Problem: Let A be an unsorted array of n floating numbers. Propose an O(n) time algorithm to compute the (floating-point) number x (not necessarily an element of A) for which max|A[i] - x| is as small as possible for all 1 <= i <= n. (Here |y| means absolute value of y)
Solution: The problem statement can be interpreted as finding a point x such that it's distance from the farthest point is minimized (since, |A[i] - x| is given which is actually distance between two point). Note: we don't need to minimize distance from every point, we just need to minimize the distance of the point which is farthest to it. So we try to put our x as close to the farthest point. But in doing so the point which is near may go far. So the optimal solution is finding the minimum point in the array A (let it be named MN) and finding the maximum point of A (let it be named MX) and the result is the mid-point of these two points, i.e x=(MN+MX)/2. Note: All other point between MN and MX will have distance lesser hence we do not bother it. We could not get more optimal point than this one. Now, MX and MN can be easily determined by travelling once the array. Hence the time complexity is O(n).
Problem: Let A be an unsorted array of n floating numbers. Propose an O(n) time algorithm to compute the (floating-point) number x (not necessarily an element of A) for which max|A[i] - x| is as small as possible for all 1 <= i <= n. (Here |y| means absolute value of y)
Solution: The problem statement can be interpreted as finding a point x such that it's distance from the farthest point is minimized (since, |A[i] - x| is given which is actually distance between two point). Note: we don't need to minimize distance from every point, we just need to minimize the distance of the point which is farthest to it. So we try to put our x as close to the farthest point. But in doing so the point which is near may go far. So the optimal solution is finding the minimum point in the array A (let it be named MN) and finding the maximum point of A (let it be named MX) and the result is the mid-point of these two points, i.e x=(MN+MX)/2. Note: All other point between MN and MX will have distance lesser hence we do not bother it. We could not get more optimal point than this one. Now, MX and MN can be easily determined by travelling once the array. Hence the time complexity is O(n).
Happy Coding!!!
BY Competitive Programming
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Telegram’s stand out feature is its encryption scheme that keeps messages and media secure in transit. The scheme is known as MTProto and is based on 256-bit AES encryption, RSA encryption, and Diffie-Hellman key exchange. The result of this complicated and technical-sounding jargon? A messaging service that claims to keep your data safe.Why do we say claims? When dealing with security, you always want to leave room for scrutiny, and a few cryptography experts have criticized the system. Overall, any level of encryption is better than none, but a level of discretion should always be observed with any online connected system, even Telegram.
The lead from Wall Street offers little clarity as the major averages opened lower on Friday and then bounced back and forth across the unchanged line, finally finishing mixed and little changed.The Dow added 33.18 points or 0.10 percent to finish at 34,798.00, while the NASDAQ eased 4.54 points or 0.03 percent to close at 15,047.70 and the S&P 500 rose 6.50 points or 0.15 percent to end at 4,455.48. For the week, the Dow rose 0.6 percent, the NASDAQ added 0.1 percent and the S&P gained 0.5 percent.The lackluster performance on Wall Street came on uncertainty about the outlook for the markets following recent volatility.
