Try it on GfG Practice Given a triangular array, find the minimum path sum from top to bottom. For each step, we can move to the adjacent numbers of the row below. i.e., if we are on an index i of the current row, we can move to either index i or index i + 1 on the next row. Examples : Input:…

Try it on GfG Practice Given a set of n elements, find the number of ways of partitioning it. Examples: Input: n = 2 Output: 2 Explanation: Let the set be {1, 2}. The partitions are {{1},{2}} and {{1, 2}}. Input: n = 3 Output: 5 Explanation: Let the set be {1, 2, 3}. The partitions are…

Given a convex polygon with n sides. The task is to calculate the number of ways in which triangles can be formed by connecting vertices with non-crossing line segments. Examples: Input: n = 3 Output: 1 It is already a triangle so it can only be formed in 1 way. Input: n = 4 Output: 2 It can be cut…

Try it on GfG Practice Given a rod of length n, the task is to cut the rod in such a way that the total number of segments of length x, y, and z is maximized. The segments can only be of length x, y, and z. Note: If no segment can be cut then return 0. Examples: Input: n = 4, x = 2, y = 1, z = 1…

Try it on GfG Practice Given an array of integers cost[] of length n, where cost[i] is the cost of the ith step on a staircase. Once the cost is paid, we can either climb one or two steps. We can either start from the step with index 0, or the step with index 1. The task is to find the minimum cost…

A child is running up a staircase with n steps and can hop either 1 step, 2 steps, or 3 steps at a time. The task is to implement a method to count how many possible ways the child can run up the stairs. Examples: Input: 4 Output: 7 Explanation: There are seven ways: {1, 1, 1, 1}, {1, 2, 1}, {2, 1,…

Try it on GfG Practice There are n stairs, and a person standing at the bottom wants to climb stairs to reach the top. The person can climb either 1 stair or 2 stairs at a time, the task is to count the number of ways that a person can reach at the top. Note: This problem is similar to Count ways to…

Try it on GfG Practice The tribonacci series is a generalization of the Fibonacci sequence where each term is the sum of the three preceding terms. a(n) = a(n-1) + a(n-2) + a(n-3) with a(0) = a(1) = 0, a(2) = 1. First few numbers in the Tribonacci Sequence are 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81,…

Try it on GfG Practice Given a positive integer n, the task is to find the nth Fibonacci number. The Fibonacci sequence is a sequence where the next term is the sum of the previous two terms. The first two terms of the Fibonacci sequence are 0 followed by 1. The Fibonacci sequence: 0, 1, 1, 2, 3, 5,…

Try it on GfG Practice Given a fence with n posts and k colors, the task is to find out the number of ways of painting the fence so that not more than two consecutive posts have the same color. Examples: Input: n = 2, k = 4 Output: 16 Explanation: We have 4 colors and 2 posts. Ways when both posts…

Steps to solve a Dynamic programming problem: Identify if it is a Dynamic programming problem.Decide a state expression with the Least parameters.Formulate state and transition relationship.Apply tabulation or memorization. Step 1: How to classify a problem as a Dynamic Programming Problem?…

Tabulation and memoization are two techniques used to implement dynamic programming. Both techniques are used when there are overlapping subproblems (the same subproblem is executed multiple times). Below is an overview of two approaches. Memoization: Top-down approachStores the results of function…

Dynamic Programming is a commonly used algorithmic technique used to optimize recursive solutions when same subproblems are called again. The core idea behind DP is to store solutions to subproblems so that each is solved only once. To solve DP problems, we first write a recursive solution in a way…

Try it on GfG Practice Given an integer array of coins[] of size n representing different types of denominations and an integer sum, the task is to count all combinations of coins to make a given value sum. Note: Assume that you have an infinite supply of each type of coin. Examples: Input: sum = 4,…

Try it on GfG Practice Given an array arr[] of non-negative integers and a value sum, the task is to check if there is a subset of the given array whose sum is equal to the given sum. Examples: Input: arr[] = [3, 34, 4, 12, 5, 2], sum = 9 Output: True Explanation: There is a subset (4, 5) with sum…

Try it on GfG Practice Given an array of coins[] of size n and a target value sum, where coins[i] represent the coins of different denominations. You have an infinite supply of each of the coins. The task is to find the minimum number of coins required to make the given value sum. If it is not…

You are given a 2D matrix cost[][] of dimensions m × n, where each cell represents the cost of traversing through that position. Your goal is to determine the minimum cost required to reach the bottom-right cell (m-1, n-1) starting from the top-left cell (0,0). The total cost of a path is the sum of…

Try it on GfG Practice There are n houses built in a line, each of which contains some money in it. A robber wants to steal money from these houses, but he can’t steal from two adjacent houses. The task is to find the maximum amount of money which can be stolen. Examples: Input: hval[] = {6, 7, 1,…

