Graph Algorithms and Sorting Techniques in C
1. Kruskal’s Algorithm
This C code implements Kruskal’s algorithm to find the minimum spanning tree of a graph:
#include<stdio.h>
#define INF 999
#define MAX 100
int p[MAX], c[MAX][MAX], t[MAX][2];
int find(int v) {
while (p[v]) {
v = p[v];
}
return v;
}
void union1(int i, int j) {
p[j] = i;
}
void kruskal(int n) {
int i, j, k, u, v, min, res1, res2, sum = 0;
for (k = 1; k < n; k++) {
min = INF;
for (i = 1; i < n - 1; i++) {
for (j = 1; j <=Graph Algorithms and Sorting Algorithms: A Comparative Analysis
Graph Algorithms
1. Kruskal’s Algorithm
Kruskal’s algorithm finds the minimum spanning tree (MST) of a weighted undirected graph. It iteratively adds the edge with the smallest weight to the MST, ensuring that adding the edge doesn’t create a cycle.
#include<stdio.h>
#define INF 999
#define MAX 100
int p[MAX], c[MAX][MAX], t[MAX][2];
int find(int v) {
while (p[v])
v = p[v];
return v;
}
void union1(int i, int j) {
p[j] = i;
}
void kruskal(int n) {
int i, j, k, u, v, min,Data Structures and Algorithms: C and Python Code Examples
PROGRAM 1: Kruskal’s Algorithm
C Code
#define INF 999
#define MAX 100
int p[MAX], c[MAX][MAX], t[MAX][2];
int find(int v) {
while (p[v]) {
v = p[v];
}
return v;
}
void union1(int i, int j) {
p[j] = i;
}
void kruskal(int n) {
int i, j, k, u, v, min, res1, res2, sum = 0;
for (k = 1; k < n; k++) {
min = INF;
for (i = 1; i < n - 1; i++) {
for (j = 1; j <= n; j++) {
if (i == j) continue;
if (c[i][j] < min) {
u = find(i);
v Computational Complexity: P, NP, NPC, NP-Hard, DP, Network Flow, Approximation, and LP
Dynamic Programming (DP): DP is a technique for solving problems by breaking them down into smaller overlapping subproblems and storing the solutions to these subproblems to avoid recomputing them. This can significantly improve the efficiency of algorithms, especially for problems with exponential time complexity. For example, the Fibonacci sequence can be computed in linear time using DP, whereas a naive recursive approach would take exponential time.
Example:
Consider the problem of finding the
Read MoreComputational Complexity, Dynamic Programming, Network Flow, Approximation Algorithms, and Linear Programming
Dynamic Programming (DP)
Dynamic programming is a technique for solving optimization problems by breaking them down into smaller subproblems and storing the solutions to these subproblems to avoid recomputing them. This can significantly improve the efficiency of the algorithm, especially for problems with overlapping subproblems.
Example:
Consider the problem of finding the minimum cost of reaching a destination from a starting point in a graph. We can use dynamic programming to solve this problem
Read MoreComputational Complexity, Dynamic Programming, Network Flow, Approximation, and Linear Programming: A Comprehensive Guide
Dynamic Programming (DP)
Dynamic programming is a technique for solving optimization problems by breaking them down into smaller overlapping subproblems. The solution to each subproblem is stored in a table, so that it can be reused later. This can significantly reduce the amount of computation required to solve the overall problem.
Example:
Consider the problem of finding the minimum cost of a path from a source node to a destination node in a graph. We can use dynamic programming to solve this problem
Read More