-
Notifications
You must be signed in to change notification settings - Fork 183
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
Merge pull request #831 from Prabhatsingh001/main
added three algorithms in DSA folder
- Loading branch information
Showing
3 changed files
with
256 additions
and
0 deletions.
There are no files selected for viewing
56 changes: 56 additions & 0 deletions
56
Algorithms_and_Data_Structures/bellman_ford/Bellman_ford.py
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,56 @@ | ||
def BellmanFord(src, V, graph): | ||
''' | ||
this algorithm works exactly like dijkistra algorthm except it | ||
can detect negative edge cycle in the graph | ||
this algo is little slower than dijkistra algortihm | ||
''' | ||
#src is source vertex V is no of vertex graph is graph in the form of a list of list | ||
dist = [float("Inf")]*V | ||
dist[src] = 0 | ||
|
||
for _ in range(V-1): | ||
for u,v,w in graph: | ||
if dist[u] != float("Inf") and dist[u] + w < dist[v]: | ||
dist[v] = dist[u] + w | ||
|
||
|
||
for u,v,w in graph: | ||
if dist[u] != float("Inf") and dist[u] + w < dist[v]: | ||
return -1 | ||
|
||
return dist | ||
|
||
def printArr(dist): | ||
V = len(dist) | ||
print("vertex distance from source") | ||
for i in range(V): | ||
print(f"{i}\t\t{dist[i]}") | ||
|
||
#example usage of bellman ford algorithm | ||
def main(): | ||
v = 5 | ||
graph = [] | ||
graph.append([0,1,-1]) #[u=initial vertex, final vertex, w = weight of edge btw them] | ||
graph.append([0,2,4]) | ||
graph.append([1,2,3]) | ||
graph.append([1,3,2]) | ||
graph.append([1,4,2]) | ||
graph.append([3,2,5]) | ||
graph.append([3,1,1]) | ||
graph.append([4,3,-3]) | ||
|
||
dist = BellmanFord(0,v,graph) | ||
printArr(dist) | ||
|
||
if __name__ == "__main__": | ||
main() | ||
|
||
'''output | ||
vertex distance from source | ||
0 0 | ||
1 -1 | ||
2 2 | ||
3 -2 | ||
4 1 | ||
''' |
98 changes: 98 additions & 0 deletions
98
Algorithms_and_Data_Structures/closest_pair_of_points/closest_pair_of_points.py
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,98 @@ | ||
import math | ||
|
||
class Point: | ||
def __init__(self, x, y): | ||
self.x = x | ||
self.y = y | ||
|
||
#sort array of points according to X coordinate | ||
def compareX(a, b): | ||
p1, p2 = a, b | ||
return (p1.x != p2.x) * (p1.x - p2.x) + (p1.y - p2.y) | ||
|
||
#sort array of points according to Y coordinate | ||
def compareY(a, b): | ||
p1, p2 = a, b | ||
return (p1.y != p2.y) * (p1.y - p2.y) + (p1.x - p2.x) | ||
|
||
|
||
# A utility function to find the distance between two points | ||
def dist(p1, p2): | ||
return math.sqrt((p1.x - p2.x)**2 + (p1.y - p2.y)**2) | ||
|
||
'''A Brute Force method to return the smallest distance between two points | ||
in P[] of size n''' | ||
def bruteForce(P, n): | ||
min = float('inf') | ||
for i in range(n): | ||
for j in range(i+1, n): | ||
if dist(P[i], P[j]) < min: | ||
min = dist(P[i], P[j]) | ||
return min | ||
|
||
# A utility function to find a minimum of two float values | ||
def min(x, y): | ||
return x if x < y else y | ||
|
||
'''# A utility function to find the distance between the closest points of strip of a given size. All points in strip[] are sorted according to | ||
y coordinate. They all have an upper bound on minimum distance as d.Note that this method seems to be a O(n^2) method, but it's a O(n) method as the inner loop runs at most 6 times''' | ||
def stripClosest(strip, size, d): | ||
min = d | ||
for i in range(size): | ||
for j in range(i+1, size): | ||
if (strip[j].y - strip[i].y) < min: | ||
if dist(strip[i],strip[j]) < min: | ||
min = dist(strip[i], strip[j]) | ||
|
||
return min | ||
|
