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Problem statementA tree is always a Bipartite Graph as we can always break into two disjoint sets with alternate levels.In other words, we always color it with two colors such that alternate levels have same color. The task is to compute the maximum no. of edges that can be added to the tree so that it remains Bipartite Graph.ExampleTree edges are represented in vertex pairs as follows −{1, 2}{1, 3}{2, 4}{3, 5} then we need 2 more edges to keep it Bipartite GraphIn a coloring graph the graph {1, 4, 5} and {2, 3} from two different sets. Since, 1 ... Read More
Problem statementGiven an integer N which represents the number of Vertices. The Task is to find the maximum number of edges possible in a Bipartite graph of N vertices.Bipartite GraphA Bipartite graph is one which is having 2 sets of vertices.The set are such that the vertices in the same set will never share an edge between them.ExampleIf N = 10 then there will be total 25 edges −Both sets will contain 5 vertices and every vertex of first set will have an edge to every other vertex of the second setHence total edges will be 5 * 5 = ... Read More
Problem statementGiven a string comprising of ones and zeros. The task is to find the maximum length of the segments of string such that a number of 1 in each segment is greater than 0ExampleIf input string is “10111000001011” the answer will 12 as follows −First segment is of length 7 10111000001011Second segment is of length 5 10111000001011Total length is length of (segment 1 + segment 2) = (7 + 5) = 12AlgorithmIf start == n then return 0.Run a loop from start till n, computing for each subarray till n.If character is 1 then increment the count of 1 ... Read More
Problem statementGiven lengths of n rods in an array. If any person picks any rod, half of the longest rod (or (max + 1) / 2 ) is assigned and remaining part (max – 1) / 2 is put back. It may be assumed that sufficient number of rods are always available, answer M queries given in an array q[] to find the largest length of rod available for qith person, provided qi is a valid person number starting from 1ExampleInput : a[] = {6, 5, 9, 10, 12} q[] = {1, 3} Output : 12 9 The first ... Read More
Problem statementGiven an array arr[] of N elements (0 ≤ arr[i] ≤ 1000). The task is to find the maximum length of the sub-array that contains only ugly numbers.Ugly numbers are numbers whose only prime factors are 2, 3 or 5.For Example below are the few number from series: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, …ExampleIf input array is {1, 2, 7, 9, 120, 810, 374} then answer is 3 as −Longest possible sub-array of ugly number sis {9, 120, 810}AlgorithmTake a unordered_set, and insert all the ugly numbers which are less than 1000 in ... Read More
To handle floating point number precision in JavaScript, use the toPrecision() method. It helps to format a number to a length you can specify.ExampleLive Demo var num = 28.6754; document.write(num.toPrecision(3)); document.write(""+num.toPrecision(2)); document.write(""+num.toPrecision(5)); Output28.7 29 28.675
Problem statementGiven an array, we need to find the maximum height of the triangle which we can form, from the array values such that every (i+1)th level contain more elements with the larger sum from the previous level.ExampleIf input array is {40, 100, 20, 30 } then answer is 2 as −We can have 100 and 20 at the bottom level and either 40 or 30 at the upper level of the pyramidAlgorithmOur solution just lies on the logic that if we have maximum height h possible for our pyramid then ( h * (h + 1) ) / 2 ... Read More
Problem statementThere are N players which are playing a tournament. We need to find the maximum number of games the winner can play. In this tournament, two players are allowed to play against each other only if the difference between games played by them is not more than oneExampleIf There are 3 players then 2 games are required to decide the winner as follows −Game – 1: player 1 vs player 2Game - 2: player 2 vs winner from Game - 1AlgorithmWe can solve this problem by first computing minimum number of players required such that the winner will play ... Read More
Problem statementGiven a string the task is to find the maximum length of the sub-string of that can be arranged into a Palindrome.ExampleIf input string = “5432112356” then answer is 6 as maximum palindrome substring is “321123” and its length is 6AlgorithmIf the length of the sub-string is odd, then it cannot be considered in the final solutions.If the length of the sub-string is even, then it can be a possible solution only if each character in that sub-string occurs even number of times which can be done using the dictionary count. We check if each character occurs even number ... Read More
Problem statementGiven an array arr[]. Find maximum value of prefix sum which is also suffix sum for index i in arr[].ExampleIf input array is −Arr[] = {1, 2, 3, 5, 3, 2, 1} then output is 11 as −Prefix sum = arr[0..3] = 1 + 2 + 3 + 5 = 11 andSuffix sum = arr[3..6] = 5 + 3 + 2 + 1 = 11AlgorithmTraverse the array and store prefix sum for each index in array presum[], in which presum[i] stores sum of subarray arr[0..i]Traverse array again and store suffix sum in another array suffsum[], in which suffsum[i] stores ... Read More