CS-378 Find kth smallest element in union of two sorted arrays (#9812)
* CS-378 Find the Kth Smallest Element in the Union of Two Sorted Arrays * CS-378 Fix name of unit test * CS-378 Update merge algorithm to operate only on two input arrays Co-authored-by: mikr <michael.krimgen@ximedes.com>
This commit is contained in:
Maiklins
GitHub
parent
459662daf6
commit
9ca1a0064a
|
|
@ -0,0 +1,126 @@
|
|||
package com.baeldung.algorithms.kthsmallest;
|
||||
|
||||
import java.util.Arrays;
|
||||
import java.util.NoSuchElementException;
|
||||
|
||||
import static java.lang.Math.max;
|
||||
import static java.lang.Math.min;
|
||||
|
||||
public class KthSmallest {
|
||||
|
||||
public static int findKthSmallestElement(int k, int[] list1, int[] list2) throws NoSuchElementException, IllegalArgumentException {
|
||||
|
||||
checkInput(k, list1, list2);
|
||||
|
||||
// we are looking for the minimum value
|
||||
if(k == 1) {
|
||||
return min(list1[0], list2[0]);
|
||||
}
|
||||
|
||||
// we are looking for the maximum value
|
||||
if(list1.length + list2.length == k) {
|
||||
return max(list1[list1.length-1], list2[list2.length-1]);
|
||||
}
|
||||
|
||||
// swap lists if needed to make sure we take at least one element from list1
|
||||
if(k <= list2.length && list2[k-1] < list1[0]) {
|
||||
int[] list1_ = list1;
|
||||
list1 = list2;
|
||||
list2 = list1_;
|
||||
}
|
||||
|
||||
// correct left boundary if k is bigger than the size of list2
|
||||
int left = k < list2.length ? 0 : k - list2.length - 1;
|
||||
|
||||
// the inital right boundary cannot exceed the list1
|
||||
int right = min(k-1, list1.length - 1);
|
||||
|
||||
int nElementsList1, nElementsList2;
|
||||
|
||||
// binary search
|
||||
do {
|
||||
nElementsList1 = ((left + right) / 2) + 1;
|
||||
nElementsList2 = k - nElementsList1;
|
||||
|
||||
if(nElementsList2 > 0) {
|
||||
if (list1[nElementsList1 - 1] > list2[nElementsList2 - 1]) {
|
||||
right = nElementsList1 - 2;
|
||||
} else {
|
||||
left = nElementsList1;
|
||||
}
|
||||
}
|
||||
} while(!kthSmallesElementFound(list1, list2, nElementsList1, nElementsList2));
|
||||
|
||||
return nElementsList2 == 0 ? list1[nElementsList1-1] : max(list1[nElementsList1-1], list2[nElementsList2-1]);
|
||||
}
|
||||
|
||||
private static boolean kthSmallesElementFound(int[] list1, int[] list2, int nElementsList1, int nElementsList2) {
|
||||
|
||||
// we do not take any element from the second list
|
||||
if(nElementsList2 < 1) {
|
||||
return true;
|
||||
}
|
||||
|
||||
if(list1[nElementsList1-1] == list2[nElementsList2-1]) {
|
||||
return true;
|
||||
}
|
||||
|
||||
if(nElementsList1 == list1.length) {
|
||||
return list1[nElementsList1-1] <= list2[nElementsList2];
|
||||
}
|
||||
|
||||
if(nElementsList2 == list2.length) {
|
||||
return list2[nElementsList2-1] <= list1[nElementsList1];
|
||||
}
|
||||
|
||||
return list1[nElementsList1-1] <= list2[nElementsList2] && list2[nElementsList2-1] <= list1[nElementsList1];
|
||||
}
|
||||
|
||||
|
||||
private static void checkInput(int k, int[] list1, int[] list2) throws NoSuchElementException, IllegalArgumentException {
|
||||
|
||||
if(list1 == null || list2 == null || k < 1) {
|
||||
throw new IllegalArgumentException();
|
||||
}
|
||||
|
||||
if(list1.length == 0 || list2.length == 0) {
|
||||
throw new IllegalArgumentException();
|
||||
}
|
||||
|
||||
if(k > list1.length + list2.length) {
|
||||
throw new NoSuchElementException();
|
||||
}
|
||||
}
|
||||
|
||||
public static int getKthElementSorted(int[] list1, int[] list2, int k) {
|
||||
|
||||
int length1 = list1.length, length2 = list2.length;
|
||||
int[] combinedArray = new int[length1 + length2];
|
||||
System.arraycopy(list1, 0, combinedArray, 0, list1.length);
|
||||
