DP Problems Dimension Wise (1D, 2D and 3D) Last Updated : 05 May, 2025 Summarize Comments Improve Suggest changes Share Like Article Like Report When we solve a Dynamic Programming (DP) problem, we store solution in an array. The dimensions of the array are dependent on number of variables that change in recursive (or optimal substructure) solution. If the recursive solution has only one dimension changing, then we call the problem as 1D DP because we need only dimensional array to store solutions of subproblems. Similarly, we define 2D and 3D DP. Below is classification of DP problems based on number of dimensions.1D Dynamic ProgrammingFibonacci numbersTribonacci NumbersLucas NumberClimbing StairsClimbing Stairs with 3 MovesWeighted Climbing Stairsnth Catalan NumberCount Unique BSTsCount Valid ParenthesisMin Sum in a TriangleHouse RobberDecode WaysWays to Partition a SetBinomial CoefficientPascal's TriangleNth Row of Pascal TriangleCutting a RodPartition a SetLongest Increasing SubsequenceNumber of LISs2D Dynamic ProgrammingPermutations with K InversionsLCS of 2 StringsPrinting LCSLongest Palindromic SubsequenceShortest Common SupersequenceMinimum Insertions and Deletions to TransformEdit DistanceMinimum Insertions for PalindromeLongest Common SubstringLongest Repeated SubsequenceWildcard MatchingRegular Expression Matching0/1 Knapsack Problem3D Dynamic ProgrammingLongest Subset with m 0s and n 1sLCS of 3 StringsCount Paths in a 3D GridDouble Knapsack Comment More infoAdvertise with us Next Article DP Problems Dimension Wise (1D, 2D and 3D) K kartik Follow Improve Article Tags : Dynamic Programming DSA Practice Tags : Dynamic Programming Similar Reads What is meant by dimensionality of an Array? The dimension of an array can simply be defined as the number of subscripts or indices required to specify a particular element of the array. Dimension has its own meaning in the real world too and the dimension of an array can be associated with it like:- 1-dimension array can be viewed as 1-axis i 3 min read Class 10 RD Sharma Solutions - Chapter 16 Surface Areas and Volumes - Exercise 16.2 | Set 3 Question 25. A hemispherical depression is cut from one face of a cubical wooden block of the edge 21 cm such that the diameter of the hemispherical surface is equal to the edge of the cubical surface. Determine the volume and the total surface area of the remaining block.Solution: According to the 13 min read Class 10 RD Sharma Solutions - Chapter 16 Surface Areas and Volumes - Exercise 16.2 | Set 2 Chapter 16 of RD Sharma's Class 10 textbook "Surface Areas and Volumes" explores the mathematical principles used to calculate the surface areas and volumes of the various geometric shapes. This chapter is crucial for understanding how to measure and interpret the size of three-dimensional objects w 12 min read Mensuration 3D - Solved Questions and Answers 3D Mensuration deals with the measurement of three-dimensional (solid) shapes, including their volume, surface area, lateral surface area, and diagonals. 3D shapes have length, width, and height/depth, making them occupy space.For formulas you can refer to Mensuration 3D Formulas3D Mensuration quest 4 min read Mensuration 3D | Set-2 Question 1: If the diagonal of cube is √18 cm, then its volume is Solution : Let the side of the cube is x cm. We know diagonal of cube = a√3 cm Put equal both a√3 = √18 Squaring both sides a2(3) = 18 a2 = 6 a = √6 Volume of the cube = a3 = (√6)3 = 6√6 cm3 Question 2: The areas of three consecutive 7 min read Like