用于合并 3 个有序数组的Java程序

给定 3 个按升序排序的数组（A、B、C），我们需要将它们按升序合并在一起并输出数组 D。

例子：

Input : A = [1, 2, 3, 4, 5] 
        B = [2, 3, 4]
        C = [4, 5, 6, 7]
Output : D = [1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 7]

Input : A = [1, 2, 3, 5]
        B = [6, 7, 8, 9 ]
        C = [10, 11, 12]
Output: D = [1, 2, 3, 5, 6, 7, 8, 9. 10, 11, 12]

方法1（一次两个数组）
我们在 Merging 2 Sorted arrays 中讨论过。所以我们可以先合并两个数组，然后将结果与第三个数组合并。合并两个数组 O(m+n) 的时间复杂度。因此对于合并第三个数组，时间复杂度将变为 O(m+n+o)。请注意，这确实是该问题可以实现的最佳时间复杂度。
空间复杂性：由于我们一次合并两个数组，我们需要另一个数组来存储第一次合并的结果。这将空间复杂度提高到 O(m+n)。请注意，在计算复杂度时，会忽略保存 3 个数组的结果所需的空间。

算法

function merge(A, B)
    Let m and n be the sizes of A and B
    Let D be the array to store result
   
    // Merge by taking smaller element from A and B
    while i < m and j < n
        if A[i] <= B[j]
            Add A[i] to D and increment i by 1
        else Add B[j] to D and increment j by 1

    // If array A has exhausted, put elements from B
    while j < n
        Add B[j] to D and increment j by 1
   
    // If array B has exhausted, put elements from A
    while i < n
        Add A[j] to D and increment i by 1
   
    Return D

function merge_three(A, B, C)
    T = merge(A, B)
    return merge(T, C)

下面给出了实现

Java

import java.util.*;
// Java program to merge three sorted arrays
// by merging two at a time.
class GFG {
  
    static ArrayList mergeTwo(List A,
                                       List B)
    {
        // Get sizes of vectors
        int m = A.size();
        int n = B.size();
  
        // ArrayList for storing Result
        ArrayList D = new ArrayList(m + n);
  
        int i = 0, j = 0;
        while (i < m && j < n) {
  
            if (A.get(i) <= B.get(j))
                D.add(A.get(i++));
            else
                D.add(B.get(j++));
        }
  
        // B has exhausted
        while (i < m)
            D.add(A.get(i++));
  
        // A has exhausted
        while (j < n)
            D.add(B.get(j++));
  
        return D;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        Integer[] a = { 1, 2, 3, 5 };
        Integer[] b = { 6, 7, 8, 9 };
        Integer[] c = { 10, 11, 12 };
        List A = Arrays.asList(a);
        List B = Arrays.asList(b);
        List C = Arrays.asList(c);
  
        // First Merge A and B
        ArrayList T = mergeTwo(A, B);
  
        // Print Result after merging T with C
        System.out.println(mergeTwo(T, C));
    }
}
  
/* This code contributed by PrinciRaj1992 */

输出：

[1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12]

方法2（一次三个数组）
方法1的空间复杂度可以提高，我们将三个数组合并在一起。

function merge-three(A, B, C)
    Let m, n, o be size of A, B, and C
    Let D be the array to store the result
    
    // Merge three arrays at the same time
    while i < m and j < n and k < o
        Get minimum of A[i], B[j], C[i]
        if the minimum is from A, add it to 
           D and advance i
        else if the minimum is from B add it 
                to D and advance j
        else if the minimum is from C add it 
                to D and advance k
    
   // After above step at least 1 array has 
   // exhausted. Only C has exhausted
   while i < m and j < n
       put minimum of A[i] and B[j] into D
       Advance i if minimum is from A else advance j 
   
   // Only B has exhausted
   while i < m and k < o
       Put minimum of A[i] and C[k] into D
       Advance i if minimum is from A else advance k
 
   // Only A has exhausted
   while j < n and k < o
       Put minimum of B[j] and C[k] into D
       Advance j if minimum is from B else advance k

   // After above steps at least 2 arrays have 
   // exhausted
   if A and B have exhausted take elements from C
   if B and C have exhausted take elements from A
   if A and C have exhausted take elements from B
   
   return D

复杂度：时间复杂度为 O(m+n+o)，因为我们处理了三个数组中的每个元素一次。我们只需要一个数组来存储合并的结果，所以忽略这个数组，空间复杂度是 O(1)。

该算法的实现如下：

Java

import java.util.*;
import java.io.*;
import java.lang.*;
class Sorting {
    public static void main(String[] args)
    {
        int A[] = { 1, 2, 41, 52, 84 };
        int B[] = { 1, 2, 41, 52, 67 };
        int C[] = { 1, 2, 41, 52, 67, 85 };
  
        // call the function to sort and print the sorted numbers
        merge3sorted(A, B, C);
    }
  
    // Function to merge three sorted arrays
    // A[], B[], C[]: input arrays
    static void merge3sorted(int A[], int B[], int C[])
    {
        // creating an empty list to store sorted numbers
        ArrayList list = new ArrayList();
        int i = 0, j = 0, k = 0;
  
        // using merge concept and trying to find
        // smallest of three while all three arrays
        // contains at least one element
        while (i < A.length && j < B.length && k < C.length) {
            int a = A[i];
            int b = B[j];
            int c = C[k];
            if (a <= b && a <= c) {
                list.add(a);
                i++;
            }
            else if (b <= a && b <= c) {
                list.add(b);
                j++;
            }
            else {
                list.add(c);
                k++;
            }
        }
        // next three while loop is to sort two
        // of arrays if one of the three gets exhausted
        while (i < A.length && j < B.length) {
            if (A[i] < B[j]) {
                list.add(A[i]);
                i++;
            }
            else {
                list.add(B[j]);
                j++;
            }
        }
        while (j < B.length && k < C.length) {
            if (B[j] < C[k]) {
                list.add(B[j]);
                j++;
            }
            else {
                list.add(C[k]);
                k++;
            }
        }
        while (i < A.length && k < C.length) {
            if (A[i] < C[k]) {
                list.add(A[i]);
                i++;
            }
            else {
                list.add(C[k]);
                k++;
            }
        }
  
        // if one of the array are left then
        // simply appending them as there will
        // be only largest element left
        while (i < A.length) {
            list.add(A[i]);
            i++;
        }
        while (j < B.length) {
            list.add(B[j]);
            j++;
        }
        while (k < C.length) {
            list.add(C[k]);
            k++;
        }
        
        // finally print the list
        for (Integer x : list)
            System.out.print(x + " ");
    } // merge3sorted closing braces
}

输出

[1 1 1 2 2 2 41 41 41 52 52 52 67 67 84 85 ]

注意：虽然实现合并两个或三个数组的直接过程相对容易，但如果我们要合并 4 个或更多数组，该过程会变得很麻烦。在这种情况下，我们应该遵循 Merge K Sorted Arrays 中显示的过程。

有关更多详细信息，请参阅有关 Merge 3 Sorted Arrays 的完整文章！