System.arraycopy(list2, 0, combinedArray, list1.length, list2.length);
|
||||
Arrays.sort(combinedArray);
|
||||
|
||||
return combinedArray[k-1];
|
||||
}
|
||||
|
||||
public static int getKthElementMerge(int[] list1, int[] list2, int k) {
|
||||
|
||||
int i1 = 0, i2 = 0;
|
||||
|
||||
while(i1 < list1.length && i2 < list2.length && (i1 + i2) < k) {
|
||||
if(list1[i1] < list2[i2]) {
|
||||
i1++;
|
||||
} else {
|
||||
i2++;
|
||||
}
|
||||
}
|
||||
|
||||
if((i1 + i2) < k) {
|
||||
return i1 < list1.length ? list1[k - i2 - 1] : list2[k - i1 - 1];
|
||||
} else if(i1 > 0 && i2 > 0) {
|
||||
return Math.max(list1[i1-1], list2[i2-1]);
|
||||
} else {
|
||||
return i1 == 0 ? list2[i2-1] : list1[i1-1];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,288 @@
|
|||
package com.baeldung.algorithms.kthsmallest;
|
||||
|
||||
import org.junit.jupiter.api.Nested;
|
||||
import org.junit.jupiter.api.Test;
|
||||
import org.junit.jupiter.api.function.Executable;
|
||||
|
||||
import java.util.*;
|
||||
|
||||
import static com.baeldung.algorithms.kthsmallest.KthSmallest.*;
|
||||
import static org.junit.jupiter.api.Assertions.*;
|
||||
|
||||
public class KthSmallestUnitTest {
|
||||
|
||||
@Nested
|
||||
class Exceptions {
|
||||
|
||||
@Test
|
||||
public void when_at_least_one_list_is_null_then_an_exception_is_thrown() {
|
||||
|
||||
Executable executable1 = () -> findKthSmallestElement(1, null, null);
|
||||
Executable executable2 = () -> findKthSmallestElement(1, new int[]{2}, null);
|
||||
Executable executable3 = () -> findKthSmallestElement(1, null, new int[]{2});
|
||||
|
||||
assertThrows(IllegalArgumentException.class, executable1);
|
||||
assertThrows(IllegalArgumentException.class, executable2);
|
||||
assertThrows(IllegalArgumentException.class, executable3);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_at_least_one_list_is_empty_then_an_exception_is_thrown() {
|
||||
|
||||
Executable executable1 = () -> findKthSmallestElement(1, new int[]{}, new int[]{2});
|
||||
Executable executable2 = () -> findKthSmallestElement(1, new int[]{2}, new int[]{});
|
||||
Executable executable3 = () -> findKthSmallestElement(1, new int[]{}, new int[]{});
|
||||
|
||||
assertThrows(IllegalArgumentException.class, executable1);
|
||||
assertThrows(IllegalArgumentException.class, executable2);
|
||||
assertThrows(IllegalArgumentException.class, executable3);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_k_is_smaller_than_0_then_an_exception_is_thrown() {
|
||||
Executable executable1 = () -> findKthSmallestElement(-1, new int[]{2}, new int[]{2});
|
||||
assertThrows(IllegalArgumentException.class, executable1);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_k_is_smaller_than_1_then_an_exception_is_thrown() {
|
||||
Executable executable1 = () -> findKthSmallestElement(0, new int[]{2}, new int[]{2});
|
||||
assertThrows(IllegalArgumentException.class, executable1);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_k_bigger_then_the_two_lists_then_an_exception_is_thrown() {
|
||||
Executable executable1 = () -> findKthSmallestElement(6, new int[]{1, 5, 6}, new int[]{2, 5});
|
||||
assertThrows(NoSuchElementException.class, executable1);
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
@Nested
|
||||
class K_is_smaller_than_the_size_of_list1_and_the_size_of_list2 {
|
||||
|
||||
@Test
|
||||
public void when_k_is_1_then_the_smallest_element_is_returned_from_list1() {
|
||||
int result = findKthSmallestElement(1, new int[]{2, 7}, new int[]{3, 5});
|
||||
assertEquals(2, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_k_is_1_then_the_smallest_element_is_returned_list2() {
|
||||
int result = findKthSmallestElement(1, new int[]{3, 5}, new int[]{2, 7});
|
||||
