Betacap TR 20 Capsule Prescription: Required Marketer: Sun Pharmaceutical Industries Ltd SALT COMPOSITION: Propranolol (20mg) Storage: Store below 30°CProduct introduction
Betacap TR 20 Capsule helps decrease anxiety and relieve tremors. It is also used to help prevent migraine, heart-related chest pain (angina), and bleeding in the stomach caused by high blood pressure in the liver (portal hypertension). Betacap TR 20 Capsule may also be used to treat high blood pressure and some types of abnormal heartbeat (arrhythmia). The dose will depend on what you are being treated for and how you respond to the medicine. You should always take it as prescribed by the doctor. It should be taken on an empty stomach and at about the same time each day. You should keep taking it even if you feel well, as you are still getting the benefits. If you stop taking it suddenly, your condition may worsen. The most common side effects are tiredness, weakness cold fingers and toes (Raynaud phenomenon), irregular or slow heartbeat, numbness in your fingers, and breathlessness. You may also experience nausea, vomiting, and diarrhea. Talk to your doctor if the side effects bother you or do not go away. Most side effects are short-lived and improve as your body gets used to the medicine. You should not use this medicine if you have asthma, very slow or uneven heartbeats, or a serious heart condition, including heart failure. Talk to your doctor before taking it if you have kidney or liver problems or chronic obstructive pulmonary disease (COPD). In terms of lifestyle, alcohol may affect the way this medicine works and should be avoided. You should not drive if this medicine makes you feel dizzy. Ask your doctor whether it is safe to take this medicine if you are pregnant or breastfeeding.Uses of Betacap Capsule PR
Treatment of Pheochromocytoma Treatment of Hypertension (high blood pressure) Prevention of migraine Treatment of Anxiety Treatment of Arrhythmia Prevention of Heart attack Prevention of Angina (heart-related chest pain) Treatment of TremorsBenefits of Betacap Capsule PR
In Treatment of Pheochromocytoma While carrying out surgery for the removal of pheochromocytoma, there is a risk of abnormally high blood pressure. Betacap TR 20 Capsule blocks the effect of some chemicals on your heart and blood vessels. This slows down the heart rate and helps the heartbeat with less force thereby lowering your blood pressure. It is used for the immediate reduction of very high blood pressure (hypertensive emergency). Controlled blood pressure reduces the risk of having a heart attack, stroke, or kidney problems. In Treatment of Hypertension (high blood pressure) Betacap TR 20 Capsule relaxes the blood vessels so that blood can flow more easily around your body. This lowers your blood pressure and reduces your risk of having a stroke, a heart attack, or kidney problems in the future. You do not usually feel any direct benefit from taking this medicine, but it works in the long term to keep you well. You should take it regularly as prescribed for this medicine to be most effective, even if you feel better. In Prevention of migraine Betacap TR 20 Capsule helps improve the flow of blood in your brain and prevents abnormal activity of muscles that triggers migraines. It is a very effective medicine for preventing migraine attacks, however, it does not treat an attack that has already started. By preventing and reducing the frequency of migraine attacks, the medicine can help you carry out your daily activities and improve your quality of life. In Treatment of Anxiety Betacap TR 20 Capsule stops your brain from releasing the chemicals that make you feel anxious so it can reduce the symptoms of excessive anxiety and worry. It can also reduce feelings of restlessness, tiredness, difficulty concentrating, feeling irritable and sleep problems that often come with Anxiety Disorder. Betacap TR 20 Capsule will therefore help you go about your daily activities more easily and be more productive. Keep taking this medicine even if you feel well. Stopping suddenly can cause serious problems. In Treatment of Arrhythmia Betacap TR 20 Capsule is used to stabilize heart rate. It helps in normalizing an abnormal heart rhythm, preventing it occurring in the first place or slowing down the heart rate during an episode. In Prevention of Heart attack Betacap TR 20 Capsule helps lower your blood pressure and make it easier for your heart to pump blood around your body. This reduces the chances of you having a heart attack. It can also reduce the risk of dying if it is given immediately after a heart attack. This medicine