a sum of two squares, false otherwise.
+     */
+    public static boolean isSumOfTwoSquares(int n) {
+        if (n < 0) {
+            LOGGER.warn("Input must be non-negative. Returning false for n = {}", n);
+            return false;
+        }
+        if (n == 0) {
+            return true; // 0 = 0^2 + 0^2
+        }
+
+        // 1. Reduce n to an odd number if n is even.
+        while (n % 2 == 0) {
+            n /= 2;
+        }
+
+        // 2. Iterate through odd prime factors starting from 3
+        for (int i = 3; i * i <= n; i += 2) {
+            // 2a. Find the exponent of the factor i
+            int count = 0;
+            while (n % i == 0) {
+                count++;
+                n /= i;
+            }
+
+            // 2b. Check the condition from Fermat's theorem
+            // If i is of form 4k+3 (i % 4 == 3) and has an odd exponent
+            if (i % 4 == 3 && count % 2 != 0) {
+                LOGGER.debug("Failing condition: factor {} (form 4k+3) has odd exponent {}", i, count);
+                return false;
+            }
+        }
+
+        // 3. Handle the last remaining factor (which is prime if > 1)
+        // If n itself is a prime of the form 4k+3, its exponent is 1 (odd).
+        if (n % 4 == 3) {
+            LOGGER.debug("Failing condition: remaining factor {} is of form 4k+3", n);
+            return false;
+        }
+
+        // 4. All 4k+3 primes had even exponents.
+        return true;
+    }
+}

algorithms-modules/algorithms-numeric/src/test/java/com/baeldung/algorithms/sumoftwosquares/NumberAsSumOfTwoSquaresUnitTest.java

@@ -0,0 +1,47 @@
+package com.baeldung.algorithms.sumoftwosquares;
+
+import org.junit.jupiter.api.Test;
+import org.junit.jupiter.api.DisplayName;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+import static org.junit.jupiter.api.Assertions.assertFalse;
+
+
+class NumberAsSumOfTwoSquaresUnitTest {
+
+    @Test
+    @DisplayName("Given input number can be expressed as a sum of squares, when checked, then returns true")
+    void givenNumberIsSumOfSquares_whenCheckIsCalled_thenReturnsTrue() {
+        // Simple cases
+        assertTrue(NumberAsSumOfTwoSquares.isSumOfTwoSquares(0)); // 0^2 + 0^2
+        assertTrue(NumberAsSumOfTwoSquares.isSumOfTwoSquares(1)); // 1^2 + 0^2
+        assertTrue(NumberAsSumOfTwoSquares.isSumOfTwoSquares(5)); // 1^2 + 2^2
+        assertTrue(NumberAsSumOfTwoSquares.isSumOfTwoSquares(8)); // 2^2 + 2^2
+
+        // Cases from Fermat theorem
+        assertTrue(NumberAsSumOfTwoSquares.isSumOfTwoSquares(50)); // 2 * 5^2. No 4k+3 primes.
+        assertTrue(NumberAsSumOfTwoSquares.isSumOfTwoSquares(45)); // 3^2 * 5. 4k+3 prime (3) has even exp.
+        assertTrue(NumberAsSumOfTwoSquares.isSumOfTwoSquares(18)); // 2 * 3^2. 4k+3 prime (3) has even exp.
+    }
+
+    @Test
+    @DisplayName("Given input number can't be expressed as a sum of squares, when checked, then returns false")
+    void givenNumberIsNotSumOfSquares_whenCheckIsCalled_thenReturnsFalse() {
+        // Simple cases
+        assertFalse(NumberAsSumOfTwoSquares.isSumOfTwoSquares(3));  // 3 (4k+3, exp 1)
+        assertFalse(NumberAsSumOfTwoSquares.isSumOfTwoSquares(6));  // 2 * 3 (3 has exp 1)
+        assertFalse(NumberAsSumOfTwoSquares.isSumOfTwoSquares(7));  // 7 (4k+3, exp 1)
+        assertFalse(NumberAsSumOfTwoSquares.isSumOfTwoSquares(11)); // 11 (4k+3, exp 1)
+
+        // Cases from theorem
+        assertFalse(NumberAsSumOfTwoSquares.isSumOfTwoSquares(12)); // 2^2 * 3 (3 has exp 1)
+        assertFalse(NumberAsSumOfTwoSquares.isSumOfTwoSquares(21)); // 3 * 7 (both 3 and 7 have exp 1)
+        assertFalse(NumberAsSumOfTwoSquares.isSumOfTwoSquares(28)); // 2^2 * 7 (7 has exp 1)
+    }
+
+    @Test
+    @DisplayName("Given input number is negative, when checked, then returns false")
+    void givenNegativeNumber_whenCheckIsCalled_thenReturnsFalse() {
+        assertFalse(NumberAsSumOfTwoSquares.isSumOfTwoSquares(-1)); // Negatives as hygiene
+        assertFalse(NumberAsSumOfTwoSquares.isSumOfTwoSquares(-10)); // Negatives as hygiene
+    }
+}