In this problem, a set of n points are given on the 2D plane. In this problem, we have to find the pair of points, whose distance is minimum.To solve this problem, we have to divide points into two halves, after that smallest distance between two points is calculated in a recursive way. Using distances from the middle line, the points are separated into some strips. We will find the smallest distance from the strip array. At first two lists are created with data points, one list will hold points which are sorted on x values, another will hold data ... Read More

In this problem, one positive integer string is given, we have to find the permutation whose value is maximum by swapping digits’ k times, into different places.We will solve this problem by choosing a digit and swap it with digits following it one at a time to find a maximum number. We repeat the process k times. The backtracking strategy is working here because when we find a number which is not greater than the previous value, we backtrack to old value and check again.Input and OutputInput: A number of multiple digits. The input is: 129814999 Output: The maximum value ... Read More

In the input of this problem, one sentence is given without spaces, another dictionary is also provided of some valid English words. We have to find the possible ways to break the sentence in individual dictionary words.We will try to search from the left of the string to find a valid word when a valid word is found, we will search for words in the next part of that string.Input and OutputInput: A set of valid words as dictionary, and a string where different words are placed without spaces. Dictionary: {mobile, sam, sung, man, mango, icecream, and, go, i, love, ... Read More

In this problem a set of integers are given, we have to break them into two parts, such that the difference of the sum of two subsets is minimum as possible. So our target is to divide two groups of nearly equal strength to participate in the Tug of war game.If the size of subset n is even, it must be divided into n/2, but for the odd value of n, then the size of one subset must be (n-1)/2, and size of another subset must be (n+1)/2.Input and OutputInput: A set of different weights. {23, 45, -34, 12, 0, ... Read More

In chess, we know that the knight can jump in a special manner. It can move either two squares horizontally and one square vertically or two squares vertically and one square horizontally in each direction, So the complete movement looks like English letter ‘L’.In this problem, there is an empty chess board, and a knight starting from any location in the board, our task is to check whether the knight can visit all of the squares in the board or not. When It can visit all of the squares, then place the number of jumps needed to reach that location ... Read More

In this section, we will try to solve the famous number maze problem called Sudoku. Sudoku is a 9 x 9 number grid, and the whole grid are also divided into 3 x 3 boxes There are some rules to solve the Sudoku.We have to use digits 1 to 9 for solving this problem.One digit cannot be repeated in one row, one column or in one 3 x 3 box.Using the backtracking algorithm, we will try to solve the Sudoku problem. When some cell is filled with a digit, it checks whether it is valid or not. When it is ... Read More

In this problem, there is a given set with some integer elements. And another some value is also provided, we have to find a subset of the given set whose sum is the same as the given sum value.Here backtracking approach is used for trying to select a valid subset when an item is not valid, we will backtrack to get the previous subset and add another element to get the solution.Input and OutputInput: This algorithm takes a set of numbers, and a sum value. The Set: {10, 7, 5, 18, 12, 20, 15} The sum Value: 35 Output: All ... Read More

In the crypt-arithmetic problem, some letters are used to assign digits to it. Like ten different letters are holding digit values from 0 to 9 to perform arithmetic operations correctly. There are two words are given and another word is given an answer of addition for those two words.As an example, we can say that two words ‘BASE’ and ‘BALL’, and the result is ‘GAMES’. Now if we try to add BASE and BALL by their symbolic digits, we will get the answer GAMES.NOTE &minuns; There must be ten letters maximum, otherwise it cannot be solved.Input and OutputInput: This algorithm will ... Read More

In this problem, there is a given maze of size N x N. The source and the destination location is top-left cell and bottom right cell respectively. Some cells are valid to move and some cells are blocked. If one rat starts moving from start vertex to destination vertex, we have to find that is there any way to complete the path, if it is possible then mark the correct path for the rat.The maze is given using a binary matrix, where it is marked with 1, it is a valid path, otherwise 0 for a blocked cell.NOTE: The rat can ... Read More

This problem is to find an arrangement of N queens on a chess board, such that no queen can attack any other queens on the board.The chess queens can attack in any direction as horizontal, vertical, horizontal and diagonal way.A binary matrix is used to display the positions of N Queens, where no queens can attack other queens.Input and OutputInput: The size of a chess board. Generally, it is 8. as (8 x 8 is the size of a normal chess board.) Output: The matrix that represents in which row and column the N Queens can be placed. If the ... Read More