Added a graph alg

this is another SSSP alg that can detect negative wieght cycles

Author: ash12345678987654321

Graph/SPFA SSSP/shortest-path-faster-algorithm.cpp

@@ -0,0 +1,84 @@
+//This algorithm does the same thing as bellman ford and has the same time complexity but is constant time faster
+//look idk how to do all he fancy struct stuff. so dont complain or just use the bellman ford
+#include <bits/stdc++.h>
+using namespace std;
+typedef pair<int,int> ii;
+queue<int> q;
+const int N=10003; // put number of nodes+3 here PLS CHANGE THIS ACCORDINGLY
+int w[N],c2[N];//w is shortest path to a node, c2 is number of time a node has been relaxed
+bool c[N];//c is to check whether a certain node is in the queue
+vector<ii> data [N]; //adjacency list of graph
+void edge(int x,int y, int l){ //there is a directed edge from x to y with length l
+    data[x].push_back(ii (y,l));
+}
+void initialize(){//initialize variables, may not be the fastest
+    memset(c2,0,sizeof(c2)); //i apologize for using memset
+    memset(c,true,sizeof(c));
+    memset(w,63,sizeof(w)); //depends on largest path from 1 node to another IMPORTANT
+    for (int x=0;x<N;x++){
+        data[x].clear();
+    } //note that the algorithm until the queue is empty so there is no need to initialize queue
+}
+void setup(int s){//s is the source node
+    q.push(s);
+    w[s]=0;
+}
+void bfs(int x){ //this is no mark everything under the negative weight cycle as inf length
+    int l=data[x].size(),a;
+    for (int y=0;y<l;y++){ //for each of x neighbour
+        a=data[x][y].first;
+        if (c2[a]<N){ // if neighbour is not marked as -INF length
+            c2[a]=N; //mark it as such
+            bfs(a); //mark all its neighbours as such
+        }
+    }
+}
+void SPFA(){
+    int n,l,u,d;
+    while (!q.empty()){
+    n=q.front(); // n is node to relax neighbours
+    q.pop();
+    if (c2[n]>=N) continue; // if n is part of negative weight cycle, ignore
+    c[n]=true; //mark n is not in queue
+    l=data[n].size(); //just for constant time improvement
+    for (int x=0;x<l;x++){
+        u=data[n][x].first;
+        d=data[n][x].second;
+        if (w[u]>w[n]+d){ // if u can be relaxed
+            w[u]=w[n]+d; //relaxing u
+            c2[u]++;// count number of time u has been relaxed. as u can only be relaxed N-1 times if its not in negative weight cycle
+            if (c2[u]==N){ //if n in is negative wieght cycle
+                bfs(u); //mark all of u neighbours as - INF weight
+            }
+            else if (c[u]){ //if u is not in queue
+                c[u]=false; //mark u is in queue
+                q.push(u); //push u into queue
+            }
+        }
+    }
+    }
+}
+void print(int n){ // print length of shortest path
+    if (c2[n]>=N){
+        printf("-Infinity\n"); //part of negative wieght cycle
+    }
+    else if (w[n]==1061109567){
+        printf("Impossible\n"); //unreachable form source node
+    }
+    else{
+        printf("%d\n",w[n]); //else just print its shortest path
+    }
+}
+int main(){ // the example graph has 5 nodes and 4 edges
+    initialize(); //pls initialize or weird stuff might happen
+    edge(0,1,999);
+    edge (1,2,-2);
+    edge(2,1,1);
+    edge (0,3,2);
+    setup(0); //0 is source node
+    SPFA();
+    print(1);
+    print(3);
+    print(4);
+    return 0;
+}