## Total possible solutions to linear equation of k variables

Given a linear equation of k variables, count total number of possible solutions of it.

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Given a linear equation of k variables, count total number of possible solutions of it.

The longest decreasing subsequence problem is to find a subsequence of a given sequence in which the subsequence’s elements are in sorted order, highest to lowest, and in which the subsequence is as long as possible.

Given a string, calculate its rank among all its lexicographically sorted permutations. For example, consider below lexicographically sorted permutations

Given a mobile keypad having digits from [0-9] associated with each key, count total possible combinations of digits having length n. We can start with any digit and press only four adjacent keys of any digit. Keypad also contains * and # key which we are not allowed to press.

The longest common subsequence (LCS) problem is the problem of finding the longest subsequence that is present in given two sequences in the same order. i.e. find a longest sequence which can be obtained from the first original sequence by deleting some items, and from the second original sequence by deleting other items.

Given an array of integers containing duplicates, return the majority element in an array if present. A majority element appears more than n/2 times where n is the size of the array.

Given a string and a dictionary of words, determine if string can be segmented into a space-separated sequence of one or more dictionary words.

Find optimal cost to construct binary search tree where each key can repeat several times. We are given frequency of each key in same order as corresponding keys in inorder traversal of a binary search tree.

Given a M x N matrix where each cell can have value of 1, 0 or -1, where -1 denotes a unsafe cell, collect maximum number of ones starting from first cell and by visiting only safe cells (i.e. 0 or 1). We are allowed to go only left or down if the row is …

Given a pattern, count number of times the pattern appears in the given string as a subsequence.

Longest Alternating Subsequence problem is a problem of finding a subsequence of a given sequence in which the elements are in alternating order, and in which the sequence is as long as possible. In order words, find the length of longest subsequence with alternate low and high elements.

Given an unlimited supply of coins of given denominations, find the total number of distinct ways to get a desired change.