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

A sequence is said to be bitonic if it is first increasing and then decreasing. In this problem, an array of all positive integers is given. We have to find a subsequence which is increasing first and then decreasing.To solve this problem, we will define two subsequences, they are the Longest Increasing Subsequence and the Longest Decreasing Subsequence. The LIS array will hold the length of increasing subsequence ending with array[i]. The LDS array will store the length of decreasing subsequence starting from array[i]. Using these two arrays, we can get the length of longest bitonic subsequence.Input and OutputInput: A ... Read More

An array of integers is given. We have to find the sum of all elements which are contiguous, whose sum is largest, that will be sent as output.Using dynamic programming we will store the maximum sum up to current term. It will help to find the sum for contiguous elements in the array.Input and OutputInput: An array of integers. {-2, -3, 4, -1, -2, 1, 5, -3} Output: Maximum Sum of the Subarray is: 7AlgorithmmaxSum(array, n)Input − The main array, the size of the array.Output − maximum sum.Begin    tempMax := array[0]    currentMax = tempMax    for i := ... Read More