needs to be taken regularly to be effective, so keep taking it even if you feel well. Do not stop without talking to your doctor. In Prevention of Angina (heart-related chest pain) Betacap TR 20 Capsule relaxes the blood vessels so that blood can flow more easily around your body and makes sure that your heart is getting a good supply of oxygen. This makes it less likely that you will suffer chest pain caused by angina. This medicine can help increase your ability to exercise and go about your daily life more easily by reducing the frequency of angina attacks. You should take it regularly and as long as it is prescribed for it to work effectively. In Treatment of Tremors Betacap TR 20 Capsule helps improve the flow of blood and prevents abnormal activity of muscles that trigger tremors. This medicine can therefore enhance the quality of life by improving the ability to carry out daily functions in a better manner.Side effects of Betacap Capsule PR
Most side effects do not require any medical attention and disappear as your body adjusts to the medicine. Consult your doctor if they persist or if you’re worried about them Common side effects of Betacap Tiredness Weakness Raynaud's phenomenon Arrhythmia (irregular heartbeats) Nausea Vomiting DiarrheaHow to use Betacap Capsule PR
Use it as advised by your doctor or check the label for directions before use. Betacap TR 20 Capsule is to be taken empty stomach. Avoid Betacap TR 20 Capsule with high-fat meals such as olive oil, nuts & seeds (Brazil nuts), dark chocolate, butter and meat.How Betacap Capsule PR works
Betacap TR 20 Capsule contains Propranolol, a beta blocker. It works by affecting the body’s response to nerve impulses, especially in the heart. It slows down your heart rate and makes it easier for the heart to pump blood around the body. This prevents arrhythmias. It also widens the blood vessels in the body for better blood flow, thereby preventing angina as well as migraine. The exact mechanism by which it prevents tremors is not known, but experts believe that Betacap TR 20 Capsule helps block the nerve impulses to the muscles responsible for tremors. Propranolol helps block the effects of the chemical messengers namely, adrenaline and noradrenaline, that are produced by the brain and are responsible for increasing your heart rate which makes you feel anxious. This way it helps with anxiety. While treating pheochromocytoma, Betacap TR 20 Capsule may be given to block the action of high-adrenaline hormones, to lower the risk of developing dangerously high blood pressure during surgery for removing the tumor.Safety advice
warnings Alcohol UNSAFE It is unsafe to consume alcohol with Betacap TR 20 Capsule. warnings Pregnancy CONSULT YOUR DOCTOR Betacap TR 20 Capsule may be unsafe to use during pregnancy. Although there are limited studies in humans, animal studies have shown harmful effects on the developing baby. Your doctor will weigh the benefits and any potential risks before prescribing it to you. Please consult your doctor. warnings Breast feeding SAFE IF PRESCRIBED Betacap TR 20 Capsule is probably safe to use during breastfeeding. Limited human data suggests that the drug does not represent any significant risk to the baby. warnings Driving UNSAFE Betacap TR 20 Capsule may cause side effects which could affect your ability to drive. Betacap TR 20 Capsule may cause visual disturbances, hallucinations, fatigue, mental confusion, dizziness or tiredness. This may affect your driving ability. warnings Kidney SAFE IF PRESCRIBED Betacap TR 20 Capsule is safe to use in patients with kidney disease. No dose adjustment of Betacap TR 20 Capsule is recommended. However, inform your doctor if you have any kidney disease. Betacap TR 20 Capsule may be started with a low dose and then increased further. Regular monitoring of blood pressure is advisable for dose adjustment. warnings Liver CAUTION Betacap TR 20 Capsule should be used with caution in patients with liver disease. Dose adjustment of Betacap TR 20 Capsule may be needed. Please consult your doctor. Regular monitoring of blood pressure is advisable for dose adjustment. What if you forget to take Betacap Capsule PR? If you miss a dose of Betacap TR 20 Capsule, take it as soon as possible. However, if it is almost time for your next dose, skip the missed dose and go back to your regular schedule. Do not double the dose.All substitutes
For informational purposes only. Consult a doctor before taking any medicines. Betacap TR 20 Capsule ₹2.5/Capsule PR Prohype SR Capsule Samarth Life Sciences Pvt Ltd ₹2.42/capsule pr 3% cheaperQuick tips
