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Articles by Samual Sam
Page 108 of 151
Maximum size square submatrix with all 1s
When a binary matrix is given, our task is to find a square matrix whose all elements are 1.For this problem, we will make an auxiliary size matrix, whose order is the same as the given matrix. This size matrix will help to represent, in each entry Size[i, j], is the size of a square matrix with all 1s. From that size matrix, we will get the maximum number to get the size of the biggest square matrix.Input and OutputInput: The binary matrix. 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 ...
Read MoreMinimum Cost Polygon Triangulation
When nonintersecting diagonals are forming a triangle in a polygon, it is called the triangulation. Our task is to find a minimum cost of triangulation.The cost of triangulation is the sum of the weights of its component triangles. We can find the weight of each triangle by adding their sides, in other words, the weight is the perimeter of the triangle.Input and OutputInput: The points of a polygon. {(0, 0), (1, 0), (2, 1), (1, 2), (0, 2)} Output: The total cost of the triangulation. Here the cost of the triangulation is 15.3006.AlgorithmminCost(polygon, n)Here cost() will be used to calculate ...
Read MoreMinimum Initial Points to Reach Destination
To start from the top-left corner of a given grid, one has to reach the bottom-right corner. Each cell in the grid contains a number, the number may positive or negative. When the person reaches a cell (i, j) the number of tokens he has, may be increased or decreased along with the values of that cell. We have to find the minimum number of initial tokens are required to complete the journey.There are some rules −We can either move to the right or to the bottom.We cannot move to a cell (i, j) if our total token is less ...
Read MoreHow to print maximum number of A's using given four keys
Let us consider, we will try to write the letter ‘A’, using the keyboard. Our goal is to use only four keys and try to write maximum ‘A’s on the text field. The keys are ‘A’, ‘C’, ‘V’ and ‘Ctrl’.To write the maximum number of A, we will use Ctrl + A to select All, Ctrl + C to copy and Ctrl + V to paste.Input and OutputInput: Number of keystrokes, say 7 Output: Maximum Number of A's with 7 keystrokes is: 9 Press A three times. Then Ctrl+A, Ctrl+C, Ctrl+V, Ctrl+VAlgorithmkeyNumbers(keyStrokes)Input: number of keystrokes.Output: Maximum number of letters using these ...
Read MoreCompute sum of digits in all numbers from 1 to n
In this problem, we have to find the sum of digits of all numbers in range 1 to n. For an example the sum of digits of 54 is 5 + 4 = 9, Like this, we have to find all the numbers and their sum of digits.We know that there are 10d - 1 numbers can be generated, whose number of digits is d. To find the sum of all those numbers of digit d, we can use a recursive formula.sum(10d- 1)=sum(10d-1- 1)*10+45*(10d-1)Input and OutputInput: This algorithm takes the upper limit of the range, say it is 20. Output: ...
Read MoreCount ways to reach the n'th stair
There are n stairs. One person will go to 1'st to the n'th stair. Maximum how many stairs he/she can cross in one step is also given. With this information, we have to find possible ways to go to the n'th stairs.Let us consider one can cross a maximum two stairs in each step. So we can find recursive relations to solve this problem. One can move to n'th stair, either from (n-1)'th stair or from (n-2)'th stair. So ways(n) = ways(n-1) + ways(n-2).Input and OutputInput: The number of stairs, say 10 the maximum number of stairs that can be ...
Read MoreBox Stacking Problem
In this problem a set of different boxes are given, the length, breadth, and width may differ for different boxes. Our task is to find a stack of these boxes, whose height is as much as possible. We can rotate any box as we wish. But there is a rule to maintain.One can place a box on another box if the area of the top surface for the bottom box is larger than the lower area of the top box.Input and OutputInput: A list of boxes is given. Each box is denoted by (length, bredth, height). { (4, 6, 7), ...
Read MoreLongest Path in a Directed Acyclic Graph
One weighted directed acyclic graph is given. Another source vertex is also provided. Now we have to find the longest distance from the starting node to all other vertices, in the graph.We need to sort the nodes in topological sorting technique, and the result after the topological sort is stored into a stack. After that repeatedly popped from the stack and try to find the longest distance for each vertex.Input and OutputInput: The cost matrix of the graph. 0 5 3 -∞ -∞ -∞ -∞ 0 2 6 -∞ -∞ -∞ -∞ 0 7 4 2 -∞ -∞ ...
Read MoreShortest path with exactly k Edges
One directed graph is provided with the weight between each pair of vertices, and two vertices u and v are also provided. Our task is to find the shortest distance from vertex u to vertex v, with exactly k number of edges. To solve this problem, we will start from vertex u and go to all adjacent vertices and recur for adjacent vertices using the k value as k - 1.Input and OutputInput: The cost matrix of the graph. 0 10 3 2 ∞ 0 ∞ 7 ∞ ∞ 0 6 ∞ ∞ ∞ 0 Output: Weight of the shortest ...
Read MoreConnectivity in a directed graph
To check connectivity of a graph, we will try to traverse all nodes using any traversal algorithm. After completing the traversal, if there is any node, which is not visited, then the graph is not connected.For the directed graph, we will start traversing from all nodes to check connectivity. Sometimes one edge can have the only outward edge but no inward edge, so that node will be unvisited from any other starting node.In this case, the traversal algorithm is recursive DFS traversal.Input and OutputInput: Adjacency matrix of a graph 0 1 0 0 0 0 0 1 0 ...
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