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Suppose we have a number N this represents the initial position of the person on the number line. We also have L which is the probability of the person of going left. We have to find the the probability of reaching all points on the number line after completing N moves from point N. Each move can be either to the left or to the right.So, if the input is like n = 2, l = 0.5, then the output will be [0.25, 0, 0.5, 0, 0.25]To solve this, we will follow these steps −high := 1 - lowDefine an ... Read More
Suppose we have a binary tree. As we know the succinct encoding of Binary Tree performs close to lowest possible space. The n’th Catalan number is designated by the number of structurally different binary trees with n different nodes. If the n is large, this is about 4n; thus, we require minimum about log2(4) n = 2n bits to encode it. A succinct binary tree therefore would consume 2n + O(n) bits.So, if the input is likethen the output will beencoded −Structure List 1 1 1 0 0 1 0 0 1 0 1 0 0Data List 10 20 40 ... Read More
Suppose we have a Markov chain graph g; we have the find the probability to reach the state F at time T if we start from state S when time t = 0. As we know a Markov chain is a random process consisting of various states and the probabilities to move one state to another. This can be represented as a directed graph; the nodes are states and the edges have the probability of going from one node to another. From one state to another, it takes unit time to move. The sum of the probabilities of the outgoing ... Read More
Suppose we have two arrays A and B. The size of A is the number of rows and A[i] is the number of boxes in the ith row. And B is the array of balls where B[i] denotes a number on the ball. Given that ball i (value B[i]) will be placed in a box whose position from starting is B[i]. We have to find the row and column of the boxes corresponding to each B[i].So, if the input is like A = [3, 4, 5, 6], B = [1, 3, 5, 2], then the output will be [(1, 1), ... Read More
Suppose we have a string S with lowercase letters, now two players are playing the game. The rules are as follows −The player wins the game, if, at any move, a player can shuffle the characters of the string to get a palindrome string.The player cannot win when he/she has to remove any character from the string.We have to keep in mind that both players play the game optimally and player1 starts the game. We have to find the winner of the game.So, if the input is like "pqpppq", then the output will be Player1 as player-1 in the first ... Read More
Suppose we have two arrays A and B of size N and M respectively and we also have one N X M binary matrix where 1 denotes that there was a positive integer in the original matrix and 0 means that position is holding 0 into the original matrix also. We have to generate the original matrix so that A[i] denotes the largest element in the ith row and B[j] denotes the largest element in the jth column.So, if the input is like A = [4, 2, 3], B = [3, 1, 0, 0, 4, 0, 5] matrix, then the ... Read More
Suppose we have n different tasks; these tasks are labeled from 0 to n-1. Some tasks may have prerequisites tasks, so as an example if we want to choose task 2 then we have to first finish the task 1, which is represented as a pair − [2, 1] If we have total number of tasks and a list of prerequisite pairs, we have to find the ordering of tasks to finish all tasks. If there are more than one correct order, we can just return one of them. And if it is impossible to finish all given tasks, return ... Read More
Suppose we have an array A containing the permutation of first N natural numbers and another number M is also given, where M ≤ N, we have to find the number of sub-arrays such that the median of the sequence is M. As we know the median of a sequence is defined as the value of the element which is in the middle of the sequence after sorting it according to ascending order. For even length sequence, the left of two middle elements is used.So, if the input is like A = [3, 5, 6, 4, 2] and M = ... Read More
There are n number of spectators in the stadium, and they are labeled from 1 to n. Now follow these cases −At time t1, the first spectator stands.At time t2, the second spectator stands.…At time tk, the k-th spectator stands.At time tk + 1, the (k + 1)-th spectator stands and the first spectator sits.At time tk + 2, the (k + 2)-th spectator stands and the second spectator sits.…At time tn, the n-th spectator stands and the (n – k)-th spectator sits.At time tn + 1, the (n + 1 – k)-th spectator sits.…At time tn + k, the ... Read More
Suppose we have two values n and m; we have to find the number of rectangles of size 2x1 that can be set inside a rectangle of size n x m. There are few conditions, that we have to consider −Any two small rectangles cannot overlap.Every small rectangle lies completely inside the bigger one. It is permitted to touch the edges of the bigger rectangle.So, if the input is liken = 3, m = 3, then the output will be 4To solve this, we will follow these steps −if n mod 2 is same as 0, thenreturn(n / 2) * ... Read More