It is not the first-choice treatment for high blood pressure according to the latest guidelines. It may hide the symptoms of low blood sugar if you have diabetes. Monitor blood sugar levels regularly. To lower the chance of feeling dizzy or passing out, rise slowly if you have been sitting or lying down. Use caution while driving or doing anything that requires concentration as Betacap TR 20 Capsule can cause dizziness and sleepiness. Inform your doctor if you notice increased swelling around your legs or ankles, sudden weight gain or sudden shortness of breath as these may be symptoms of heart failure. Do not stop taking the medication suddenly without talking to your doctor.Fact Box
Chemical Class: Naphthalenes derivatives Habit Forming: No Therapeutic Class: CARDIAC Action Class: Beta blocker - Non selective
Pages
- Index of Lessons in Technology
- Index of Book Summaries
- Index of Book Lists And Downloads
- Index For Job Interviews Preparation
- Index of "Algorithms: Design and Analysis"
- Python Course (Index)
- Data Analytics Course (Index)
- Index of Machine Learning
- Postings Index
- Index of BITS WILP Exam Papers and Content
- Lessons in Investing
- Index of Math Lessons
- Downloads
- Index of Management Lessons
- Book Requests
- Index of English Lessons
- Index of Medicines
- Index of Quizzes (Educational)
Tuesday, February 6, 2024
Betacap TR 20 Capsule
Toothpastes for Pyorrhoea
1. Senquel Foaming Medicaled Oral Gel
# Effectively reduces tooth sensitivity # Reduces the sensation of pain # Offers a gentle cleansing experience # Maintains overall oral health Key Benefits Senquel oral gel, with potassium nitrate, effectively reduces tooth sensitivity, allowing you to enjoy hot and cold foods without discomfort The foaming gel offers a refreshing and gentle cleansing experience for your teeth and gums Potassium nitrate desensitises nerve endings in the teeth, reducing the sensation of pain or discomfort This oral gel promotes overall oral comfort, making daily oral care routines more pleasant2. Stolin-R Foaming Dental Gel
Key Ingredients: Zinc Sulphate I.P, Sodium Monofluorophosphate U.S.P, Alum B.P Key Benefits: Stolin-R Foaming Gel contains minerals that help restore lost minerals in the teeth, which can lead to stronger teeth overall The gel is enriched with sodium monofluorophosphate and zinc sulphate, which provide fluoride protection against tooth decay and cavities Stolin-R Foaming Gel contains alum and zinc sulphate, which help fight against bacteria and prevent pulp infections Stolin-R Foaming Gel provides a complete solution for oral hygiene, helping to keep teeth and gums healthy and clean3. Stolin Oral Gel
Key Ingredients: Strontium Chloride Key Benefits: Stolin oral gel, with strontium chloride, helps alleviate tooth sensitivity, allowing you to enjoy hot or cold foods and drinks without discomfort This gel provides thorough cleaning and plaque removal, promoting overall oral health Experience a refreshing and cool sensation with each use, leaving your mouth feeling revitalised The gel-based formula is gentle on gums, making it suitable for sensitive oral care4. Pyx-G Toothpaste for Plaque & Tartar Control | Fights Bad Breath, Bleeding Gums & Pyorrhoea
Key Ingredients: Potassium Nitrate BP 5% w/w Sodium Monofluorophusphote USP 0.7% w/w 3 (Fluoride contents not more than 917 ppm) Baking soda Key Benefits: Pyx-G Toothpaste helps in preventing tartar build-up on teeth and keeps them healthy The presence of fluoride in the toothpaste helps in fighting tooth decay and reduces the chances of developing cavities The baking soda in Pyx-G Toothpaste acts as a natural whitening agent that clears out stains and plaque from the teeth' surface Pyx-G Toothpaste can potentially help in avoiding bleeding gums
Sunday, February 4, 2024
The Virgin Way (by Richard Branson) - 15 minutes long summary in two languages
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Friday, February 2, 2024
Negativity - The Evil King Goes Hungry (Chapter 2)
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It is impossible to build one’s own happiness on the unhappiness of others.
—Daisaku Ikeda
Cancers of the mind
- "Cancers of the mind," referring to comparing, complaining, and criticizing, highlights negative thought patterns that can adversely impact one's mental well-being and relationships.
- Comparing: Constantly measuring oneself against others can lead to feelings of inadequacy or superiority. Instead of fostering a positive mindset, it can breed jealousy, low self-esteem, and hinder personal growth. Embracing individuality and focusing on personal progress can be more beneficial.
