countPaths(0, 0, 2, 2) returns 6 countPaths (0, 0, 1, 1) returns 2 countPaths (2, 1, 2, 2) returns 1 Hint! Find first the base case(s). The examples above will be useful. Then, think about how to educe the path length by 1 for recursive call(s). For example, one possibility to reach (2, 2) is to each first (1, 2) and make right move. countPaths can be used to count paths to reach (1, 2).

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For example,
countPaths (0, 0, 2, 2) returns 6
countPaths (0, 0, 1, 1) returns 2
countPaths(2, 1, 2, 2) returns 1
Hint! Find first the base case(s). The examples above will be useful. Then, think about how to
reduce the path length by 1 for recursive call(s). For example, one possibility to reach (2, 2) is to
reach first (1, 2) and make right move. countPaths can be used to count paths to reach (1, 2).
A large penalty will be applied to non recursive solutions. Hardcoding will always get zero point.
static int countPaths (int x1, int y1, int x2, int y2){
Transcribed Image Text:For example, countPaths (0, 0, 2, 2) returns 6 countPaths (0, 0, 1, 1) returns 2 countPaths(2, 1, 2, 2) returns 1 Hint! Find first the base case(s). The examples above will be useful. Then, think about how to reduce the path length by 1 for recursive call(s). For example, one possibility to reach (2, 2) is to reach first (1, 2) and make right move. countPaths can be used to count paths to reach (1, 2). A large penalty will be applied to non recursive solutions. Hardcoding will always get zero point. static int countPaths (int x1, int y1, int x2, int y2){
Consider a grid of size (x, y) where x and y are positive integers. The following figure
shows an example grid of size (2,3) and two points p1 and p2 in the grid. Assume that x and
y of p2 is greater than x and y of p1.
p2(2,2)
ectangular Snip
p1(0,0)
Write a recursive method named countPaths that returns the number of distinct shortest paths
from p1 to p2. The method takes 4 ints as the parameters – i.e., x and y values of the two
points: x1, y1, x2, and y2. Note that you do not need to print the paths. Count only.
To be shortest, a path will only consist of only upward and rightward movements where each
movement increases x- or y-coordinate value by 1. In the figure above,
|(right, up, right, up) or (right, right, up, up) are both shortest paths from p1 to p2.
For example,
countPaths (0, 0, 2, 2) returns 6
countPaths (0, 0, 1, 1) returns 2
countPaths (2, 1, 2, 2) returns 1
Transcribed Image Text:Consider a grid of size (x, y) where x and y are positive integers. The following figure shows an example grid of size (2,3) and two points p1 and p2 in the grid. Assume that x and y of p2 is greater than x and y of p1. p2(2,2) ectangular Snip p1(0,0) Write a recursive method named countPaths that returns the number of distinct shortest paths from p1 to p2. The method takes 4 ints as the parameters – i.e., x and y values of the two points: x1, y1, x2, and y2. Note that you do not need to print the paths. Count only. To be shortest, a path will only consist of only upward and rightward movements where each movement increases x- or y-coordinate value by 1. In the figure above, |(right, up, right, up) or (right, right, up, up) are both shortest paths from p1 to p2. For example, countPaths (0, 0, 2, 2) returns 6 countPaths (0, 0, 1, 1) returns 2 countPaths (2, 1, 2, 2) returns 1
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