||
'''A recursive function to find the smallest distance. | ||
The array Px contains all points sorted according to x coordinates and Py contains all points sorted according to y coordinates''' | ||
def closestUtil(Px, Py, n): | ||
if n <= 3: | ||
return bruteForce(Px, n) | ||
|
||
mid = n // 2 | ||
midPoint = Px[mid] | ||
|
||
Pyl = [None] * mid | ||
Pyr = [None] * (n-mid) | ||
li = ri = 0 | ||
for i in range(n): | ||
if ((Py[i].x < midPoint.x or (Py[i].x == midPoint.x and Py[i].y < midPoint.y)) and li<mid): | ||
Pyl[li] = Py[i] | ||
li += 1 | ||
else: | ||
Pyr[ri] = Py[i] | ||
ri += 1 | ||
|
||
dl = closestUtil(Px, Pyl, mid) | ||
dr = closestUtil(Px[mid:], Pyr, n-mid) | ||
|
||
d = min(dl, dr) | ||
strip = [None] * n | ||
j = 0 | ||
for i in range(n): | ||
if abs(Py[i].x - midPoint.x) < d: | ||
strip[j] = Py[i] | ||
j += 1 | ||
return stripClosest(strip, j, d) | ||
|
||
|
||
def closest(P, n): | ||
Px = P | ||
Py = P | ||
Px.sort(key=lambda x:x.x) | ||
Py.sort(key=lambda x:x.y) | ||
|
||
return closestUtil(Px, Py, n) | ||
|
||
#example usage | ||
if __name__ == '__main__': | ||
P = [Point(2, 3), Point(12, 30), Point(40, 50), Point(5, 1), Point(12, 10), Point(3, 4)] | ||
n = len(P) | ||
print("The smallest distance is", closest(P, n)) | ||
|
||
'''output | ||
The smallest distance is 1.4142135623730951 | ||
''' |
102 changes: 102 additions & 0 deletions
102
Algorithms_and_Data_Structures/graham_scan/convex_hull_graham_scan.py
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,102 @@ | ||
from functools import cmp_to_key | ||
|
||
class Point: | ||
def __init__(self,x=None,y=None): | ||
self.x = x | ||
self.y = y | ||
|
||
p0 = Point(0,0) | ||
|
||
def nextToTop(s): | ||
return s[-2] | ||
|
||
def distSq(p1,p2): | ||
return ((p1.x - p2.x)*(p1.x - p2.x) + (p1.y - p2.y)*(p1.y - p2.y)) | ||
|
||
''' | ||
To find orientation of ordered triplet (p, q, r). | ||
The function returns following values | ||
0 --> p, q and r are collinear | ||
1 --> Clockwise | ||
2 --> Counterclockwise | ||
''' | ||
|
||
def orientation(p,q,r): | ||
val = ((q.y - p.y)*(r.x - q.x) - (q.x - p.x)*(r.y-q.y)) | ||
|
||
if val == 0: | ||
return 0 | ||
elif val > 0: | ||
return 1 | ||
else: | ||
return 2 | ||
|
||
def compare(p1,p2): | ||
''' | ||
function that checks orientation | ||
''' | ||
|
||
o = orientation(p0,p1,p2) | ||
if o == 0: | ||
if distSq(p0,p2) >= distSq(p0,p1): | ||
return -1 | ||
else: | ||
return 1 | ||
else: | ||
if o == 2: | ||
return -1 | ||
else: | ||
return 1 | ||
|
||
def convexHull(points,n): | ||
ymin = points[0].y | ||
min = 0 | ||
for i in range(1,n): | ||
y = points[i].y | ||
|
||
if((y<min) or (ymin == y and points[i].x < points[min].x)): | ||
ymin = points[i].y | ||
min = i | ||
|
||
points[0],points[min] = points[min],points[0] | ||
|
||
p0 = points[0] | ||
points = sorted(points,key=cmp_to_key(compare)) | ||
|
||
m = 1 | ||
for i in range(1,n): | ||
|
||
while((i<n-1) and (orientation(p0,points[i],points[i+1])==0)): | ||
i += 1 | ||
|
||
points[m] = points[i] | ||
m+=1 | ||
|
||
if m < 3: | ||
return | ||
|
||
S = [] | ||
S.append(points[0]) | ||
S.append(points[1]) | ||
S.append(points[2]) | ||
|
||
for i in range(3, m): | ||
|
||
while ((len(S) > 1) and | ||
(orientation(nextToTop(S), S[-1], points[i]) != 2)): | ||
S.pop() | ||
S.append(points[i]) | ||
|
||
while S: | ||
p = S[-1] | ||
print("(" + str(p.x) + ", " + str(p.y) + ")") | ||
S.pop() | ||
|
||
|
||
#example usage | ||
input_points = [(0, 3), (1, 1), (2, 2), (4, 4),(0, 0), (1, 2), (3, 1), (3, 3)] | ||
points = [] | ||
for point in input_points: | ||
points.append(Point(point[0], point[1])) | ||
n = len(points) | ||
convexHull(points, n) |