Found 547 Articles for Algorithms

Two numbers are given as a binary string, our task is to find the result of multiplication for those numbers in a faster and efficient way.Using the Divide and Conquer strategy, we can solve the problem, in a very efficient manner. We will split the numbers into two halves.let Xleft and Xright are two parts of first number X, and Yleft, Yright are two parts of second number Y. So the product;To make it simple, we can perform this operationInput and OutputInput: Two binary numbers: 1101 and 0111 Output: The result is: 91AlgorithmaddBitString(num1, num2)Input: Two numbers to add.Output: The result after ... Read More

A directed graph is given. Another two vertices u and v are also given, u is the starting vertex, and v is the ending vertex. Our task is to find a number of walks from vertex u to v with exactly k edges. The value of k is also provided in the algorithm.By using dynamic programming, we need to create a 3D table, Where the row will point the values of u, columns will point the values v and depth will be used to track the number of edges from start to end.Input and OutputInput: The adjacency matrix of the ... Read More

Roman numbers are non-positional numbers. Some numerals are placed together to form a number in roman numbers. For an example the number 75 can be expressed as 75 = 50 + 10 + 10 + 5, so the roman numerals are LXXV.In this problem one number is provided in a decimal format, our task is to convert it into the Roman numeral strings.There are different symbols and their value, like this.IIVVIXXXLLXCCCDDCMMMMMMV’145910405090100400500900100040005000Using this table, we can easily find the roman numerals of a given number.Input and OutputInput: Decimal number: 3569 Output: The Roman equivalent of 3569 is: MMMDLXIXAlgorithmdecToRoman(nuList, num)Input: The numeral list ... Read More

There are N ropes of given lengths. We have to connect with them. The cost of connecting one rope with other is the sum of their lengths. Our goal is to connect the N ropes with minimum cost.This problem can be solved using a heap tree. We will create min heap to insert all different lengths first, then remove minimum and second minimum item from min heap, connect them and again insert into the heap tree. When the heap will hold only one element, we can stop the process and get the connected rope with minimum costs.Input and OutputInput: The ... Read More

Three points of a triangle are given; another point P is also given to check whether the point P is inside the triangle or not.To solve the problem, let consider the points of the triangle are A, B, and C. When the area of triangle Δ𝐴𝐵𝐶 = Δ𝐴𝐵𝑃 + Δ𝑃𝐵𝐶 + Δ𝐴𝑃𝐶, then the point P is inside the triangle.Input and OutputInput: Points of the triangle {(0, 0), (20, 0), (10, 30)} and point p (10, 15) to check. Output: Point is inside the triangle.AlgorithmisInside(p1, p2, p3, p)Input: Three points of a triangle, the point p to check.Output: True, when ... Read More

Let two line-segments are given. The points p1, p2 from the first line segment and q1, q2 from the second line segment. We have to check whether both line segments are intersecting or not.We can say that both line segments are intersecting when these cases are satisfied:When (p1, p2, q1) and (p1, p2, q2) have a different orientation and(q1, q2, p1) and (q1, q2, p2) have a different orientation.There is another condition is when (p1, p2, q1), (p1, p2, q2), (q1, q2, p1), (q1, q2, p2) are collinear.Input and OutputInput: Points of two line-segments Line-segment 1: (0, 0) to (5, ... Read More

Two sets are disjoint set when they have no common elements. In other words, if we get the intersection of two sets, then we will get null set.The method is simple, in this algorithm, two sets are given. We assume that both sets are already sorted, items are compared between two sets. when there is a match, then it is not a disjoint set, when no items are matched, they are disjoint sets.Input and OutputInput: Two sets: set1: {15, 12, 36, 21, 14} set2: {7, 89, 56, 32} Output: Both sets are disjointAlgorithmisDisjoint(set1, set2)Input: Two sets.Output: True when both sets ... Read More

A number is said to be a perfect square number if the square root of that number is an integer. In other words, when a square root is a whole number, then the number is called a perfect square number.We can check perfect square by finding the square root of that number and match with i again and again to get exact square root. When the square root crosses the value, it is not a perfect square number.But here to reduce effort, we have not checked the square root again and again. As we know that the square root of ... Read More

In this problem, one polygon is given, and a point P is also given. We need to check whether the point is inside the polygon or outside the polygon.For solving it we will draw a straight line from the point P. It extends to the infinity. The line is horizontal, or it is parallel to the x-axis.From that line, we will count how many times the line intersects the sides of a polygon. When the point is inside the polygon, it will intersect the sides, an odd number of times, if P is placed on any side of the polygon, ... Read More

In computers, variables are stored in memory locations. But the size of the memory location is fixed, so when we try to find the factorial of some greater value like 15! or 20! the factorial value exceeds the memory range and returns wrong results.For calculation of large numbers, we have to use an array to store results. In each element of the array, is storing different digits of the result. But here we cannot multiply some number with the array directly, we have to perform manual multiplication process for all digits of the result array.Input and OutputInput: A big number: ... Read More