In the Iterative approach we have to create 2 Queues, one queue saves the left child and another queue saves the right child value. If the tree is empty, then it is symmetrical to the vertical axis going through its root node. Else, check if the value at the root node of both subtrees is the same. If it is, then check if the left subtree and the right subtree are symmetrical. Enqueue the left child value and right child value into the queue1 and enqueue the right child and left child value into the queue1Examplepublic class TreesPgm{    public ... Read More

CoinChangeBottomUpApproach takes 3 parameters as input n is the amount, coins array contains the total number of coins, t contains total number of coins. Declare a dynamic array which stores the previously calculated values. loop through the array and calculate the minimum coins required to calculate the amount. If the calculation is already done the take the value from the dynamic array.Time complexity − O(N)Space complexity − O(N)Examplepublic class DynamicProgramming{    public int CoinChangeBottomUpApproach(int n, int[] coins, int t){       int[] dp = new int[100];       for (int i = 1; i < n; i++){   ... Read More

CoinChangeTopDownApproach takes 4 parameters, n is the amount, coins array contains the coins from which the amount needs to be calculated, t is the total number of coins, dp array will store all the pre calculated values. If amount is 0 then return 0. If the value is already calculated then return from the dp array. if the value is not calculated then call the CoinChangeTopDownApproach recursively.Time complexity − O(N)Space complexity − O(N)Examplepublic class DynamicProgramming{    public int CoinChangeTopDownApproach(int n, int[] coins, int t, int[] dp){       if (n == 0){          return 0;   ... Read More

MinimumStepstoOneBottomdownApproachtakes integer n as input. Parameter n contains the total number of elements. Initial condition checks whether n is equal to 1. If n is equal to 1 then return 0. Initialize op1, op2 and op3 to max value. If n mod 3 is equal to 0 then call MinimumStepstoOneBottomdownApproach recursively and assign it to op1, if n mod 3 is equal to 0 then call MinimumStepstoOneBottomdownApproach recursively and assign it to op2 else subtract n by 1 and call MinimumStepstoOneBottomdownApproach. Finally return the value from the dp arrayTime complexity − O(N)Space complexity − O(N)Examplepublic class DynamicProgramming{    public int ... Read More

MinimumStepstoOneTopdownApproach takes integer n and an integer array as input. Parameter n contains the total number of elements. Initial condition checks whether n is equal to 1. If n is equal to 1 then return 0. Initialize op1, op2 and op3 to max value . If n mod 3 is equal to 0 then call MinimumStepstoOneTopdownApproach recursively and assign it to op1 , If n mod 3 is equal to 0 then call MinimumStepstoOneTopdownApproach recursively and assign it to op2 else subtract n by 1 and call MinimumStepstoOneTopdownApproach . Finally call the Math.Min to calculate the minimum of three elements ... Read More

The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the preceding two numbers. The bottom-up approach first focuses on solving the smaller problems at the fundamental level and then integrating them into a whole and complete solution.Time complexity − O(N)Space complexity − O(N)Examplepublic class DynamicProgramming{    public int fibonacciBottomupApproach(int n){       int[] dpArr = new int[150];       dpArr[1] = 1;       for (int i = 2; i

The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the preceding two numbers. The top-down approach focuses on breaking down a big problem into smaller and understandable chunks. Space complexity is O(N) because we are creating an extra array memory which is equal to the size of number.Time complexity − O(N)Space complexity − O(N)Examplepublic class DynamicProgramming{    public int fibonacciTopdownApproach(int n, int[] dpArr ){       if(n==0 || n ... Read More

LongestIncreaingSubsequence returns integer of the continuous subsequence from the array. The method has a for loop, which iterates and keeps the track of the numbers. the final result will have the Max calculated. Time complexity is O(N) because every element is visited once and the space complexity is O(1) because we are not making use of any storage space.Time complexity − O(N)Space complexity − O(1)Example   − {2, 4, 6, 5, 8}Output − 3Examplepublic class Arrays{    public int longestIncreaingSubsequence(int[] nums){       if (nums == null || nums.Length == 0){          return -1;     ... Read More

From the given string input, use the sliding window technique by having 2 pointers i and j . both i and j will point to the same character in the string. Traverse through the string and add it to the list. If the repeated character is found then remove it from the list else append to the list.Example 1Input − s = "abcabcbb"Output − 3Explanation − The answer is "abc", with the length of 3.Example 2Input − s = "bbbbb"Output − 1Explanation − The answer is "b", with the length of 1.Time complexity − O(N)Space complexity − O(N)Examplepublic class Arrays{    public int LongestSubstringWithNoRepeatingCharacters(string s){   ... Read More

Two strings, X and Y, are called isomorphic if all occurrences of each character in X can be replaced with another character to get Y and vice-versa. For example, consider strings ACAB and XCXY. All occurrences of a character must be replaced with another character while preserving the order of characters. No two characters may map to the same character, but a character may map to itself.Example 1Input − s = "egg", t = "add"Output − trueExample 2Input − s = "foo", t = "bar"Output − falseTime complexity − O(N)Space complexity − O(N)codepublic class Arrays{    public bool IsStringIsomorphic(string s, string t){     ... Read More