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Articles by Arnab Chakraborty
Page 4 of 377
Program to find number of ways we can select sequence from Ajob Sequence in Python
Suppose there is a strange language called Ajob language with infinite letters. We know n words in this language where the first word is one character long, second is two characters long, and so on. All letters in a word are unique. We need to select any word and form a subsequence from it where the subsequence length should be k less than the original word length. If a word length is L, then subsequence length should be (L - k). Words with length smaller than k cannot be chosen. Two subsequences are different if they have different ...
Read MoreProgram to find number of pairs between x, whose multiplication is x and they are coprime in Python
Suppose there is a function f(x) that counts the number of (p, q) pairs such that: 1 < p
Read MoreProgram to find out the position of a ball after n reversals in Python
Suppose there are n balls arranged in positions 1, 2, 3, 4, ..., n. These balls undergo a series of reversals where each reversal starts from a different position, moving one step to the right each time. We need to find the final position of a ball that was initially at a given index. Understanding the Problem Let's trace through an example with 5 balls and find where the ball at index 2 ends up ? Initial arrangement: 1, 2, 3, 4, 5 Reversal operations: Reverse from position 0 to 4: 5, 4, 3, 2, ...
Read MoreProgram to reset a polygon to its initial state in Python
A polygon can be transformed through rotations and flips along specific axes. This problem involves tracking these transformations and determining what operation is needed to reset the polygon to its initial state. Understanding Polygon Transformations For a polygon with n vertices, there are specific rules for transformation axes: If n is odd, each flipping axis passes through one vertex and the middle of the opposite side If n is even, half the axes pass through opposite vertices, half through opposite sides Adjacent axes have an angle of 360/(2n) degrees The transformation operations work as ...
Read MoreProgram to find out the cells containing maximum value in a matrix in Python
Suppose, there is a n x n matrix initialized with 0s. Now, a list is given and it contains some pairs that contain a particular row and a column position. For each item i in the list, the contents of the cells increase by 1 where the row number and the column number are less than the row value and column value of item i in the list. After all the list elements have been traversed, we have to find out the number of cells in the matrix that contains the maximum value. (row and column index start at 0) ...
Read MoreProgram to find out number of blocks that can be covered in Python
Suppose there are n blocks in a path, and a worker is putting colored tiles on the blocks. The worker puts tiles on blocks whose numbers are divisible by 4 or 2, but not by 42. We need to find how many blocks can be covered with k colored tiles. The key insight is that in every 42 consecutive blocks, exactly 20 blocks satisfy our condition (divisible by 2 or 4, but not by 42). Since each tile covers 2 blocks, we can cover 42 blocks with 20 tiles in each complete cycle. Algorithm To solve this ...
Read MoreProgram to apply Russian Peasant Multiplication in Python
The Russian Peasant Multiplication method is an ancient algorithm for performing exponentiation of complex numbers of the form (p + q·i)^r using recursive multiplication. This method efficiently computes the result by breaking down the exponent using binary representation. Given four integers p, q, r, and k, we need to calculate (p + q·i)^r = x + y·i and return (x mod k, y mod k). Algorithm Steps The Russian Peasant method follows these recursive steps: If r = 0, return 1 (any number to power 0 is 1) If r = 1, return (p mod ...
Read MoreProgram to find out the number of integral coordinates on a straight line between two points in Python
When we have two points (p1, q1) and (p2, q2), we can find the number of integral coordinates (points where both x and y are integers) that lie on the straight line between them. This problem uses the mathematical concept that the number of lattice points on a line segment equals the GCD of the coordinate differences. So, if the input is like p1 = 3, q1 = 3, p2 = 6, q2 = 6, then the output will be 2. The integral points (4, 4) and (5, 5) lie on the straight line between (3, 3) and (6, ...
Read MoreProgram to find number of possible moves to start the game to win by the starter in Python
Suppose Amal and Bimal are playing a game with n containers, each containing chocolates. The containers are numbered from 1 to N, where the ith container has count[i] chocolates. Players take turns selecting a non-empty container and removing one or more chocolates from it. The player who cannot make a move loses. We need to find how many winning first moves Amal has. Game Rules The game follows these rules: Players alternate turns, starting with Amal On each turn, a player must select a non-empty container The player removes one or more chocolates from the selected ...
Read MoreProgram to find winner of a rower breaking game in Python
Suppose we have an array of tower heights. There are n different towers with different heights. Amal and Bimal are playing a tower breaking game with specific rules. Game Rules Amal always plays first During each move, the current player selects a tower of height X and breaks it down into Y different towers of height Z each, where Y*Z = X and both X and Y > 1 The player who cannot make a move loses the game Algorithm Approach This is a classic game theory problem that can be solved using the ...
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