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Algorithm to find 2 numbers that add up to 600 from a list of numbers with O(N) complexity.
Use a hash table to store the difference between each number and 600.
Iterate through the list and check if the difference is in the hash table.
If the difference is in the hash table, return the current number and the difference.
Probability of an 8 bit string with no more than 2 consecutive 1's using dynamic programming.
Use dynamic programming to calculate the probability of a string with no more than 2 consecutive 1's
Create a 2D array to store the probabilities of each bit position and number of consecutive 1's
Use recurrence relation to calculate the probability for each bit position based on the previous bit position
Sum up the probabilities ...
Efficiently determine if a given graph contains a 3 cycle.
Use depth-first search (DFS) to traverse the graph
For each node, check if there is a path of length 3 that ends at that node
If such a path exists, return true
If DFS completes without finding a 3 cycle, return false
e^π is greater than π^e.
e^π ≈ 23.14
π^e ≈ 22.46
e^π > π^e
Expected number of trials for 4 consecutive heads with a fair coin.
The probability of getting 4 consecutive heads is 1/2^4 = 1/16
The expected number of trials for 4 consecutive heads is 1/p = 16
This is because the expected value of a geometric distribution with probability p is 1/p
Therefore, the expected number of flips for 4 consecutive heads is 16
I manage my team by setting clear goals, providing support and resources, and fostering open communication.
Set clear goals and expectations
Provide support and resources
Foster open communication
Encourage collaboration and teamwork
Recognize and reward achievements
Address conflicts and challenges promptly
I would try to understand the reasons behind their differing opinions and facilitate a discussion to find a common ground.
I would schedule a team meeting to discuss the issue
I would encourage everyone to share their opinions and listen actively
I would try to find common ground and work towards a solution that everyone can agree on
I would emphasize the importance of teamwork and collaboration
I would follow up with the t...
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