Given two points (x1, y1) and (x2, y2) in 2-D coordinate system. The task is to count all the paths whose distance is equal to the Manhattan distance between both the given points.
Input: x1 = 2, y1 = 3, x2 = 4, y2 = 5
Input: x1 = 2, y1 = 6, x2 = 4, y2 = 9
Approach: The Manhattan distance between the points (x1, y1) and (x2, y2) will be abs(x1 – x2) + abs(y1 – y2)
Let abs(x1 – x2) = m and abs(y1 – y2) = n
Every path with distance equal to the Manhattan distance will always have m + n edges, m horizontal and n vertical edges. Hence this is a basic case of Combinatorics which is based upon group formation. The idea behind this is the number of ways in which (m + n) different things can be divided into two groups, one containing m items and the other containing n items which is given by m + nCn i.e. (m + n)! / m! * n!.
Below is the implementation of the above approach:
- Pairs with same Manhattan and Euclidean distance
- Find the integer points (x, y) with Manhattan distance atleast N
- Maximum Manhattan distance between a distinct pair from N coordinates
- Sum of Manhattan distances between all pairs of points
- Find a point such that sum of the Manhattan distances is minimized
- Find the original coordinates whose Manhattan distances are given
- Distance of chord from center when distance between center and another equal length chord is given
- Count of binary strings of length N having equal count of 0's and 1's and count of 1's ≥ count of 0's in each prefix substring
- Count of palindromic plus paths in a given Matrix
- Count of paths in given Binary Tree with odd bitwise AND for Q queries
- Minimize count of unique paths from top left to bottom right of a Matrix by placing K 1s
- Count all possible paths from top left to bottom right of a Matrix without crossing the diagonal
- Count unique paths with given sum in an N-ary Tree
- Count of root to leaf paths whose permutation is palindrome in a Binary Tree
- Number of Paths of Weight W in a K-ary tree
- Print all shortest paths between given source and destination in an undirected graph
- Count of binary strings of length N having equal count of 0's and 1's
- Number of ways to select equal sized subarrays from two arrays having atleast K equal pairs of elements
- Check whether two strings can be made equal by reversing substring of equal length from both strings
- Split an Array A into Subsets having equal Sum and sizes equal to elements of Array B
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