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Added Some algorithms. Changed Some. (Graph Directory) #631

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124 changes: 51 additions & 73 deletions Graph/Dijsktra.cpp
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Original file line number Diff line number Diff line change
@@ -1,84 +1,62 @@
#include<bits/stdc++.h>
using namespace std;
#include <bits/stdc++.h>

#define f(i,x,n) for(int i=x;i<n;i++)
#define ll long long
#define pb(i) push_back(i)
#define mp(i,j) make_pair(i,j)
#define test ll t; cin>>t; while(t--)
#define dbg(x) cerr << #x << ": " << x << endl;
#define FOR(i, a, b) for(int i = (a); i < (b); ++i)
#define FORD(i, a, b) for(int i = (a); i >= (b); --i)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define pb push_back
#define mp make_pair
#define fi first
#define se second

#define v 9
#define INF 1000000000
#define MAXN 1000005
#define EPS 1e-9

int minDistance(int dist[], bool visited[])
{
int min = INT_MAX, minIndex;

f(i,0,v)
{
if (visited[i]==false && dist[i]<=min)
{
min = dist[i];
minIndex = i;
}
}

return minIndex;
}
typedef long long ll;
typedef std::vector<int> vi;
typedef std::vector<long long> vll;
typedef std::pair<int, int> pii;
typedef std::pair<ll, ll> pllll;
typedef std::set<int> si;
typedef std::set<ll> sll;
typedef std::unordered_map<int , int> mii;
typedef std::unordered_map<ll , ll> mllll;
typedef std::unordered_map<char , int> mci;
typedef std::unordered_map<char , ll> mcll;

void print(int dist[])
{
cout<<"Vertex \t\t Distance from Source"<<endl;

f(i,0,v)
{
cout<<i<<"\t\t "<<dist[i]<<endl;
}
}
ll N;
bool vis[MAXN];
vll dist(MAXN);
std::vector<pllll> adj_dijkstra[MAXN]; //{v, w}

void dijsktra(int g[][v], int s)
{
int dist[v];
bool visited[v];

f(i,0,v)
{
dist[i] = INT_MAX;
visited[i] = false;
}

dist[s] = 0;

f(i,0,v-1)
{
int u = minDistance(dist,visited);
visited[u] = true;

f(j,0,v)
{
if (!visited[j] && g[u][j] && dist[u]!=INT_MAX && dist[u]+g[u][j]<dist[j])
{
dist[j] = dist[u] + g[u][j];
}
}
}

print(dist);
void dijkstra(int s) {
FOR(i, 0, N) {
dist[i] = INF;
vis[i] = false;
}
std::priority_queue<pllll> q; //{w, v}
dist[s] = 0;
q.push({0, s});
while(!q.empty()) {
ll u = q.top().se; q.pop();
if(vis[u]) continue;
vis[u] = true;
for(auto pr : adj_dijkstra[u]) {
ll v, w;
std::tie(v, w) = pr;
if(vis[v]) continue;

if(dist[u] + w < dist[v]) {
dist[v] = dist[u] + w;
q.push({-dist[v], v});
}
}
}
}

int main()
{
int g[v][v] = { { 0, 4, 0, 0, 0, 0, 0, 8, 0 },
{ 4, 0, 8, 0, 0, 0, 0, 11, 0 },
{ 0, 8, 0, 7, 0, 4, 0, 0, 2 },
{ 0, 0, 7, 0, 9, 14, 0, 0, 0 },
{ 0, 0, 0, 9, 0, 10, 0, 0, 0 },
{ 0, 0, 4, 14, 10, 0, 2, 0, 0 },
{ 0, 0, 0, 0, 0, 2, 0, 1, 6 },
{ 8, 11, 0, 0, 0, 0, 1, 0, 7 },
{ 0, 0, 2, 0, 0, 0, 6, 7, 0 } };

//source vertex is 0
dijkstra(g,0);

return 0;
}
162 changes: 76 additions & 86 deletions Graph/Kruskal's(MST).cpp
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Original file line number Diff line number Diff line change
@@ -1,96 +1,86 @@
//weighted undirected graph
//greedy algorithm
//spanning tree which connects all vertices of graph i.e v-1 edges , no cycles , subsets of edges
//single connected edges
#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
#include <bits/stdc++.h>

class DSU{
int *parent;
int *rank;
#define dbg(x) cerr << #x << ": " << x << endl;
#define FOR(i, a, b) for(int i = (a); i < (b); ++i)
#define FORD(i, a, b) for(int i = (a); i >= (b); --i)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define pb push_back
#define mp make_pair
#define fi first
#define se second

public:
DSU(int n){
parent=new int[n];
rank=new int[n];
#define INF 1000000000
#define MAXN 1000005
#define EPS 1e-9