Try it on GfG Practice Given a distance 'dist', count total number of ways to cover the distance with 1, 2 and 3 steps. Examples: Input: n = 3 Output: 4 Explanation: Below are the four ways => 1 step + 1 step + 1 step => 1 step + 2 step => 2 step + 1 step => 3 step Input: n = 4 Output: 7…

Try it on GfG Practice Given two strings s1 and s2. The task is to remove/delete and insert the minimum number of characters from s1 to transform it into s2. It could be possible that the same character needs to be removed/deleted from one point of s1 and inserted at another point. Example 1: Input:…

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Try it on GfG Practice Given a string str, containing only digits from '0' to '9'. Your task is to find the minimum number of operations required to delete all the digits of string, where in each operation we can delete a palindromic substring. Note: After deleting the substring, the remaining parts…

Try it on GfG Practice Given a positive integer K, the task is to find the minimum number of operations of the following two types, required to change 0 to K. Add one to the operandMultiply the operand by 2. Examples: Input: K = 1 Output: 1 Explanation: Step 1: 0 + 1 = 1 = K Input: K = 4 Output: 3…

Try it on GfG Practice Catalan numbers are defined as a mathematical sequence that consists of positive integers, which can be used to find the number of possibilities of various combinations. The nth term in the sequence denoted Cn, is found in the following formula: \frac{(2n)!}{((n + 1)! n!)} The…

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Try it on GfG Practice Given a binary string of 0s and 1s. The task is to find the length of the substring which is having a maximum difference between the number of 0s and the number of 1s (number of 0s - number of 1s). In case of all 1s print -1. Examples: Input : S = "11000010001" Output : 6 From…

Try it on GfG Practice Given a string s, the task is to find the minimum number of cuts needed for palindrome partitioning of the given string. A partitioning of the string is a palindrome partitioning if every sub-string of the partition is a palindrome. Examples: Input: s = "geek" Output: 2…

Try it on GfG Practice Given an array arr[] and k, where the array represents the boards and each element of the given array represents the length of each board. k numbers of painters are available to paint these boards. Consider that each unit of a board takes 1 unit of time to paint. The task is…

Given an n*m matrix, the task is to find the maximum sum of elements of cells starting from the cell (0, 0) to cell (n-1, m-1). However, the allowed moves are right, downwards or diagonally right, i.e, from location (i, j) next move can be (i+1, j), or, (i, j+1), or (i+1, j+1). Find the maximum sum…

Try it on GfG Practice The longest Zig-Zag subsequence problem is to find length of the longest subsequence of given sequence such that all elements of this are alternating. If a sequence {x1, x2, .. xn} is alternating sequence then its element satisfy one of the following relation : x1 < x2 > x3 <…

Try it on GfG Practice Given an array arr[] of size n, the task is to divide it into two sets S1 and S2 such that the absolute difference between their sums is minimum. If there is a set S with n elements, then if we assume Subset1 has m elements, Subset2 must have n-m elements and the value of…

Try it on GfG Practice Given a boolean expression s that contain symbols and operators. The task is to count the number of ways we can parenthesize the expression so that the value of the expression evaluates to true. Symbols T ---> true F ---> false Operators & ---> boolean AND| ---> boolean OR^…

Try it on GfG Practice Given the time taken by n tasks. Find the minimum time needed to finish the tasks such that skipping of tasks is allowed, but can not skip two consecutive tasks. Examples : Input : arr[] = {10, 5, 7, 10} Output : 12 We can skip first and last task and finish these task in 12…

Given a string s of length n, the task is to count number of palindromic subsequence (need not necessarily be distinct) present in the string s. Example: Input: s = "abcd" Output: 4 Explanation: Palindromic subsequence are : "a" ,"b", "c" ,"d" Input: s = "aab" Output: 4 Explanation: palindromic…

Try it on GfG Practice Given an array arr[] of non-negative numbers. Each number tells you the maximum number of steps you can jump forward from that position. For example: If arr[i] = 3, you can jump to index i + 1, i + 2, or i + 3 from position i.If arr[i] = 0, you cannot jump forward from that…

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Try it on GfG Practice Given a positive integer n, the task is to find the minimum number of squares that sum to n. Note: A number can always be represented as a sum of squares of other numbers. Because 1 is a square number and we can always break any number as (1*1 + 1*1 + 1*1 + ... ). Examples :…

Try it on GfG Practice Given an array arr[] of n positive integers. The task is to find the sum of the maximum sum subsequence of the given array such that the integers in the subsequence are sorted in strictly increasing order. Examples: Input: arr[] = [1, 101, 2, 3, 100] Output: 106 Explanation:…