From c1f70c8733e51145f27f6b9d5fcf00eceb0fe0f5 Mon Sep 17 00:00:00 2001 From: xiaowei wan Date: Tue, 13 Aug 2019 00:52:42 -0700 Subject: [PATCH] Add LC 547 friend circles en version --- README.en.md | 1 + assets/problems/547.friend-circle-1.png | Bin 0 -> 118370 bytes assets/problems/547.friend-circle-bfs.png | Bin 0 -> 181138 bytes assets/problems/547.friend-circle-dfs.png | Bin 0 -> 176213 bytes assets/problems/547.friend-circle-uf.png | Bin 0 -> 415778 bytes problems/547.friend-circles-en.md | 231 ++++++++++++++++++++++ 6 files changed, 232 insertions(+) create mode 100644 assets/problems/547.friend-circle-1.png create mode 100644 assets/problems/547.friend-circle-bfs.png create mode 100644 assets/problems/547.friend-circle-dfs.png create mode 100644 assets/problems/547.friend-circle-uf.png create mode 100644 problems/547.friend-circles-en.md diff --git a/README.en.md b/README.en.md index 69c5cec31..b1d0877de 100644 --- a/README.en.md +++ b/README.en.md @@ -202,6 +202,7 @@ The data structures mainly includes: - [0494.target-sum](./problems/494.target-sum.md) - [0516.longest-palindromic-subsequence](./problems/516.longest-palindromic-subsequence.md) - [0518.coin-change-2](./problems/518.coin-change-2.md) +- [0547.friend-circles](./problems/547.friend-circles-en.md) 🆕 - [0609.find-duplicate-file-in-system](./problems/609.find-duplicate-file-in-system.md) - [0875.koko-eating-bananas](./problems/875.koko-eating-bananas.md) - [0877.stone-game](./problems/877.stone-game.md) diff --git a/assets/problems/547.friend-circle-1.png b/assets/problems/547.friend-circle-1.png new file mode 100644 index 0000000000000000000000000000000000000000..ef6a32a30abdf4869314ed3b8c44f010038314c4 GIT binary patch literal 118370 zcmeFZ2{@GR`ZzukiZn^Gn+n;IvSc@v5JL8)kfm%%_HE3Nkadz!!X$)*WGQ>uMfP>9 zW8ckK#xUFe)#r20=bZEZ{?7TI^Zj1m^Z#AfdAQ8`KJ(o7^W69Iy!Za14pXN2gAkcH*2SmkyV$}Sc9)LhPIv`OH2y_HQM{^QH3tZ6vKOh<|5Z$k95J-!L`_I<~ zG{V1+IRpYlIDroTKE?w0JZJ#s1L)sBY2VWPf${C3KaHj@cuV`IYuc;8Xb^P`BzN1< 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z(kyvnz?tw;LX{bJI~Gw!8(6ZG#cb7nv#(04<7lJKukDYntor~wM(9wIEwCi&(_UEY ze$#Z(wVe+oa2{5U5+P|yI?c0$S=7z z`699)N|2&ScmcCzkWkM%Vtp_d)T`M%uLtK5Ux>s2W|5M2LGFC923SnZ{hDGzO!)}( zOXDO^`+;S#HL(Gj&dQPSa*g_8qGMPD=wTI!ySRJpsKYu|+71lf>9&%*#KzbXpodit zzQDa52es_E5D82XRo)8!=f46k{5iKo5Hw?84nE zLQN8*SpY2yqH{;H0QQD4JRgi^0n{P~Jpnn4)&i(S4n}%%7_9~HS5J+jwE%$z#b`r_ zK!akmAw-~sHrf!vsJKvjDx(b{jEW211_D=bqYa_ah7f8gJlY*b%^{fWz#-Tj{(pa+ z>@5Zc1_hqq|FiQVn%1ayyb@G!XkcJuV&M=_a8Tglh)|kg3FX0su`mvVI~@4*^@|%8 zDVSj}DFId%9lXG*cK|7>m{#U_izD z=YwN{fT@8F2ZRou;UvQPeZYWPzuX)Wzj#e;)KEz1On63&_3@01r>|d@#+puSUEilO zFo>MzBX@3WAD9lk8}cr8LQoCR3yk7%f=`Ysrcf zNx<43W3qmbhI=j+=y)$?M{t$r?7XYkjj$LN`JI89W6~qOH)E2 rFgiGeb8u?3G(`%5(bAOY(v(^5|I+R0r7~i`!E**rS3j3^P6 **Note:** here using weighted-union-find to avoid Union and Find take `O(n)` in the worst case. + +#### Complexity Analysis +- *Time Complexity:* `O(n*n*log(n) - traverse n*n matrix, weighted-union-find, union and find takes log(n) time complexity.