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Here is a sample walkthrough of how we are applying binary search.TextPad is a Windows text editor that provides many more features than the standard tools bundled into the operating system. We apply binary search in this range, to find the value whose square is equal to 13 (up to 6 decimal places). We know that the square root will lie between (3, 4). In order to find the decimal places, we can use Binary Search. Now that we have the value of R(3), let’s find abcdef. So we can be sure that the square root of 13 as well will be something like 3.abcdef. Since the square of 4 is 16, which is greater than 13, the square root of 13 has to be less than 4. Observe that the maximum perfect square less than 13 is 9 whose square root is 3. Let’s say we need to find the square root of 13, which is not a perfect square. So, we need a way to find the nearest approximate value for the square root (up to 6 decimal places for now).
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Numbers that are not a perfect square will have a real number (decimal) as their square root. You: That’s great, but what about numbers that are not a perfect square? So, if we want to calculate the square root of X which is a perfect square, we need to find a number which when multiplied with itself equals X. On the other hand, 10 is not a perfect square because it cannot be represented as the square of an integer. Here, 9 is a perfect square because 9 is the square of 3.
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Hence, we will try to find the square root in the right side of mid by repeating repeat step 3 for (mid, high)Ī perfect square is an integer which is the square of an integer.
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This Implies, the square root of n must be greater than mid, since any value less than mid can never satisfy the condition mid * mid = n. else mid * mid Hence, we will try to find the square root in the left side of mid by repeating step 3 for (low, mid) This Implies, the square root of n must be less than mid, since any value higher than mid can never satisfy the condition mid * mid = n. if mid * mid > n, it means that the assumption we made is incorrect.if mid * mid = n, it means we assume that mid is the square root of n.Apply binary search in the range (low, high).if i * i > n, it means the square root must lie between (i-1, i), let’s call them (low, high).Start from i = 1, if i * i = n, then i is the square root of n as n is a perfect square.Let me propose an algorithm first and then we’ll break it down one step at a time. Now that we have looked at a few ways to find the square root of a number using inbuilt functions in Java, let’s look at a way without using any such inbuilt function. Neat right? The same function is used to calculate two different operations. ( "The square root of " + X + " is " + R) Just multiply the number by itself and you’re good to go. There are a couple of ways to find the square of a number in Java. Now that we know what we mean by the square and square root of a number, let’s see how we can write a program for it in Java. It’s alright, try to breathe that in for a moment ? In a nutshell, if the square of a number X is S, then X is the square root of S. This is important, keep reading to find out why ? The square root of X can also be represented by X 1/2. The square root of a number X is the number that when multiplied by itself equals X. Square root is exactly the opposite of the square of a number. Square of 3 = 3 * 3 = 9 What is Square Root? In other words, if we multiply a number by itself, the result is the square of that number. Simply put, the square of a number is the number multiplied by itself. Let’s start by defining what a square and square root actually means. If that doesn’t excite you, they are a hot topic in interviews as well ? Square and square root of a number is one of the principles which are used in many real-life applications as well as programming concepts, for example prime factors of a number, binary exponentiation etc. As a programmer, I always find it fascinating to write programs for mathematical operations I used to do by hand back in school.