Lec 1: Prove the following statements are equal:1. Connected subgraph with no cycles2. Connected subgraph with n-1 edgesLec 5:Solve the Fibonacci Sequence N₁-Nk-1+Nk-2 and find the expression of NkLec 6:Show that the upper bound of the total rank can be raised for every node in a BANDis ≤nLec 10:Show that T(n)=O(n) for the recurrence T(n)= T(n/5)+ T(7n/10)+O(n)Lec 11: Find a counter-example that the greedy method sort items by pi/w; does notgive the optimal solution.Lec 12: Work out the exact number possible of chords given a polygon with nvertices.Lec 14: Using Fibonacci Heap to implement Dijkstra algorithm in given timecomplexity O(F+VlogV).Lec 16: Solve the recurrence T(n)=C(2n-1)/[n(n+1)]+ T(n-1)||

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Lec 1: Prove the following statements are equal: 1. Connected subgraph with no cycles 2. Connected subgraph with n-1 edges

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.

Question

Lec 1: Prove the following statements are equal:
1. Connected subgraph with no cycles
2. Connected subgraph with n-1 edges
Lec 5:
Solve the Fibonacci Sequence N₁-Nk-1+Nk-2 and find the expression of Nk
Lec 6:
Show that the upper bound of the total rank can be raised for every node in a BAND
is ≤n
Lec 10:Show that T(n)=O(n) for the recurrence T(n)= T(n/5)+ T(7n/10)+O(n)
Lec 11: Find a counter-example that the greedy method sort items by pi/w; does not
give the optimal solution.
Lec 12: Work out the exact number possible of chords given a polygon with n
vertices.
Lec 14: Using Fibonacci Heap to implement Dijkstra algorithm in given time
complexity O(F+VlogV).
Lec 16: Solve the recurrence T(n)=C(2n-1)/[n(n+1)]+ T(n-1)||

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