` +- *Space Complexity:* `O(n) - parent and rank array of size n` + +## Key Points +1. Transform Adjacency matrix into Graph +2. Notice that it actually is to find number of connected components problem. +3. Connected components problem approaches (DFS, BFS, Union-Find). + +## Code (`Java`) +*Java code* - **DFS** +```java +class FindCirclesDFS { + public int findCircleNumDFS(int[][] M) { + if (M == null || M.length == 0 || M[0].length == 0) return 0; + int n = M.length; + int numCircles = 0; + boolean[] visited = new boolean[n]; + for (int i = 0; i < n; i++) { + if (!visited[i]) { + dfs(M, i, visited, n); + numCircles++; + } + } + return countCircle; + } + + private void dfs(int[][] M, int i, boolean[] visited, int n) { + for (int j = 0; j < n; j++) { + if (M[i][j] == 1 && !visited[j]) { + visited[j] = true; + dfs(M, j, visited, n); + } + } + } +} +``` + +*Java code* - **BFS** +```java +class FindCircleBFS { + public int findCircleNumBFS(int[][] M) { + if (M == null || M.length == 0) return 0; + int numCircle = 0; + int n = M.length; + boolean[] visited = new boolean[n]; + Queue queue = new LinkedList<>(); + for (int i = 0; i < n; i++) { + // already visited, skip + if (visited[i]) continue; + queue.add(i); + while (!queue.isEmpty()) { + int curr = queue.poll(); + visited[curr] = true; + for (int j = 0; j < n; j++) { + if (M[curr][j] == 1 && !visited[j]) { + queue.add(j); + } + } + } + numCircle++; + } + return numCircle; + } +} +``` + +*Java code* - **Union-Find** +```java +class FindCircleUF { + public int findCircleNumUF(int[][] M) { + if (M == null || M.length == 0 || M[0].length == 0) return 0; + int n = M.length; + UnionFind uf = new UnionFind(n); + for (int i = 0; i < n - 1; i++) { + for (int j = i + 1; j < n; j++) { + // union friends + if (M[i][j] == 1) { + uf.union(i, j); + } + } + } + return uf.count; + } +} + +class UnionFind { + int count; + int[] parent; + int[] rank; + + public UnionFind(int n) { + count = n; + parent = new int[n]; + rank = new int[n]; + for (int i = 0; i < n; i++) { + parent[i] = i; + } + } + + public int find(int a) { + return parent[a] == a ? a : find(parent[a]); + } + + public void union(int a, int b) { + int rootA = find(a); + int rootB = find(b); + if (rootA == rootB) return; + if (rank[rootA] <= rank[rootB]) { + parent[rootA] = rootB; + rank[rootB] += rank[rootA]; + } else { + parent[rootB] = rootA; + rank[rootA] += rank[rootB]; + } + count--; + } + + public int count() { + return count; + } +} +``` + +## References (Further reading) +1. [Adjacency Matrix Wiki](https://www.wikiwand.com/en/Adjacency_matrix) +2. [Union-Find Wiki](https://www.wikiwand.com/en/Disjoint-set_data_structure) +3. [Algorighms 4 union-find](https://www.cs.princeton.edu/~rs/AlgsDS07/01UnionFind.pdf) + +## Similar Problems +1. [323. Number of Connected Components in an Undirected Graph](https://leetcode.com/problems/number-of-connected-components-in-an-undirected-graph/) +2. [1101. The Earliest Moment When Everyone Become Friends](https://leetcode.com/problems/the-earliest-moment-when-everyone-become-friends/)

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