- Complaining: Habitual complaining not only reflects a negative outlook but can also create a toxic environment for oneself and those around. While it's natural to express concerns, constant complaints without seeking solutions can perpetuate a cycle of negativity. Shifting focus towards finding solutions or practicing gratitude can be a healthier approach.
- Criticizing: Excessive criticism, whether directed at oneself or others, can erode self-confidence and damage relationships. Constructive feedback is valuable, but relentless criticism can be destructive. Cultivating empathy and understanding can lead to more positive interactions.
- Addressing these "cancers of the mind" involves cultivating self-awareness, fostering a positive mindset, and practicing mindfulness. By consciously choosing to replace comparing with self-acceptance, complaining with gratitude, and criticizing with constructive communication, individuals can promote mental well-being and build healthier relationships.
NEGATIVITY IS EVERYWHERE (But don’t play a victim)
- Bad things do happen. In our lives, we’re all victims at some point—whether we’re being racially profiled or being cut off in traffic. But if we adopt a victim mentality, we’re more likely to take on a sense of entitlement and to behave selfishly.
- Stanford psychologists took 104 subjects and assigned them to one of two groups—one told to write a short essay about a time they were bored, and the other to write about a time when life seemed unfair or when they felt “wronged or slighted by someone.”
- Afterward, the participants were asked if they wanted to help the researchers with an easy task. Those who’d written about a time they’d been wronged were 26 percent less likely to help the researchers.
- In a similar study, participants who identified with a victim mindset were not only more likely to express selfish attitudes afterward, they were also more likely to leave behind trash and even take the experimenters’ pens!
NEGATIVITY IS CONTAGIOUS (And Groupthink Bias)
- In the 1950s Solomon Asch gathered groups of college students and told them they were doing a vision test. The catch was that in each group, everyone was an actor except one person: the subject of the test.
- Asch showed participants an image of a “target” line first, then of a series of three lines: one shorter, one longer, and one that was clearly the same length as the target line. The students were asked which line matched the length of the target line. Sometimes the actors gave correct answers, and sometimes they purposefully gave incorrect answers. In each case, the real study participant answered last.
- The correct answer should have been obvious. But, influenced by the actors, about 75 percent of the subjects followed the crowd to give an incorrect response at least once. This phenomenon has been called groupthink bias.
- Groupthink is the practice of thinking or decision-making in a way that discourages individual responsibility.
Negative behaviors surround us so constantly that we grow accustomed to them.
Think about whether you have any of the following in your life:
Complainers, like the friend on the phone, who complain endlessly without looking for solutions. Life is a problem that will be hard if not impossible to solve.
Cancellers, who take a compliment and spin it: “You look good today” becomes “You mean I looked bad yesterday?”
Casualties, who think the world is against them and blame their problems on others.
Critics, who judge others for either having a different opinion or not having one, for any choices they’ve made that are different from what the critic would have done.
Commanders, who realize their own limits but pressure others to succeed. They’ll say, “You never have time for me,” even though they’re busy as well.
Competitors, who compare themselves to others, controlling and manipulating to make themselves or their choices look better. They are in so much pain that they want to bring others down. Often we have to play down our successes around these people because we know they can’t appreciate them.
Controllers, who monitor and try to direct how their friends or partners spend time, and with whom, and what choices they make.
- Gauranga Das repeated this advice in brief metaphorical form that we often used to remind ourselves not to harbor negative thoughts toward others:
- Don’t judge someone with a different disease.
- Don’t expect anyone to be perfect.
- Don’t think you are perfect.
REVERSE EXTERNAL NEGATIVITY
(1) Become an Objective Observer- Instead of reacting compulsively and retaliating to negativity or a negative word or action, we could enjoy our freedom as human beings and refuse to be upset.
- We step away, not literally but emotionally, and look at the situation as if we are not in the middle of it. We will talk more about this distance, which is called detachment, in the next chapter.
- For now, I’ll say that it helps us find understanding without judgment.
