{ "data": { "question": { "questionId": "1840", "questionFrontendId": "1722", "categoryTitle": "Algorithms", "boundTopicId": 551154, "title": "Minimize Hamming Distance After Swap Operations", "titleSlug": "minimize-hamming-distance-after-swap-operations", "content": "
You are given two integer arrays, source
and target
, both of length n
. You are also given an array allowedSwaps
where each allowedSwaps[i] = [ai, bi]
indicates that you are allowed to swap the elements at index ai
and index bi
(0-indexed) of array source
. Note that you can swap elements at a specific pair of indices multiple times and in any order.
The Hamming distance of two arrays of the same length, source
and target
, is the number of positions where the elements are different. Formally, it is the number of indices i
for 0 <= i <= n-1
where source[i] != target[i]
(0-indexed).
Return the minimum Hamming distance of source
and target
after performing any amount of swap operations on array source
.
\n
Example 1:
\n\n\nInput: source = [1,2,3,4], target = [2,1,4,5], allowedSwaps = [[0,1],[2,3]]\nOutput: 1\nExplanation: source can be transformed the following way:\n- Swap indices 0 and 1: source = [2,1,3,4]\n- Swap indices 2 and 3: source = [2,1,4,3]\nThe Hamming distance of source and target is 1 as they differ in 1 position: index 3.\n\n\n
Example 2:
\n\n\nInput: source = [1,2,3,4], target = [1,3,2,4], allowedSwaps = []\nOutput: 2\nExplanation: There are no allowed swaps.\nThe Hamming distance of source and target is 2 as they differ in 2 positions: index 1 and index 2.\n\n\n
Example 3:
\n\n\nInput: source = [5,1,2,4,3], target = [1,5,4,2,3], allowedSwaps = [[0,4],[4,2],[1,3],[1,4]]\nOutput: 0\n\n\n
\n
Constraints:
\n\nn == source.length == target.length
1 <= n <= 105
1 <= source[i], target[i] <= 105
0 <= allowedSwaps.length <= 105
allowedSwaps[i].length == 2
0 <= ai, bi <= n - 1
ai != bi
给你两个整数数组 source
和 target
,长度都是 n
。还有一个数组 allowedSwaps
,其中每个 allowedSwaps[i] = [ai, bi]
表示你可以交换数组 source
中下标为 ai
和 bi
(下标从 0 开始)的两个元素。注意,你可以按 任意 顺序 多次 交换一对特定下标指向的元素。
相同长度的两个数组 source
和 target
间的 汉明距离 是元素不同的下标数量。形式上,其值等于满足 source[i] != target[i]
(下标从 0 开始)的下标 i
(0 <= i <= n-1
)的数量。
在对数组 source
执行 任意 数量的交换操作后,返回 source
和 target
间的 最小汉明距离 。
\n\n
示例 1:
\n\n输入:source = [1,2,3,4], target = [2,1,4,5], allowedSwaps = [[0,1],[2,3]]\n输出:1\n解释:source 可以按下述方式转换:\n- 交换下标 0 和 1 指向的元素:source = [2,1,3,4]\n- 交换下标 2 和 3 指向的元素:source = [2,1,4,3]\nsource 和 target 间的汉明距离是 1 ,二者有 1 处元素不同,在下标 3 。\n\n\n
示例 2:
\n\n输入:source = [1,2,3,4], target = [1,3,2,4], allowedSwaps = []\n输出:2\n解释:不能对 source 执行交换操作。\nsource 和 target 间的汉明距离是 2 ,二者有 2 处元素不同,在下标 1 和下标 2 。\n\n
示例 3:
\n\n输入:source = [5,1,2,4,3], target = [1,5,4,2,3], allowedSwaps = [[0,4],[4,2],[1,3],[1,4]]\n输出:0\n\n\n
\n\n
提示:
\n\nn == source.length == target.length
1 <= n <= 105
1 <= source[i], target[i] <= 105
0 <= allowedSwaps.length <= 105
allowedSwaps[i].length == 2
0 <= ai, bi <= n - 1
ai != bi
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