# Merge Sorted Array ### Source - leetcode: [Merge Sorted Array | LeetCode OJ](https://leetcode.com/problems/merge-sorted-array/) - lintcode: [(6) Merge Sorted Array](http://www.lintcode.com/en/problem/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. ~~~ ### 题解 因为本题有 in-place 的限制，故必须从数组末尾的两个元素开始比较；否则就会产生挪动，一旦挪动就会是 O(n2)O(n^2)O(n2) 的。自尾部向首部逐个比较两个数组内的元素，取较大的置于数组 A 中。由于 A 的容量较 B 大，故最后 `m == 0` 或者 `n == 0` 时仅需处理 B 中的元素，因为 A 中的元素已经在 A 中，无需处理。 ### 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--; } } } ~~~ ### 源码分析 第一个 while 只能用条件与。 ### 复杂度分析 最坏情况下需要遍历两个数组中所有元素，时间复杂度为 O(n)O(n)O(n). 空间复杂度 O(1)O(1)O(1).