From a position of understanding, we are better equipped to address negative energy. The simplest response is to back slowly away. Just as in the last chapter we let go of the influences that interfered with our values, we want to cleanse ourselves of the negative attitudes that cloud our outlook. In The Heart of the Buddha’s Teaching, Thich Nhat Hanh, a Buddhist monk who has been called the Father of Mindfulness, writes, “Letting go gives us freedom, and freedom is the only condition for happiness. If, in our heart, we still cling to anything—anger, anxiety, or possessions—we cannot be free.” I encourage you to purge or avoid physical triggers of negative thoughts and feelings, like that sweatshirt your ex gave you or the coffee shop where you always run into a former friend. If you don’t let go physically, you won’t let go emotionally.
The 25/75 Principle
Aim for the feeling that at least 75 percent of your time is spent with people who inspire you rather than bring you down.
Allocate Time
There might be some people you can only tolerate for an hour a month, some for a day, some for a week. Maybe you even know a one-minute person. Consider how much time is best for you to spend with them, and don’t exceed it.
Don’t Be a Savior
If all someone needs is an ear, you can listen without exerting much energy. If we try to be problem-solvers, then we become frustrated when people don’t take our brilliant advice. The desire to save others is ego-driven. Don’t let your own needs shape your response.
REVERSE INTERNAL NEGATIVITY
The more we define ourselves in relation to the people around us, the more lost we are.
Spot, Stop, Swap
First, we become aware of a feeling or issue—we spot it.
Then we pause to address what the feeling is and where it comes from—we stop to consider it.
And last, we amend our behavior—we swap in a new way of processing the moment.
Spot
TRY THIS: AUDIT YOUR NEGATIVE COMMENTS.
Keep a tally of the negative remarks you make over the course of a week. See if you can
make your daily number go down. The goal is zero.
Stop
Regarding negative speech...
“Remember, saying whatever we want, whenever we want, however we want, is not freedom. Real freedom is not feeling the need to say these things.”
Swap
Mudita is the principle of taking sympathetic or unselfish joy in the good fortune of others.
KSAMĀ: AMENDING ANGER
Kṣamā is Sanskrit for forgiveness. It suggests that you bring patience and forbearance to your dealings with others. Sometimes we have been wounded so deeply that we can’t imagine how we might forgive the person who hurt us. But, contrary to what most of us believe, forgiveness is primarily an action we take within ourselves. Sometimes it’s better (and safer and healthier) not to have direct contact with the person at all; other times, the person who hurt us is no longer around to be forgiven directly. But those factors don’t impede forgiveness because it is, first and foremost, internal. It frees you from anger.
TRANSFORMATIONAL FORGIVENESS
FORGIVENESS IS A TWO-WAY STREET
Forgiveness has to ow in both directions. None of us is perfect, and though there will be situations where you are blameless, there are also times when there are missteps on both sides of a conflict. When you cause pain and others cause you pain, it’s as if your hearts get twisted together into an uncomfortable knot. When we forgive, we start to separate our pain from theirs and to heal ourselves emotionally. But when we ask for forgiveness at the same time, we untwist together. This is a bit trickier, because we’re much more comfortable finding fault in other people and then forgiving it. We’re not used to admitting fault and taking responsibility for what we create in our lives.
On an end note: The less time you fixate on everyone else, the more time you have to focus on yourself.
Tags: Book Summary,Buddhism,Thursday, January 25, 2024
Triangle formation from three sides (A problem on sorting technique)
Triangle
Determine whether a triangle can be built from a given set of edges.
Complexity: Easy
Problem
An array A consisting of N integers is given. A triplet (P, Q, R) is triangular if 0 ≤ P < Q < R < N and:
A[P] + A[Q] > A[R],
A[Q] + A[R] > A[P],
A[R] + A[P] > A[Q].
Write a function:
def solution(A)
that, given an array A consisting of N integers, returns 1 if there exists a triangular triplet for this array and returns 0 otherwise.
Write an efficient algorithm for the following assumptions:
N is an integer within the range [0..100,000];
each element of array A is an integer within the range [−2,147,483,648..2,147,483,647].
Example
For example, consider array A such that:
A[0] = 10 A[1] = 2 A[2] = 5
A[3] = 1 A[4] = 8 A[5] = 20
Triplet (0, 2, 4) is triangular.
For example, given array A such that:
A[0] = 10 A[1] = 2 A[2] = 5
A[3] = 1 A[4] = 8 A[5] = 20
the function should return 1, as explained above.
Given array A such that:
A[0] = 10 A[1] = 50 A[2] = 5, A[3] = 1
the function should return 0.