assertEquals(2, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_kth_element_is_smallest_element_and_occurs_in_both_lists() {
|
||||
int[] list1 = new int[]{1, 2, 3};
|
||||
int[] list2 = new int[]{1, 2, 3};
|
||||
int result = findKthSmallestElement(1, list1, list2);
|
||||
assertEquals(1, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_kth_element_is_smallest_element_and_occurs_in_both_lists2() {
|
||||
int[] list1 = new int[]{1, 2, 3};
|
||||
int[] list2 = new int[]{1, 2, 3};
|
||||
int result = findKthSmallestElement(2, list1, list2);
|
||||
assertEquals(1, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_kth_element_is_largest_element_and_occurs_in_both_lists_1() {
|
||||
int[] list1 = new int[]{1, 2, 3};
|
||||
int[] list2 = new int[]{1, 2, 3};
|
||||
int result = findKthSmallestElement(5, list1, list2);
|
||||
assertEquals(3, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_kth_element_is_largest_element_and_occurs_in_both_lists_2() {
|
||||
int[] list1 = new int[]{1, 2, 3};
|
||||
int[] list2 = new int[]{1, 2, 3};
|
||||
int result = findKthSmallestElement(6, list1, list2);
|
||||
assertEquals(3, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_kth_element_and_occurs_in_both_lists() {
|
||||
int[] list1 = new int[]{1, 2, 3};
|
||||
int[] list2 = new int[]{0, 2, 3};
|
||||
int result = findKthSmallestElement(3, list1, list2);
|
||||
assertEquals(2, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void and_kth_element_is_in_first_list() {
|
||||
int[] list1 = new int[]{1,2,3,4};
|
||||
int[] list2 = new int[]{1,3,4,5};
|
||||
int result = findKthSmallestElement(3, list1, list2);
|
||||
assertEquals(2, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void and_kth_is_in_second_list() {
|
||||
int[] list1 = new int[]{1,3,4,4};
|
||||
int[] list2 = new int[]{1,2,4,5};
|
||||
int result = findKthSmallestElement(3, list1, list2);
|
||||
assertEquals(2, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void and_elements_in_first_list_are_all_smaller_than_second_list() {
|
||||
int[] list1 = new int[]{1,3,7,9};
|
||||
int[] list2 = new int[]{11,12,14,15};
|
||||
int result = findKthSmallestElement(3, list1, list2);
|
||||
assertEquals(7, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void and_elements_in_first_list_are_all_smaller_than_second_list2() {
|
||||
int[] list1 = new int[]{1,3,7,9};
|
||||
int[] list2 = new int[]{11,12,14,15};
|
||||
int result = findKthSmallestElement(4, list1, list2);
|
||||
assertEquals(9, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void and_only_elements_from_second_list_are_part_of_result() {
|
||||
int[] list1 = new int[]{11,12,14,15};
|
||||
int[] list2 = new int[]{1,3,7,9};
|
||||
int result = findKthSmallestElement(3, list1, list2);
|
||||
assertEquals(7, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void and_only_elements_from_second_list_are_part_of_result2() {
|
||||
int[] list1 = new int[]{11,12,14,15};
|
||||
int[] list2 = new int[]{1,3,7,9};
|
||||
int result = findKthSmallestElement(4, list1, list2);
|
||||
assertEquals(9, result);
|
||||
}
|
||||
}
|
||||
|
||||
@Nested
|
||||
class K_is_bigger_than_the_size_of_at_least_one_of_the_lists {
|
||||
|
||||
@Test
|
||||
public void k_is_smaller_than_list1_and_bigger_than_list2() {
|
||||
int[] list1 = new int[]{1, 2, 3, 4, 7, 9};
|
||||
int[] list2 = new int[]{1, 2, 3};
|
||||
int result = findKthSmallestElement(5, list1, list2);
|
||||
assertEquals(3, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void k_is_bigger_than_list1_and_smaller_than_list2() {
|
||||
int[] list1 = new int[]{1, 2, 3};
|
||||
int[] list2 = new int[]{1, 2, 3, 4, 7, 9};
|
||||
int result = findKthSmallestElement(5, list1, list2);
|
||||
