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 More

A matrix of the different cost is given. Also, the destination cell is provided. We have to find minimum cost path to reach the destination cell from the starting cell (0, 0).Each cell of the matrix represents the cost to traverse through that cell. From a cell, we cannot move anywhere, we can move either to the right or to the bottom or to the lower right diagonal cell, to reach the destination.Input and OutputInput: The cost matrix. And the destination point. In this case the destination point is (2, 2). 1 2 3 4 8 2 1 5 3 ... Read More

A matrix is given. We need to find a rectangle (sometimes square) matrix, whose sum is maximum.The idea behind this algorithm is to fix the left and right columns and try to find the sum of the element from the left column to right column for each row, and store it temporarily. We will try to find top and bottom row numbers. After getting the temporary array, we can apply the Kadane’s Algorithm to get maximum sum sub-array. With it, the total rectangle will be formed.Input and OutputInput: The matrix of integers.  1  2 -1 -4 -20 -8 -3  4 ... Read More

Maximum Sum Increasing subsequence is a subsequence of a given list of integers, whose sum is maximum and in the subsequence, all elements are sorted in increasing order.Let there is an array to store max sum increasing subsequence, such that L[i] is the max sum increasing subsequence, which is ending with array[i].Input and OutputInput: Sequence of integers. {3, 2, 6, 4, 5, 1} Output: Increasing subsequence whose sum is maximum. {3, 4, 5}.AlgorithmmaxSumSubSeq(array, n)Input: The sequence of numbers, number of elements.Output: Maximum sum of the increasing sub sequence.Begin    define array of arrays named subSeqLen of size n.    add ... Read More

In a trading, one buyer buys and sells the shares, at morning and the evening respectively. If at most two transactions are allowed in a day. The second transaction can only start after the first one is completed. If stock prices are given, then find the maximum profit that the buyer can make.Input and OutputInput: A list of stock prices. {2, 30, 15, 10, 8, 25, 80} Output: Here the total profit is 100. As buying at price 2 and selling at price 30. so profit 28. Then buy at price 8 and sell it again at price 80. So ... Read More

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 More

There is a chain of pairs is given. In each pair, there are two integers and the first integer is always smaller, and the second one is greater, the same rule can also be applied for the chain construction. A pair (x, y) can be added after a pair (p, q), only if q < x.To solve this problem, at first, we have to sort given pairs in increasing order of the first element. After that, we will compare the second element of a pair, with the first element of the next pair.Input and OutputInput: A chain of number pairs. ... Read More

Longest Palindromic Subsequence is the subsequence of a given sequence, and the subsequence is a palindrome.In this problem, one sequence of characters is given, we have to find the longest length of a palindromic subsequence.To solve this problem, we can use the recursive formula, If L (0, n-1) is used to store a length of longest palindromic subsequence, thenL (0, n-1) := L (1, n-2) + 2 (When 0'th and (n-1)'th characters are same).Input and OutputInput: A string with different letters or symbols. Say the input is “ABCDEEAB” Output: The longest length of the largest palindromic subsequence. Here it is ... Read More

Longest Increasing Subsequence is a subsequence where one item is greater than its previous item. Here we will try to find Longest Increasing Subsequence length, from a set of integers.Input and OutputInput: A set of integers. {0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15} Output: The length of longest increasing subsequence. Here it is 6. The subsequence is 0, 2, 6, 9, 13, 15.AlgorithmlongestSubSeq(subarray, n)Input − The sub array and the size of sub array.Output − Longest increasing sub sequence length.Begin    define array length of size n    initially set 0 ... Read More

A matrix of different characters is given. Starting from one character we have to find the longest path by traversing all characters which are greater than the current character. The characters are consecutive to each other.To find the longest path, we will use the Depth First Search algorithm. During DFS, some subproblems may arise multiple times. To avoid the computation of that, again and again, we will use a dynamic programming approach.Input and OutputInput: The matrix as shown above. And the starting point. Here the starting point is e. Output: Enter Starting Point (a-i): e Maximum consecutive path: 5AlgorithmfindLongestLen(i, j, ... Read More