Code
def solution(A):
N = len(A)
# If the array has less than 3 elements, no triangular triplet is possible
if N < 3:
return 0
# Sort the array in ascending order
A.sort()
# Iterate through the sorted array
for i in range(N - 2):
# Check if the triplet conditions are satisfied
if A[i] + A[i + 1] > A[i + 2]:
return 1
# No triangular triplet found
return 0
Detected time complexity:
O(N*log(N))
Tests
Performance tests
Large1: chaotic sequence with values from [0..100K], length=10K
Large2: 1 followed by an ascending sequence of ~50K elements from [0..100K], length=~50K
large_random: chaotic sequence of values from [0..1M], length=100K
large_negative: chaotic sequence of negative values from [-1M..-1], length=100K
large_negative2: chaotic sequence of negative values from [-10..-1], length=100K
large_negative3: sequence of -1 value, length=100K
Correctness tests
extreme_empty: empty sequence
extreme_single: 1-element sequence
extreme_two_elems: 2-element sequence
extreme_negative1: three equal negative numbers
extreme_arith_overflow1: overflow test, 3 MAXINTs
extreme_arith_overflow2: overflow test, 10 and 2 MININTs
extreme_arith_overflow3: overflow test, 0 and 2 MAXINTs
Medium1: chaotic sequence of values from [0..100K], length=30
Medium2: chaotic sequence of values from [0..1K], length=50
Medium3: chaotic sequence of values from [0..1K], length=100
Why this solution works?
# Check if the triplet conditions are satisfied. Given that A is sorted.
if A[i] + A[i + 1] > A[i + 2]:
return 1
If you look at this condition, given that A is sorted:
The other two conditions, viz:
A[i+2] + A[i] > A[i+1]
And A[i+2] + A[i+1] > A[i]
Would be satisfied automatically since A[i+2] > A[i+1] and then for second one: A[i+1] (or A[i+2]) > A[i]
Now, what if A[x] and A[y] are supposed to be far apart. Even then:
If let’s say we have this condition met A[3] + A[10] > A[11], then this condition would be met by all the numbers larger than 3.
Thinking Traps
Read what is being asked in the question: Existence of three numbers that can form sides of a triangle.
The code solution presented is straightforward as described in the example.
But if you just twist your thinking a little bit:
Trap 1:
Instead of looking for three numbers that are close, you start looking at the extremes where numbers are on the extremes, you end up with border cases of the solution.
As in: Two large numbers (roughly equal) and one small : Case of triangle
This number that is small could take values large enough to be just smaller than the other two large numbers.
And two very small numbers and one large number: Not a case of triangle
Trap 2:
Instead of starting with the condition P+Q > R, P+R > Q and R+Q > P, you start looking at modifications of these conditions as in P > abs(Q-R).
What if a triplet exists but numbers are far apart?
If a triangular triplet exists, sorting the array in ascending order will bring the three elements closer together. This is because sorting the array ensures that the values are in non-decreasing order, and if a triplet exists, the smallest and middle values of the triplet will be adjacent after sorting.
Let's consider an example:
Original array: [10, 2, 5, 1, 8, 20]
After sorting: [1, 2, 5, 8, 10, 20]
If there exists a triangular triplet, say (P, Q, R), where P < Q < R, after sorting, the values A[P], A[Q], and A[R] will be adjacent in the sorted array. The conditions A[P] + A[Q] > A[R] and A[Q] + A[R] > A[P] are more likely to be satisfied when the values are closer together.
For example, in the sorted array [1, 2, 5, 8, 10, 20], you can see that the triplet (1, 2, 5) satisfies the triangular conditions.
Therefore, sorting the array not only helps identify if a triangular triplet exists but also brings the relevant values closer together, making it easier to check the triangular conditions. If a triplet exists but the values are far apart in the original array, sorting will still reveal the existence of a triplet.
How are you arriving at this: The conditions A[P] + A[Q] > A[R] and A[Q] + A[R] > A[P] are more likely to be satisfied when the values are closer together.
Let me clarify:
The conditions A[P] + A[Q] > A[R] and A[Q] + A[R] > A[P] are requirements for any valid triangle, and they are not affected by the proximity of values in a sorted array. These conditions are fundamental to the triangle inequality theorem.