//parent -1,rank 1
for(int i=0;i<n;i++){
parent[i]=-1;
rank[i]=1;
}
}
typedef long long ll;
typedef std::vector<int> vi;
typedef std::vector<long long> vll;
typedef std::pair<int, int> pii;
typedef std::pair<ll, ll> pllll;
typedef std::set<int> si;
typedef std::set<ll> sll;
typedef std::unordered_map<int , int> mii;
typedef std::unordered_map<ll , ll> mllll;
typedef std::unordered_map<char , int> mci;
typedef std::unordered_map<char , ll> mcll;

//find function
int find(int i){
if(parent[i]==-1){
return i;
}
//otherwise
return parent[i]=find(parent[i]);
ll N;
vll rank(MAXN), size(MAXN), parent(MAXN);
std::vector<std::tuple<ll, ll, ll>> edges;

//Helping functions
void init() {
FOR(i, 0, N) {
parent[i] = i;
size[i] = 1;
rank[i] = 0;
}
}

ll find(int a) {
if(a == parent[a]) return a;
return parent[a] = find(parent[a]);
}
//unite (union)
void unite(int x,int y){
int s1=find(x);
int s2=find(y);

if(s1!=s2){
//union by rank
if(rank[s1]<rank[s2]){
parent[s1]=s2;
rank[s2]+=rank[s1];
}
else
{
parent[s2]=s1;
rank[s1]+=rank[s2];
}
}
}
void unite(ll a, ll b) {
a = find(a);
b = find(b);

//By rank
if(a != b) {
if(rank[a] < rank[b])
std::swap(a, b);
parent[b] = a;
if(rank[a] == rank[b])
rank[a]++;
}

};
class Graph{
vector<vector<int>>edgelist;
int V;
public:
Graph(int V){
this->V=V;
}
void addEdge(int x,int y,int w){
edgelist.push_back({w,x,y});
}
int kruskal_mst(){
//sort all the edges
sort(edgelist.begin(),edgelist.end());
//init a DSU
DSU s(V);
//By size
if(a != b) {
if(size[a] < size[b])
std::swap(a, b);
parent[b] = a;
size[a] += size[b];
}
}

int ans=0;
for(auto edge:edgelist){
int w=edge[0];
int x=edge[1];
int y=edge[2];
//take that edge in MST if it doesnt form a cycle
if(s.find(x)!=s.find(y)){
s.unite(x,y);
ans+=w;
}
}
return ans;
}
};
bool same(ll a, ll b) {
return find(a) == find(b);
}

int main(){
Graph g(4);
g.addEdge(0,1,1);
g.addEdge(1,3,3);
g.addEdge(3,2,4);
g.addEdge(2,0,2);
g.addEdge(0,3,2);
g.addEdge(1,2,2);
//Actual Kruskal
void kruskal() {
std::sort(all(edges));
for(auto edge : edges) {
ll u, v, w;
std::tie(w, u, v) = edge;
if(!same(u, v)) unite(u, v);
}
}

cout<<g.kruskal_mst()<<endl;
return 0;
}
int main()
{
return 0;
}
52 changes: 52 additions & 0 deletions Graph/bfsQueue.cpp
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Original file line number Diff line number Diff line change
@@ -0,0 +1,52 @@
#include <bits/stdc++.h>

#define dbg(x) cerr << #x << ": " << x << endl;
#define FOR(i, a, b) for(int i = (a); i < (b); ++i)
#define FORD(i, a, b) for(int i = (a); i >= (b); --i)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define pb push_back
#define mp make_pair
#define fi first
#define se second

#define INF 1000000000
#define MAXN 1000005
#define EPS 1e-9

typedef long long ll;
typedef std::vector<int> vi;
typedef std::vector<long long> vll;
typedef std::pair<int, int> pii;
typedef std::pair<ll, ll> pllll;
typedef std::set<int> si;
typedef std::set<ll> sll;
typedef std::unordered_map<int , int> mii;
typedef std::unordered_map<ll , ll> mllll;
typedef std::unordered_map<char , int> mci;
typedef std::unordered_map<char , ll> mcll;

ll N;
bool seen[MAXN];
vll dist(MAXN), adj[MAXN];

void bfs(int x) {
std::queue<ll> q;
seen[x] = true;
dist[x] = 0;
q.push(x);
while(!q.empty()) {
ll u = q.front(); q.pop();
for(auto v : adj[u]) {
if(seen[v]) continue;
seen[v] = true;
dist[v] = dist[u] + 1;
q.push(v);
}
}
}

int main()
{
return 0;
}
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