Merge Sorted Array

Question

• leetcode: Merge Sorted Array | LeetCode OJ
• lintcode: (6) Merge Sorted Array

Given two sorted integer arrays A and B, merge B into A as one sorted array.

Example
A = [1, 2, 3, empty, empty], B = [4, 5]

After merge, A will be filled as [1, 2, 3, 4, 5]

Note
You may assume that A has enough space (size that is greater or equal to m + n)
to hold additional elements from B.
The number of elements initialized in A and B are m and n respectively.

題解

因為本題有 in-place 的限制，故必須從陣列末尾的兩個元素開始比較；否則就會產生挪動，一旦挪動就會是 $O(n^2)$ 的。 自尾部向首部逐個比較兩個陣列內的元素，取較大的置於陣列 A 中。由於 A 的容量較 B 大，故最後 m == 0 或者 n == 0 時僅需處理 B 中的元素，因為 A 中的元素已經在 A 中，無需處理。

Python

class Solution:
    """
    @param A: sorted integer array A which has m elements,
              but size of A is m+n
    @param B: sorted integer array B which has n elements
    @return: void
    """
    def mergeSortedArray(self, A, m, B, n):
        if B is None:
            return A

        index = m + n - 1
        while m > 0 and n > 0:
            if A[m - 1] > B[n - 1]:
                A[index] = A[m - 1]
                m -= 1
            else:
                A[index] = B[n - 1]
                n -= 1
            index -= 1

        # B has elements left
        while n > 0:
            A[index] = B[n - 1]
            n -= 1
            index -= 1

C++

class Solution {
public:
    /**
     * @param A: sorted integer array A which has m elements,
     *           but size of A is m+n
     * @param B: sorted integer array B which has n elements
     * @return: void
     */
    void mergeSortedArray(int A[], int m, int B[], int n) {
        int index = m + n - 1;
        while (m > 0 && n > 0) {
            if (A[m - 1] > B[n - 1]) {
                A[index] = A[m - 1];
                --m;
            } else {
                A[index] = B[n - 1];
                --n;
            }
            --index;
        }

        // B has elements left
        while (n > 0) {
            A[index] = B[n - 1];
            --n;
            --index;
        }
    }
};

Java

class Solution {
    /**
     * @param A: sorted integer array A which has m elements,
     *           but size of A is m+n
     * @param B: sorted integer array B which has n elements
     * @return: void
     */
    public void mergeSortedArray(int[] A, int m, int[] B, int n) {
        if (A == null || B == null) return;

        int index = m + n - 1;
        while (m > 0 && n > 0) {
            if (A[m - 1] > B[n - 1]) {
                A[index] = A[m - 1];
                m--;
            } else {
                A[index] = B[n - 1];
                n--;
            }
            index--;
        }

        // B has elements left
        while (n > 0) {
            A[index] = B[n - 1];
            n--;
            index--;
        }
    }
}

源碼分析

第一個 while 只能用條件與(conditional AND)。

複雜度分析

最壞情況下需要遍歷兩個陣列中所有元素，時間複雜度為 $O(n)$. 空間複雜度 $O(1)$.