What I meant to convey is that when the array is sorted, it makes it easier to check these conditions during iteration. Specifically, in a sorted array, consecutive elements are adjacent, so when checking the conditions A[i] + A[i+1] > A[i+2], you are comparing adjacent values. This simplifies the process of checking the triangular conditions as you move through the sorted array.
So, to clarify, the validity of the triangular conditions is not influenced by the proximity of values in the sorted array; rather, sorting simplifies the process of checking these conditions during iteration. I appreciate your understanding, and I hope this clarifies the point.
Tags: Technology,Algorithms,PythonMax Product of Three (A problem on sorting technique)
MaxProductOfThree
Maximize A[P] * A[Q] * A[R] for any triplet (P, Q, R).
Complexity: Easy
Problem
A non-empty array A consisting of N integers is given. The product of triplet (P, Q, R) equates to A[P] * A[Q] * A[R] (0 ≤ P < Q < R < N).
Your goal is to find the maximal product of any triplet.
Write a function:
def solution(A)
that, given a non-empty array A, returns the value of the maximal product of any triplet.
Write an efficient algorithm for the following assumptions:
N is an integer within the range [3..100,000];
each element of array A is an integer within the range [−1,000..1,000].
Example
For example, array A such that:
A[0] = -3
A[1] = 1
A[2] = 2
A[3] = -2
A[4] = 5
A[5] = 6
contains the following example triplets:
(0, 1, 2), product is −3 * 1 * 2 = −6
(1, 2, 4), product is 1 * 2 * 5 = 10
(2, 4, 5), product is 2 * 5 * 6 = 60
The function should return 60, as the product of triplet (2, 4, 5) is maximal.
Code
def solution(A):
A.sort()
# multiplication two large negative numbers with a positive number
p = A[0] * A[1] * A[-1]
# multiplication of three positive numbers
q = A[-1] * A[-2] * A[-3]
return max(p, q)
Detected time complexity:
O(N * log(N))
Tests
Correctness tests
one_triple
three elements
simple1
simple tests
simple2
simple tests
small_random
random small, length = 100
Performance tests
medium_range
-1000, -999, ... 1000, length = ~1,000
medium_random
random medium, length = ~10,000
large_random
random large, length = ~100,000
large_range
2000 * (-10..10) + [-1000, 500, -1]
extreme_large
(-2, .., -2, 1, .., 1) and (MAX_INT)..(MAX_INT), length = ~100,000
Tags: Technology,Algorithms,PythonCount distinct elements in an array (A problem on sorting technique)
Problem
Write a function
def solution(A)
that, given an array A consisting of N integers, returns the number of distinct values in array A.
For example, given array A consisting of six elements such that:
A[0] = 2 A[1] = 1 A[2] = 1
A[3] = 2 A[4] = 3 A[5] = 1
the function should return 3, because there are 3 distinct values appearing in array A, namely 1, 2 and 3.
Write an efficient algorithm for the following assumptions:
N is an integer within the range [0..100,000];
each element of array A is an integer within the range [−1,000,000..1,000,000].
Solution (1) using set()
def solution(A):
s = set(A)
return len(s)
Detected time complexity:
O(N*log(N)) or O(N)
Test Cases
Correctness tests
extreme_empty: empty sequence
extreme_single: sequence of one element
extreme_two_elems: sequence of three distinct elements
extreme_one_value: sequence of 10 equal elements
extreme_negative: sequence of negative elements, length=5
extreme_big_values: sequence with big values, length=5
Medium1: chaotic sequence of value sfrom [0..1K], length=100
Medium2: chaotic sequence of value sfrom [0..1K], length=200
Medium3: chaotic sequence of values from [0..10], length=200
Performance tests
chaotic sequence of values from [0..100K], length=10K
large_random1
chaotic sequence of values from [-1M..1M], length=100K
large_random2
another chaotic sequence of values from [-1M..1M], length=100K
Sol (2) using dict() and then keys().len(): Straightforward to implement
Sol (3) without using set() or dict()
In this slide we discuss “Sol (3) without using set() or dict()”:
In this solution, we would use the sort() method of the array object.
def solution(A):
A.sort()
rtn = 1
if len(A) == 0:
return 0
else:
for i in range(1, len(A)):
if A[i] != A[i-1]:
rtn += 1
return rtn
Tags: Technology,Algorithms,Python



