Seidal Algorithm
The Seidal Algorithm is an efficient graph traversal algorithm that is specifically designed to find the shortest path between two nodes in an undirected and unweighted graph. Developed by Raimund Seidel in 1995, the algorithm is based on the concept of "graph decomposition" and utilizes a divide-and-conquer approach to efficiently process the input graph. By breaking the graph into smaller pieces and recursively solving subproblems, the Seidal Algorithm is able to find the shortest path between two nodes with an impressive time complexity of O(n^1.585), where n is the number of vertices in the graph. This makes the Seidal Algorithm an attractive choice for solving large-scale graph problems where other shortest path algorithms, such as Dijkstra's or Floyd-Warshall, may be too slow.
In the Seidal Algorithm, the input graph is first decomposed into two smaller subgraphs by selecting a random set of vertices and isolating the vertices with even distances from the rest of the graph. The algorithm then recursively finds the shortest path for each subgraph and combines the results to obtain the shortest path for the entire graph. The key to the algorithm's efficiency lies in its ability to prune the search space and exploit the properties of the graph's structure. The Seidal Algorithm is particularly well-suited for graphs with low doubling dimension, where the density of vertices decreases rapidly with increasing distance from a given vertex. This allows the algorithm to handle large, sparse graphs with millions of vertices and edges, while still maintaining its fast performance.
#include<stdio.h>
#include<conio.h>
#include<math.h>
void main()
{
float a,b,c,a1,a2,a3,b1,b2,b3,c1,c2,c3,d1,d2,d3,x1,x2,x3;
clrscr();
printf("Enter values of eq1:");
scanf("%f%f%f%f",&a1,&a2,&a3,&d1);
printf("Enter values of eq2:");
scanf("%f%f%f%f",&b1,&b2,&b3,&d2);
printf("Enter values of eq3:");
scanf("%f%f%f%f",&c1,&c2,&c3,&d3);
x1=x2=x3=0.0;
do
{
a=x1;
b=x2;
c=x3;
x1=(1/a1)*(d1-(a2*x2)-(a3*x3));
x2=(1/b2)*(d2-(b1*x1)-(b3*x3));
x3=(1/c3)*(d3-(c1*x1)-(c2*x2));
}while(fabs(x1-a)>0.0001&&fabs(x2-b)>0.0001&&fabs(x3-c)>0.0001);
printf("x1=%f\nx2=%f\nx3=%f",x1,x2,x3);
getch();
}
