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def BFS(G, source): for v in G: color[v] <- WHITE Q <- MAKE-QUEUE() ADD(Q, source) color[source] <- GRAY while Q not empty: v <- REMOVE(Q) color[v] <- BLACK for u adjacent to v: if color[u] == WHITE color[u] = GRAY ADD(Q, u) Initialize Relax
![def BFS(G, source): for v in G: color[v] <- WHITE Q <- MAKE-QUEUE() ADD(Q, source) color[source] <- GRAY while Q not empty: v <- REMOVE(Q) color[v] <- BLACK for u adjacent to v: if color[u] == WHITE color[u] = GRAY ADD(Q, u) Initialize Relax](http://images.slideplayer.com./15/4860552/slides/slide_1.jpg "def BFS(G, source): for v in G: color[v] <- WHITE Q <- MAKE-QUEUE() ADD(Q, source) color[source] <- GRAY while Q not empty: v <- REMOVE(Q) color[v] <- BLACK for u adjacent to v: if color[u] == WHITE color[u] = GRAY ADD(Q, u) Initialize Relax")
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def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax
![def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax](http://images.slideplayer.com./15/4860552/slides/slide_2.jpg "def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax")
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def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax
![def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax](http://images.slideplayer.com./15/4860552/slides/slide_3.jpg "def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax")
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SIMPLIFICATION (Dijkstra)
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def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax
![def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax](http://images.slideplayer.com./15/4860552/slides/slide_5.jpg "def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax")
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def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax
![def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax](http://images.slideplayer.com./15/4860552/slides/slide_6.jpg "def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax")
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def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v Initialize Relax
![def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v Initialize Relax](http://images.slideplayer.com./15/4860552/slides/slide_7.jpg "def DIJKSTRA(G, source): for v in G: color[v] dist[v]+weight(u,v) dist[u] = dist[v]+weight(u,v) parent[u] <- v Initialize Relax")
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SIMPLIFICATION (PRIM)
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def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax
![def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax](http://images.slideplayer.com./15/4860552/slides/slide_9.jpg "def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax")
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def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax
![def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax](http://images.slideplayer.com./15/4860552/slides/slide_10.jpg "def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v if color[u] == WHITE: color[u] <- GRAY ADD(Q, u) Initialize Relax")
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def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v Initialize Relax
![def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v Initialize Relax](http://images.slideplayer.com./15/4860552/slides/slide_11.jpg "def PRIM(G, source): for v in G: color[v] weight(u,v): dist[u] = weight(u,v) parent[u] <- v Initialize Relax")
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BFS utilizing dist[], parent[] fields dist[] keeps track of the level parent[] keep track of how vertex was reached
![BFS utilizing dist[], parent[] fields dist[] keeps track of the level parent[] keep track of how vertex was reached](http://images.slideplayer.com./15/4860552/slides/slide_12.jpg "BFS utilizing dist[], parent[] fields dist[] keeps track of the level parent[] keep track of how vertex was reached")
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def DIJKSTRA(G, source): for v in G: color[v] <- WHITE dist[v] <- INF parent[v] <- NIL dist[source] <- 0 Q <- MAKE-QUEUE() ADD(Q, source) color[source] <- GRAY while Q not empty: v <- REMOVE(Q) color[v] <- BLACK for u adjacent to v: if color[u] == WHITE: dist[u] = dist[v]+1 parent[u] <- v color[u] <- GRAY ADD(Q, u) Initialize Relax
![def DIJKSTRA(G, source): for v in G: color[v] <- WHITE dist[v] <- INF parent[v] <- NIL dist[source] <- 0 Q <- MAKE-QUEUE() ADD(Q, source) color[source] <- GRAY while Q not empty: v <- REMOVE(Q) color[v] <- BLACK for u adjacent to v: if color[u] == WHITE: dist[u] = dist[v]+1 parent[u] <- v color[u] <- GRAY ADD(Q, u) Initialize Relax](http://images.slideplayer.com./15/4860552/slides/slide_13.jpg "def DIJKSTRA(G, source): for v in G: color[v] <- WHITE dist[v] <- INF parent[v] <- NIL dist[source] <- 0 Q <- MAKE-QUEUE() ADD(Q, source) color[source] <- GRAY while Q not empty: v <- REMOVE(Q) color[v] <- BLACK for u adjacent to v: if color[u] == WHITE: dist[u] = dist[v]+1 parent[u] <- v color[u] <- GRAY ADD(Q, u) Initialize Relax")
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