LeetCode 1722 Walkthrough

LeetCode 1722 asks a swap question, but the cleaner way to solve it is to stop thinking about individual swaps and start thinking about groups of indices that can all reach each other. (leetcode.com) The problem, “Minimize Hamming Distance After Swap Operations,” gives two arrays of length *n* and a list of allowed index pairs; the goal is to minimize the number of positions where `source[i]!= target[i]` after any number of allowed swaps. LeetCode’s statement says each allowed pair can be used multiple times and in any order. (leetcode.com) That rule turns the swap list into a graph: each index is a node, and each allowed swap is an edge. If two indices sit in the same connected component, values can be rearranged anywhere inside that component through a chain of swaps, even if no direct swap exists between every pair. (algo.monster, leetcode.ca) A new YouTube walkthrough posted this week by codestorywithMIK teaches the problem from that graph angle instead of simulating swap sequences one by one. The video, “Minimize Hamming Distance After Swap Operations | Detailed | Simple Steps | Leetcode 1722 | MIK,” was crawled April 22, 2026, with 907 views and 117 likes in the search snapshot. (youtube.com) The core move is to build connected components with either Disjoint Set Union — also called Union-Find — or Depth-First Search. Both methods answer the same question: which indices belong to the same movable group. (walkccc.me, algo.monster) Once those groups are known, the task becomes a counting problem. For each component, count the values present in `source`, then scan the corresponding `target` values and cancel matches; whatever cannot be matched contributes to the final Hamming distance. (walkccc.me, leetcode.doocs.org) That is why many published solutions store a frequency map for each component root instead of trying to generate actual swap orders. Walkccc’s reference solution lists time complexity as near-linear, written as `O(n log* n)`, with `O(n)` space. (walkccc.me) The pattern shows up well beyond this one problem. Union-Find is a standard interview tool for grouping items connected by edges, and LeetCode tags 1722 under Union Find and Depth-First Search rather than under sorting or greedy simulation. (leetcode.com, algo.monster) In practice, the walkthrough’s lesson is that the swaps are not the real object of study; the components are. Once the indices are partitioned into movable buckets, the minimum mismatch count drops out of a multiset comparison instead of a costly search over swap sequences. (youtube.com, walkccc.me)