Princess Esra Birgin and her tryst with HyderabadDayamani Surya
Turkey born Princess, Esra Birgin was married to Prince Mukkaram Jah. She is credited with restoration of Nizam's Palaces like Chowmohallah Palace and Falaknuma Palace.
- This is by courtesy of AlKauthar Institute & their "Just Go Do It" initiative.
- Just Go Do It is available @ http://www.justgodoit.net/
- This document also available from their website
Este documento no contiene información relevante y solo consiste en una serie de caracteres sin sentido. No es posible resumirlo en menos de 3 oraciones dado que no comunica ningún contenido comprensible.
이번 슬라이드는 Graph mining의 기초에 대한 것이다.
고전 문제인 Graph cut에 대한 개념과 수학적인 배경을 설명하고, 이 개념이 clustering (클러스터링)에서 어떻게 사용되는지를 설명한다.
Graph mining, cut, clustring의 기초를 알기에 매우 적합한 자료이다.
Princess Esra Birgin and her tryst with HyderabadDayamani Surya
Turkey born Princess, Esra Birgin was married to Prince Mukkaram Jah. She is credited with restoration of Nizam's Palaces like Chowmohallah Palace and Falaknuma Palace.
- This is by courtesy of AlKauthar Institute & their "Just Go Do It" initiative.
- Just Go Do It is available @ http://www.justgodoit.net/
- This document also available from their website
Este documento no contiene información relevante y solo consiste en una serie de caracteres sin sentido. No es posible resumirlo en menos de 3 oraciones dado que no comunica ningún contenido comprensible.
이번 슬라이드는 Graph mining의 기초에 대한 것이다.
고전 문제인 Graph cut에 대한 개념과 수학적인 배경을 설명하고, 이 개념이 clustering (클러스터링)에서 어떻게 사용되는지를 설명한다.
Graph mining, cut, clustring의 기초를 알기에 매우 적합한 자료이다.
The document discusses using bitwise operators and dynamic programming to solve problems efficiently. It provides examples of using bitwise OR, AND, XOR operators to add, remove and check for elements in a set represented as a bitmask. It then describes several problems involving bitmasks and dynamic programming including finding the number of possible paths in a graph and the maximum score in a traveling salesman problem. The examples demonstrate how bitwise operators can be used to optimize set operations and dynamic programming can reduce exponential time complexity problems to polynomial time.
The document discusses several algorithms and data structures:
1. It discusses using dynamic programming to solve problems with optimal substructure in O(N^3) time, storing solutions to subproblems in 2D tables.
2. It presents the Knapsack problem and discusses a dynamic programming solution using a 3D DP table to store solutions for all possible combinations of items and capacity.
3. It discusses representing numbers in a factorial number system and calculating factorials efficiently using dynamic programming in O(logK) time.
This document discusses various algorithms and their time complexities:
1. Section A discusses sorting algorithms and their O(N) linear time complexity for small/large inputs.
2. Section B discusses interval intersection algorithms with O(M*N) quadratic time for small inputs using nested loops, and O(M*logM) logarithmic time for large inputs using disjoint set data structures.
3. Section C discusses image quilting algorithms with O(W*3H) cubic time for small images and O(W*H) linear time for large images using dynamic programming.
4. Section D discusses connected component labeling with linear time for small images using scanning and O(N*M) time for
The document discusses using bitwise operators and dynamic programming to solve problems efficiently. It provides examples of using bitwise OR, AND, XOR operators to add, remove and check for elements in a set represented as a bitmask. It then describes several problems involving bitmasks and dynamic programming including finding the number of possible paths in a graph and the maximum score in a traveling salesman problem. The examples demonstrate how bitwise operators can be used to optimize set operations and dynamic programming can reduce exponential time complexity problems to polynomial time.
The document discusses several algorithms and data structures:
1. It discusses using dynamic programming to solve problems with optimal substructure in O(N^3) time, storing solutions to subproblems in 2D tables.
2. It presents the Knapsack problem and discusses a dynamic programming solution using a 3D DP table to store solutions for all possible combinations of items and capacity.
3. It discusses representing numbers in a factorial number system and calculating factorials efficiently using dynamic programming in O(logK) time.
This document discusses various algorithms and their time complexities:
1. Section A discusses sorting algorithms and their O(N) linear time complexity for small/large inputs.
2. Section B discusses interval intersection algorithms with O(M*N) quadratic time for small inputs using nested loops, and O(M*logM) logarithmic time for large inputs using disjoint set data structures.
3. Section C discusses image quilting algorithms with O(W*3H) cubic time for small images and O(W*H) linear time for large images using dynamic programming.
4. Section D discusses connected component labeling with linear time for small images using scanning and O(N*M) time for
17. Unbounded Knapsack
• 무게와 가격이 각각 𝑤𝑖와 𝑣𝑖인 𝑛개의 물건
이 있다. 무게의 총합이 𝑊를 초과하지 않
도록 물건을 선택했을 때, 가격 총합의 최
대값을 구하라. (단, 같은 종류의 물건을 몇
개라도 고르는 것이 가능하다)
• 1 <= 𝑛 <= 1000
• 1 <= 𝑤𝑖, 𝑣𝑖 <= 1000
• 1 <= 𝑊 <= 10000
18. Unbounded Knapsack
• 𝑑𝑝[𝑖][𝑗] : 1 ~ 𝑖번 물건을 고려하여 무게 합이
𝑗가 되도록 선택했을 때 최대 가격
• 𝑑𝑝[0][0] = 0, 𝑑𝑝[0][𝑖] = −∞ (0 < 𝑖 <= 𝑛)
• 𝑑𝑝[𝑖][𝑗] = max ( 𝑑𝑝[𝑖 – 1][𝑗 – 𝑘 ∗ 𝑠𝑖] +
𝑘 ∗ 𝑣𝑖) (𝑘 >= 0)
시간복잡도 O(𝑛𝑊K
)
𝐾를 없앨 수는 없을까?
32. Knapsack 마무리
• 최대/최소 외에도 경우의 수/판정 문제 등
다양한 곳에 응용 가능
• 𝑛, 𝑤, 𝑣 등 인자의 범위에 따라 dp식을 다르
게 정의
– 𝑛이 매우 작고 𝑤, 𝑣가 매우 큰 경우 dp로 불가
=> meet in the middle
• 그 외에도 다양한 냅색 유형 / 최적화 방법
존재함