सामग्री पर जाएँ
The Lumenary
स्नातक (प्रारंभिक)Computationनियोजित

Algorithm design and analysis

Recursion and divide and conquer, greedy algorithms, dynamic programming, graph algorithms (breadth- and depth-first search, shortest paths, spanning trees), asymptotic analysis and correctness proofs.

math.comp.algorithm-design

इस विषय का पाठ अभी लिखा नहीं गया है। नीचे दी गई रूपरेखा पाठ्यक्रम-मानचित्र का हिस्सा है और इसकी समीक्षा नहीं हुई है।

इस पर आधारित

18 अनिवार्य पूर्वापेक्षाएँ (बिल्कुल नीचे तक)

आप सीखेंगे

  • Design divide-and-conquer algorithms and analyse them with recurrences, as for mergesort.
  • Prove the correctness of greedy algorithms such as Kruskal's algorithm and Dijkstra's algorithm with non-negative weights.
  • Design dynamic-programming algorithms for problems such as longest common subsequence.

परिभाषा

  • Divide and conquer splits a problem into smaller instances, solves them recursively and combines the results.
  • Dynamic programming solves a problem by combining solutions of overlapping subproblems, storing them to avoid recomputation.

प्रमेय

  • Mergesort runs in O(n log n) time.
  • Dijkstra's algorithm finds shortest paths from a source vertex when all edge weights are non-negative.
  • Kruskal's algorithm finds a minimum spanning tree of a connected weighted graph.

आम भ्रांतियाँ

  • Using Dijkstra's algorithm when some edge weights are negative.
  • Assuming a greedy algorithm is correct without a proof.

आगे ले जाता है

वैकल्पिक खोजें

अधिगम पथ

आगे पढ़ने के लिए

  • Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein, Introduction to Algorithms
  • Jon Kleinberg and Éva Tardos, Algorithm Design (2005)