joney000 / Java Competitive Programming
Licence: gpl-3.0
I have written some important Algorithms and Data Structures in an efficient way in Java with proper references to time and space complexity. These Pre-cooked and well-tested codes help to implement larger hackathon problems in lesser time. DFS, BFS, LCA, All Pair Shortest Path, Longest Common Subsequence, Binary Search, Lower Bound Search, Maximal Matching, Matrix Exponentiation, Segment Tree, Sparse Table, Merge Sort, Miller Prime Test, Prims - Minimum Spanning Tree, BIT - Binary Index Tree, Two Pointers, BST - Binary Search Tree, Maximum Subarray Sum, Immutable Data Structures, Persistent Data Structurs - Persistent Trie, Dijkstra, Z - Function, Minimum Cost Maximal Matching, Heavy Light Decomposition, Knapsack, Suffix Array and LCP - Longest Common Prefix, Squre Root Decomposition, Kth Order Statics, Trie / Prefix Tree, LIS - Longest Increasing Subsequence, Hashing
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Java-Competitive-Programming
In This Repository, I have written some of the important Algorithms and Data Structures efficiently in Java with proper references to time and space complexity. These Pre-cooked and well-tested codes helps to implement larger hackathon problems in lesser time.
Algorithms:
| Algorithm | Big-O Time, Big-O Space | Comments/Symbols |
|---|---|---|
| DFS - 2-D Grid | O(M * N), O(M * N) | M * N = dimensions of matrix |
| DFS - Adjency List | O(V + E), O(V + E) | V = No of vertices in Graph, E = No of edges in Graph |
| BFS - 2-D Grid | O(M * N), O(M * N) | M * N = dimensions of matrix |
| BFS - Adjency List | O(V + E), O(V + E) | V = No of vertices in Graph, E = No of edges in Graph |
| LCA - Lowest Common Ancestor | O(V), O(V) | |
| LCA - Using Seg Tree | O(log V), O(V + E) | Using Euler tour and Segment Tree, preprocessing/building tree = O(N) & Each Query = O(log N) |
| All Pair Shortest Path | O(V^3), O(V + E) | Floyd Warshall algorithm |
| Longest Common Subsequence | O(M * N), O(M * N) | Finding LCS of N & M length string using Dynamic Programming |
| Binary Search | O(log(N), O(N) | Search in N size sorted array |
| Lower Bound Search | O(log(N), O(1) | Unlike C, Java Doesn't Provide Lower Bound, Upper Bound for already sorted elements in the Collections |
| Upper Bound Search | O(log(N), O(1) | |
| Maximal Matching | O(√V x E), O(V + E) | Maximum matching for bipartite graph using Hopcroft-Karp algorithm |
| Minimum Cost Maximal Matching - Hungarian algorithm | O(N^3), O(N^2) | |
| Matrix Exponentiation | O(N^3 * log(X)) ,O(M * N) | Exponentiation by squaring / divide and conquer MATRIX[N, N] ^ X |
| Segment Tree | O(Q * log(N)), O(N) | Q = no of queries , N = no of nodes , per query time = O(log N) |
| Segment Tree Lazy Propagation | O(Q * log(N)), O(N) | Q = no of queries , N = no of nodes , tree construction time = O(N), per query time = O(log N), range update time: O(log N) |
| Sparse Table | O(Q * O(1) + N * log(N)), O(N * log(N)) | per query time = O(1) and precompute time and space: O(N * log(N)) |
| Merge Sort | O(N * log(N)), O(N) | divide and conquer algorithm |
| Miller Prime Test | soft-O notation Õ((log n)^4) with constant space | |
| Kruskal- Minimum Spanning Tree | O(E log V) , O(V + E) | |
| BIT - Binary Index Tree / Fenwick Tree | O(log N), O(N) | per query time: O(log(N)) |
| Two Pointers | O(N), O(N) | two directional scan on sorted array |
| Binary Search Tree - BST | O(N), O(N) | |
| Maximum Subarray Sum | O(N), O(N) | Kadane's algorithm |
| Immutable Data Structures, Persistent Data Structurs - Persistent Trie | O(N * log N), O(N) | query & update time: O(log N). It's frequently used where you have to maintain multiple version of your data structure typically in lograthimic time. |
| Dijkstra | O((E+v) log V)), O(V + E) | |
| Z - Function | O(P + T), O(P + T) | Leaner time string matching / occurrence finding of pattern string P into Large Text string T. |
| Heavy Light Decomposition | O(N * log^2 N), O(N) | per query time = (log N)^2 |
| Interval Merge | O(log N), O(N) | |
| Knapsack | O(N * S), (N * S) | N = elements, S = MAX_Sum |
| Suffix Array and LCP - Longest Common Prefix | O(N * log(N)), O(N) | |
| Squre Root Decomposition | O(N * √N), O(N) | the range of N number can be divided in √N blocks |
| Kth Order Statics | O(N), O(N) | K’th Smallest/Largest Element in Unsorted Array |
| Trie / Prefix Tree | O(N * L), O(N * L) | if there are N strings of L size, per query time(Prefix information) = O(L) |
| LIS - Longest Increasing Subsequence | O(N * log(N)), O(N) |
Contributions
Want to contribute in corrections or enhancement? Great! Please raise a PR, or drop a mail at [email protected] .
I also highly recommed to read Introduction to Algorithms(CLRS book) and other authors implementations, it will give you diverse set of ideas to solve same algorithmic challenges.
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