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Commit 6fa300e

Browse files
Added Graph Theory Algorithms
1 parent d035b0c commit 6fa300e

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3 files changed

+355
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3 files changed

+355
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lines changed

‎25-Graph Theory/bipartiteGraphTest.cpp

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#include<bits/stdc++.h>
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using namespace std;
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#define ll long long
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#define ld long double
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#define rep(i,a,b) for(ll i=a;i<b;i++)
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#define repp(i,a,b) for(ll i=a;i<=b;i++)
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#define rrep(i,a,b) for(ll i=a;i>=b;i--)
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#define endl "\n"
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#define deb(x) cerr << #x << "=" << x << endl
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#define debb(x, y) cerr << #x << "=" << x << "," << #y << "=" << y << endl
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#define mod ((ll)1e18)
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#define N ((ll)2e6)
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#define pb push_back
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#define in insert
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#define F first
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#define S second
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#define mp make_pair
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#define lb lower_bound
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#define ub upper_bound
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#define PI 3.1415926535897932384626
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#define all(x) x.begin(), x.end()
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#define rall(x) x.rbegin(), x.rend()
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#define speed ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
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#define test ll t; cin>>t; while(t--)
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typedef pair<ll, ll> pll;
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typedef vector<pll> vpll;
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ll dr[] = { -1, 1, 0, 0};
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ll dc[] = {0, 0, 1, -1};
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/*Functions*/
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ll gcd(ll a, ll b);
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ll exp(ll x, ll y, ll p);
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ll exp(ll x, ll y);
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void InverseofNumber();
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void InverseofFactorial();
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void factorial();
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ll Binomial(ll n, ll R);
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ll factorialNumInverse[N + 1];
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ll naturalNumInverse[N + 1];
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ll fact[N + 1];
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void fileIO() {
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#ifndef ONLINE_JUDGE
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freopen("input.txt", "r", stdin);
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freopen("output.txt", "w", stdout);
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#endif
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}
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ll n, m; //no of vertices and number of edges
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vector<ll> v[N]; //the graph representation
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ll vis[N]; //visited array
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ll color[N]; //color array
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bool dfs(ll x, ll c) {
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vis[x] = 1;
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color[x] = c;
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for (auto i : v[x]) {
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if (vis[i] == 0) {
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if (dfs(i, c ^ 1) == false) //invert color
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return false;
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}
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else {
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if (color[x] == color[i])
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return false;
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}
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}
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return true;
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}
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int main() {
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speed
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// InverseofNumber(),InverseofFactorial(),factorial();
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fileIO();
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cin >> n >> m;
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while (m--) {
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ll xx, yy; cin >> xx >> yy;
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v[xx].pb(yy);
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v[yy].pb(xx);
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}
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ll ans = 0;
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bool answer;
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for (ll i = 1; i <= n; i++) {
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if (!vis[i]) {
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answer = dfs(i, 0); //dfs calls for unvisited nodes
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if (!answer) {
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cout << "NOT BIPARTITE" << endl;
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exit(0);
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}
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}
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}
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cout << "BIPARTITE" << endl;
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return 0;
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}
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/*All Functions*/
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ll gcd(ll a, ll b) {
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if (b == 0)
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return a;
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return gcd(b, a % b);
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}
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ll exp(ll x, ll y, ll p) {
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ll res = 1;
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while (y) {
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if (y % 2)
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res = (res * x % p) % p;
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x = (x * x) % p;
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y /= 2;
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}
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return res;
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}
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ll exp(ll x, ll y) {
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ll res = 1;
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while (y) {
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if (y % 2)
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res = (res * x ) ;
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x = (x * x) ;
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y /= 2;
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}
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return res;
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}
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void InverseofNumber() {
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naturalNumInverse[0] = naturalNumInverse[1] = 1;
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for (ll i = 2; i <= N; i++)
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naturalNumInverse[i] = naturalNumInverse[mod % i] * (mod - mod / i) % mod;
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}
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void InverseofFactorial() {
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factorialNumInverse[0] = factorialNumInverse[1] = 1;
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for (ll i = 2; i <= N; i++)
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factorialNumInverse[i] = (naturalNumInverse[i] * factorialNumInverse[i - 1]) % mod;
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}
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void factorial() {
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fact[0] = 1;
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for (ll i = 1; i <= N; i++)
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fact[i] = (fact[i - 1] * i) % mod;
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}
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ll Binomial(ll n, ll R) {
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ll ans = ((fact[n] * factorialNumInverse[R]) % mod * (factorialNumInverse[n - R]) % mod) % mod;
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return ans;
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}