assertEquals(3, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_k_is_bigger_than_the_size_of_both_lists_and_elements_in_second_list_are_all_smaller_than_first_list() {
|
||||
int[] list1 = new int[]{9, 11, 13, 55};
|
||||
int[] list2 = new int[]{1, 2, 3, 7};
|
||||
int result = findKthSmallestElement(6, list1, list2);
|
||||
assertEquals(11, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_k_is_bigger_than_the_size_of_both_lists_and_elements_in_second_list_are_all_bigger_than_first_list() {
|
||||
int[] list1 = new int[]{1, 2, 3, 7};
|
||||
int[] list2 = new int[]{9, 11, 13, 55};
|
||||
int result = findKthSmallestElement(6, list1, list2);
|
||||
assertEquals(11, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_k_is_bigger_than_the_size_of_both_lists() {
|
||||
int[] list1 = new int[]{3, 7, 9, 11, 55};
|
||||
int[] list2 = new int[]{1, 2, 3, 7, 13};
|
||||
int result = findKthSmallestElement(7, list1, list2);
|
||||
assertEquals(9, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_k_is_bigger_than_the_size_of_both_lists_and_list1_has_more_elements_than_list2() {
|
||||
int[] list1 = new int[]{3, 7, 9, 11, 55, 77, 100, 200};
|
||||
int[] list2 = new int[]{1, 2, 3, 7, 13};
|
||||
int result = findKthSmallestElement(11, list1, list2);
|
||||
assertEquals(77, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void max_test() {
|
||||
int[] list1 = new int[]{100, 200};
|
||||
int[] list2 = new int[]{1, 2, 3};
|
||||
int result = findKthSmallestElement(4, list1, list2);
|
||||
assertEquals(100, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void max_test2() {
|
||||
int[] list1 = new int[]{100, 200};
|
||||
int[] list2 = new int[]{1, 2, 3};
|
||||
int result = findKthSmallestElement(5, list1, list2);
|
||||
assertEquals(200, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_k_is_smaller_than_the_size_of_both_lists_and_kth_element_in_list2() {
|
||||
int[] list1 = new int[]{1, 2, 5};
|
||||
int[] list2 = new int[]{1, 3, 4, 7};
|
||||
int result = findKthSmallestElement(4, list1, list2);
|
||||
assertEquals(3, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_k_is_smaller_than_the_size_of_both_lists_and_kth_element_is_smallest_in_list2() {
|
||||
int[] list1 = new int[]{1, 2, 5};
|
||||
int[] list2 = new int[]{3, 4, 7};
|
||||
int result = findKthSmallestElement(3, list1, list2);
|
||||
assertEquals(3, result);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void when_k_is_smaller_than_the_size_of_both_lists_and_kth_element_is_smallest_in_list23() {
|
||||
int[] list1 = new int[]{3, 11, 27, 53, 90};
|
||||
int[] list2 = new int[]{4, 20, 21, 100};
|
||||
int result = findKthSmallestElement(5, list1, list2);
|
||||
assertEquals(21, result);
|
||||
}
|
||||
}
|
||||
|
||||
// @Test
|
||||
// public void randomTests() {
|
||||
// IntStream.range(1, 100000).forEach(i -> random());
|
||||
// }
|
||||
|
||||
private void random() {
|
||||
|
||||
Random random = new Random();
|
||||
int length1 = (Math.abs(random.nextInt())) % 1000 + 1;
|
||||
int length2 = (Math.abs(random.nextInt())) % 1000 + 1;
|
||||
|
||||
int[] list1 = sortedRandomIntArrayOfLength(length1);
|
||||
int[] list2 = sortedRandomIntArrayOfLength(length2);
|
||||
|
||||
int k = (Math.abs(random.nextInt()) % (length1 + length2)) + 1 ;
|
||||
|
||||
int result = findKthSmallestElement(k, list1, list2);
|
||||
|
||||
int result2 = getKthElementSorted(list1, list2, k);
|
||||
|
||||
int result3 = getKthElementMerge(list1, list2, k);
|
||||
|
||||
assertEquals(result2, result);
|
||||
assertEquals(result2, result3);
|
||||
}
|
||||
|
||||
private int[] sortedRandomIntArrayOfLength(int length) {
|
||||
int[] intArray = new Random().ints(length).toArray();
|
||||
Arrays.sort(intArray);
|
||||
return intArray;
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue