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Copy path04 Bellman Ford [Single Source Shortest Path].cpp
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04 Bellman Ford [Single Source Shortest Path].cpp
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/**
Complexity : O(EV)
Note : Works with negative weight , but not with negative cycle
**/
/**Which of the favors of your Lord will you deny ?**/
#include<bits/stdc++.h>
using namespace std;
#define LL long long
#define PII pair<int,int>
#define PLL pair<LL,LL>
#define MP make_pair
#define F first
#define S second
#define ALL(x) (x).begin(), (x).end()
#define DBG(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << endl
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<class TIn>
using indexed_set = tree<
TIn, null_type, less<TIn>,
rb_tree_tag, tree_order_statistics_node_update>;
/*
PBDS
-------------------------------------------------
1) insert(value)
2) erase(value)
3) order_of_key(value) // 0 based indexing
4) *find_by_order(position) // 0 based indexing
*/
inline void optimizeIO()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
}
const int nmax = 2e5+7;
const int INF = 1e9;
const LL LINF = 1e17;
string to_str(LL x)
{
stringstream ss;
ss<<x;
return ss.str();
}
//bool cmp(const PII &A,const PII &B)
//{
//
//}
struct edge
{
int a,b,w;
};
int n,m;
vector<edge>e;
void bellman_ford(int s)
{
vector<int>dist(nmax,INF);
bool is_negcycle;
dist[s] = 0;
for(int i=0; i<n; i++) /** n-1 + 1 times , last 1 time is to check if there is a negative weight cycles **/
{
is_negcycle = false;
for(int j=0; j<m; j++)
{
if(dist[e[j].a]<INF)
{
if(dist[e[j].a] + e[j].w < dist[e[j].b])
{
dist[e[j].b] = max(-INF, dist[e[j].a] + e[j].w);
is_negcycle = true; /** if there is a relaxation in nth iteration this will become true **/
}
}
}
}
if(is_negcycle)
{
cout<<"Negative Cycle Exists"<<endl;
}
for(int i=1; i<=n; i++)
cout<<i<<" -> "<<dist[i]<<endl;
}
int main()
{
optimizeIO();
cin>>n>>m;
for(int i=0; i<m; i++)
{
int a,b,w;
cin>>a>>b>>w;
e.push_back({a,b,w}); /** Directed **/
//e.push_back({b,a,w});
}
while(true)
{
int v;
cin>>v;
bellman_ford(v);
}
return 0;
}