‎25-Graph Theory/connectedComponents.cpp

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#include<bits/stdc++.h>
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// #warning x&1=0 if x is even and x&1=1 if x is odd
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// #include<ext/pb_ds/assoc_container.hpp>
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// #include <ext/pb_ds/tree_policy.hpp>
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// using namespace __gnu_pdbs;
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using namespace std;
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#define ll long long
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#define rep( i, a, b) for(ll i=a;i<b;i++)
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#define repp(i,a,b) for(ll i=a;i<=b;i++)
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#define rrep(i,a,b) for(ll i=a;i>=b;i--)
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#define ld long double
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#define endl "\n"
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#define mod ((ll)1e18)
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#define N ((ll)2e6+10)
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#define pb push_back
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#define in insert
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#define f first
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#define s second
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#define lb lower_bound
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#define ub upper_bound
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#define all(x) x.begin(), x.end()
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#define speed ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
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#define test ll t; cin>>t; while(t--)
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ll gcd(ll a, ll b) {if (b == 0)return a; return gcd(b, a % b);}
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ll exp(ll x, ll y, ll p) { ll res = 1; while (y) {if (y % 2) res = (res * x % p) % p; x = (x * x) % p; y /= 2; } return res;}
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ll exp(ll x, ll y) { ll res = 1; while (y) {if (y % 2) res = (res * x ) ; x = (x * x) ; y /= 2; } return res;}
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ll sv[1000000] = {0};
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ll factorialNumInverse[N + 1];
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ll naturalNumInverse[N + 1];
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ll fact[N + 1];
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void InverseofNumber() {naturalNumInverse[0] = naturalNumInverse[1] = 1; for (ll i = 2; i <= N; i++)naturalNumInverse[i] = naturalNumInverse[mod % i] * (mod - mod / i) % mod;}
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void InverseofFactorial() {factorialNumInverse[0] = factorialNumInverse[1] = 1; for (ll i = 2; i <= N; i++)factorialNumInverse[i] = (naturalNumInverse[i] * factorialNumInverse[i - 1]) % mod;}
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void factorial() {fact[0] = 1; for (ll i = 1; i <= N; i++) {fact[i] = (fact[i - 1] * i) % mod;}}
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ll Binomial(ll n, ll R) {ll ans = ((fact[n] * factorialNumInverse[R]) % mod * (factorialNumInverse[n - R]) % mod) % mod; return ans;}
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/*TOIENT FUNCTION*/ll phi(ll n) {ll ans = n; for (ll i = 2; i * i <= n; i++) {if (n % i == 0) {while (n % i == 0) n /= i; ans -= ans / i;}} if (n > 1) ans -= ans / n; return ans;}
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void fileIO() {
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#ifndef ONLINE_JUDGE
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freopen("input.txt", "r", stdin);
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freopen("output.txt", "w", stdout);
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#endif
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}
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ll n, k; ll vis[N] ;
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ll counter = 0;
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ll component[N];
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vector<ll> v[N];
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void dfs(ll at) {
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if (vis[at] == 1) return;
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vis[at] = 1;
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component[at] = counter;
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for (auto i : v[at]) {
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dfs(i);
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}
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}
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int main() {
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speed
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// InverseofNumber(),InverseofFactorial(),factorial();
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fileIO();
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cin >> n >> k;
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rep(i, 0, k) {
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ll xx, yy; cin >> xx >> yy;
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v[xx].pb(yy);
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v[yy].pb(xx);
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}
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fill(vis, vis + N, 0);
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repp(i, 1, n) {
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if (!vis[i]) {
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counter++;
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dfs(i);
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}
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}
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repp(i, 0, n) {
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cout << component[i] << " ";
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}
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cout << endl;
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return 0;
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}

