Warshall’s Algorithm
The Floyd–Warshall algorithm is used for finding shortest paths in a weighted graph with positive or negative edge weights (but with no negative cycles). It is used to determine if a path exists between two vertices i,j just the vertices among 1, . . . , k allowed as intermediate in the kth iteration. R(k)[i,j] = R(k-1)[i,j] ; path using just 1, . . , k-1 and R(k)[i,j] = R(k-1)[i,k] and R(k-1)[k,j] ; path from i to k and from k to i using just 1, . . , k-1. It is a recurrence relation relating el
Summary
The Floyd–Warshall algorithm is used for finding shortest paths in a weighted graph with positive or negative edge weights (but with no negative cycles). It is used to determine if a path exists between two vertices i,j just the vertices among 1, . . . , k allowed as intermediate in the kth iteration. R(k)[i,j] = R(k-1)[i,j] ; path using just 1, . . , k-1 and R(k)[i,j] = R(k-1)[i,k] and R(k-1)[k,j] ; path from i to k and from k to i using just 1, . . , k-1. It is a recurrence relation relating el
Things to Remember
- The Floyd–Warshall algorithm is used for finding shortest paths in a weighted graph with positive or negative edge weights (but with no negative cycles).
- It is used to determine if a path exists between two vertices i,j just the vertices among 1, . . . , k allowed as intermediate in the kth iteration.
- R(k)[i,j] = R(k-1)[i,j] ; path using just 1, . . , k-1 and R(k)[i,j] = R(k-1)[i,k] and R(k-1)[k,j] ; path from i to k and from k to i using just 1, . . , k-1.
- It is a recurrence relation relating elements R(k) to elements R(k-1).
MCQs
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Subjective Questions
Q1:
How impetigo can be treated and list the nursing management for impetigo?
Type: Long Difficulty: Easy
<ol>
<li>Systematic antibodies</li>
</ol>
<p>This therapy is usual treatment. It reduces contagious spread, treats deep infections and prevents acute glomerulonephritis which may occur as an aftermath of streptococcal skin disease.</p>
<p> </p>
<ol start="2">
<li>Topical antibacterial therapy</li>
</ol>
<p>This therapy may be prescribed when the disease is limited to a small area. However, topical therapy requires that the medication is applied to the lession several times daily for a week.</p>
<p> </p>
<ol start="3">
<li>An anti septic solution</li>
</ol>
<p>An antiseptic solution such as povidone-iodine (betadine) may be used to clean the skin, reduce the bacterial content in the infected area, and prevent spread.</p>
<p> </p>
<p>Nursing management</p>
<ol>
<li>The nurse instruct the patient and family members to bath at least once a day with bacterial soap.</li>
<li>Major nursing activities include patient education, particularly in proper skin care techniques and managing potential problems related to the skin disorder.</li>
<li>Health education on</li>
<li>Nutrition</li>
<li>Hygiene</li>
<li>Providing positive reassurance.</li>
<li>Each person should have a separate towel and wash cloth.</li>
</ol>
Q2:
Define impetigo?
Type: Short Difficulty: Easy
Q3:
How it is caused and write the symptoms?
Type: Short Difficulty: Easy
<p>Causes</p>
<p>You're exposed to the bacteria that cause impetigo when you come into contact with the sores of someone who's infected or with items they've touched &mdash; such as clothing, bed linen, towels and even toys.</p>
<p> </p>
<p>Classic signs and symptoms of impetigo involve red sores that quickly rupture, ooze for a few days and then form a yellowish-brown crust. The sores usually occur around the nose and mouth but can be spread to other areas of the body by fingers, clothing and towels.</p>
<p>A less common form of the disorder, called bullous impetigo, may feature larger blisters that occur on the trunk or diaper area of infants and young children.</p>
<p>A more serious form of impetigo, called ecthyma, penetrates deeper into the skin &mdash; causing painful fluid- or pus-filled sores that turn into deep ulcers.</p>
Q4:
What are the factors that increase the risk of impetigo?
Type: Long Difficulty: Easy
<p>-Age. Although anyone can develop impetigo, it most commonly occurs in children ages 2 to 6.</p>
<p>-Crowded conditions. Impetigo spreads easily in schools and child care settings.</p>
<p>-Warm, humid weather. Impetigo infections are more common in summer.</p>
<p>-Certain sports. Participation in sports that involve skin-to-skin contacts, such as football or wrestling, increases your risk of developing impetigo.</p>
<p>-Broken skin. The bacteria that cause impetigo often enter your skin through a small skin injury, insect bite or rash.</p>
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Warshall’s Algorithm
The Floyd–Warshall algorithm is usedfor finding shortest paths in a weighted graphwith positive or negative edge weights (but with no negative cycles).A single execution of the algorithm will find the lengths (summed weights) of the shortest paths betweenall pairs of vertices, though it does not return details of the paths themselves. It is also used to find thetransitive closureof a relation R,
Itis used to determine if a path exists between two vertices i,j just the vertices among 1, . . . , k allowed as intermediate in the kth iteration.
R(k)[i,j] = R(k-1)[i,j] ; path using just 1, . . , k-1
= R(k-1)[i,k] and R(k-1)[k,j] ; path from i to k and from k to i using just 1, . . , k-1
Warshall's Algorithm
Recurrence relation relating elements R(k) to elements R(k-1) is:
R(k)[i,j] = R(k-1)[i,k] and R(k-1)[k,j]
It implies the following rules for generating R(k) and R(k-1):
- Rule 1: If an element in row i and column j is 1 in R(k-1), it remains 1 in R(k)
- Rule 2: If an element in row i and column j is 0 in R(k-1), it has to be changed to 1 in R(k) iff the element in its row i and column k and the element k and element in its column j and row k are both 1's in R(k-1).
Example:
References:
1. Karumanchi, N. "Data Structures and Algorithms Made Easy"
2. Y. Langsam, M. J. Augenstein and A. M Tenenbaum, “Data Structures using C and C++”
3. R. L. Kruse, B. P. Leung, C. L. Tondo, “Data Structure and Program design in C”
Lesson
Graphs
Subject
Computer Engineering
Grade
Engineering
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