‎25-Graph Theory/dijkstras.cpp

Lines changed: 133 additions & 0 deletions
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#include<bits/stdc++.h>
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using namespace std;
3+
#define ll long long
4+
#define ld long double
5+
#define rep(i,a,b) for(ll i=a;i<b;i++)
6+
#define repp(i,a,b) for(ll i=a;i<=b;i++)
7+
#define rrep(i,a,b) for(ll i=a;i>=b;i--)
8+
#define endl "\n"
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#define deb(x) cerr << #x << "=" << x << endl
10+
#define debb(x, y) cerr << #x << "=" << x << "," << #y << "=" << y << endl
11+
#define mod ((ll)1e18)
12+
#define N ((ll)2e6+10)
13+
#define pb push_back
14+
#define in insert
15+
#define F first
16+
#define S second
17+
#define lb lower_bound
18+
#define ub upper_bound
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#define PI 3.1415926535897932384626
20+
#define all(x) x.begin(), x.end()
21+
#define speed ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
22+
#define test ll t; cin>>t; while(t--)
23+
typedef pair<ll, ll> pll;
24+
typedef vector<pll> vpll;
25+
26+
/*Functions*/
27+
ll gcd(ll a, ll b);
28+
ll exp(ll x, ll y, ll p);
29+
ll exp(ll x, ll y);
30+
void InverseofNumber();
31+
void InverseofFactorial();
32+
ll Binomial(ll n, ll R);
33+
34+
35+
ll factorialNumInverse[N + 1];
36+
ll naturalNumInverse[N + 1];
37+
ll fact[N + 1];
38+
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void fileIO() {
40+
#ifndef ONLINE_JUDGE
41+
freopen("input.txt", "r", stdin);
42+
freopen("output.txt", "w", stdout);
43+
#endif
44+
}
45+
46+
ll n, m;
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vector<pll> v[N];
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ll ids[N] = {0};
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ll dist[N] = {0};
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ll vis[N] = {0};
51+
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int main() {
53+
speed
54+
// InverseofNumber(),InverseofFactorial(),factorial();
55+
fileIO();
56+
57+
cin >> n >> m;
58+
rep(i, 0, m) {
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ll xx, yy, wt; cin >> xx >> yy >> wt;
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v[xx].pb({yy, wt});
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}
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fill(dist, dist + N, mod);
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dist[1] = 0;
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multiset < pair < ll , ll > > s;
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s.in({1, 0});
66+
while (!s.empty()) {
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pll x = *s.begin();
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s.erase(s.begin());
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vis[x.F] = 1;
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for (auto i : v[x.F]) {
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ll d = dist[x.F] + i.S;
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if (d < dist[i.F]) {
73+
dist[i.F] = d;
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s.in({i.F, d});
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}
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}
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}
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repp(i, 1, n) {
80+
cout << dist[i] << " ";
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}
82+
cout << endl;
83+
return 0;
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}
85+
86+
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/*All Functions*/
88+
ll gcd(ll a, ll b) {
89+
if (b == 0)
90+
return a;
91+
return gcd(b, a % b);
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}
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ll exp(ll x, ll y, ll p) {
95+
ll res = 1;
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while (y) {
97+
if (y % 2)
98+
res = (res * x % p) % p;
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x = (x * x) % p;
100+
y /= 2;
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}
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return res;
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}
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ll exp(ll x, ll y) {
105+
ll res = 1;
106+
while (y) {
107+
if (y % 2)
108+
res = (res * x ) ;
109+
x = (x * x) ;
110+
y /= 2;
111+
}
112+
return res;
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}
114+
void InverseofNumber() {
115+
naturalNumInverse[0] = naturalNumInverse[1] = 1;
116+
for (ll i = 2; i <= N; i++)
117+
naturalNumInverse[i] = naturalNumInverse[mod % i] * (mod - mod / i) % mod;
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}
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void InverseofFactorial() {
120+
factorialNumInverse[0] = factorialNumInverse[1] = 1;
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for (ll i = 2; i <= N; i++)
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factorialNumInverse[i] = (naturalNumInverse[i] * factorialNumInverse[i - 1]) % mod;
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}
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void factorial() {
125+
fact[0] = 1;
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for (ll i = 1; i <= N; i++)
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fact[i] = (fact[i - 1] * i) % mod;
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}
129+
ll Binomial(ll n, ll R) {
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ll ans = ((fact[n] * factorialNumInverse[R]) % mod * (factorialNumInverse[n - R]) % mod) % mod;
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return ans;
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}
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