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Add References to Ford-Fulkerson
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‎README.md

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@@ -54,6 +54,7 @@ Programming assignment solutions are not available in order to respect Coursera
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- Bellman-Ford
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- Floyd-Warshall
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- Johnson (APSP)
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- Ford-Fulkerson
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To visualize some Pathfinding Algorithms check: [Pathfinding Visualizer](https://lyanghiga.github.io/pathfinding-visualizer/)
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‎data-structures/graph/README.md

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@@ -3,10 +3,8 @@
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- BFS
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- [BFS' lectures](https://www.coursera.org/learn/algorithms-graphs-data-structures/lecture/JZRXz/breadth-first-search-bfs-the-basics)
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- [Algorithm Design 1st Edition](https://www.amazon.com/Algorithm-Design-Jon-Kleinberg/dp/0321295358)
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- Undirected connectivity
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- [BFS and Undirected Connectivity - Lecture
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](https://www.coursera.org/learn/algorithms-graphs-data-structures/lecture/BTVWn/bfs-and-undirected-connectivity)
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- [Algorithm Design 1st Edition](https://www.amazon.com/Algorithm-Design-Jon-Kleinberg/dp/0321295358)
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- Undirected connectivity - [BFS and Undirected Connectivity - Lecture
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](https://www.coursera.org/learn/algorithms-graphs-data-structures/lecture/BTVWn/bfs-and-undirected-connectivity) - [Algorithm Design 1st Edition](https://www.amazon.com/Algorithm-Design-Jon-Kleinberg/dp/0321295358)
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- DFS
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- [DFS' lectures](https://www.coursera.org/learn/algorithms-graphs-data-structures/lecture/pKr0Y/depth-first-search-dfs-the-basics)
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- [Algorithm Design 1st Edition](https://www.amazon.com/Algorithm-Design-Jon-Kleinberg/dp/0321295358)
@@ -36,3 +34,7 @@
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- Johnson
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- [Johnson's Algorithm Lectures](https://www.coursera.org/learn/algorithms-npcomplete/lecture/eT0Xt/johnsons-algorithm-i)
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- [Introduction to Algorithms, 3rd Edition](https://en.wikipedia.org/wiki/Introduction_to_Algorithms)
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- Ford-Fulkerson
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- [Ford-Fulkerson Algorithm Lectures](https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-046j-design-and-analysis-of-algorithms-spring-2015/lecture-videos/lecture-13-incremental-improvement-max-flow-min-cut/)
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- [Introduction to Algorithms, 3rd Edition](https://en.wikipedia.org/wiki/Introduction_to_Algorithms)
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- [Algorithm Design 1st Edition](https://www.amazon.com/Algorithm-Design-Jon-Kleinberg/dp/0321295358)

‎data-structures/graph/graph.js

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Original file line numberDiff line numberDiff line change
@@ -189,50 +189,61 @@ class Graph {
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}
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return min;
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};
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// Returns the initial Residual Graph (Gr)
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// with original edges, and residual edges with zero capacity
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this.createResidualGraph = () => {
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const rg = new Graph(true);
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for (let [u, vertexList] of this.list) {
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for (let v in vertexList) {
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// original edge = c(u,v) - f(u,v)
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// original edge = c(u,v)
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rg.addVertecesAndEdge(u, vertexList[v].node, vertexList[v].weight);
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// residual edges
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rg.addVertecesAndEdge(vertexList[v].node, u, 0);
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}
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}
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return rg;
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};
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// Update the edeges (orignal and residual) of Gr that are used in this path
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// using the bottleneck value
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this.updateResidualGraph = (g, path, bottleneck) => {
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// for each edge of this path
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for (let i = 0; i < path.length - 1; i++) {
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// we need to check if edge(u,v) is from the original Graph or from the Residual Graph
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// let isResidual = true;
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// nodes u,v from the edge (u,v)
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const u = path[i];
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const v = path[i + 1];
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// ajd list (capacity of each edge that remains) of u and v
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const listU = g.list.get(u);
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const listV = g.list.get(v);
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// values that will be updated
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let updatedEdgeUV;
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let updatedEdgeVU;
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// search for edge(u,v) in residual graph
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// serach for v in adj list of u
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for (let i = 0; i < listU.length; i++) {
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const t = listU[i];
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if (v == t.node) {
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// remove <bottleneck> from the remaining capacity of the edge (u,v)
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updatedEdgeUV = {
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node: t.node,
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weight: t.weight - bottleneck,
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};
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// updated adj list of u and set in Gr's map
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const updatedList = [...listU];
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updatedList[i] = updatedEdgeUV;
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g.list.set(u, updatedList);
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break;
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}
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}
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// search for edge(v,v) in residual graph
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// search for u in the adj list of v
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for (let i = 0; i < listV.length; i++) {
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const t = listV[i];
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if (u == t.node) {
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// add <bottleneck> from the remaining capacity of the edge (v,u)
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// edges (u,v) and (v,u) are complementary, residual and original
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updatedEdgeVU = {
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node: t.node,
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weight: t.weight + bottleneck,
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};
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// update adj list of v and set to Gr's map
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const updatedList = [...listV];
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updatedList[i] = updatedEdgeVU;
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g.list.set(v, updatedList);
@@ -841,23 +852,24 @@ class Graph {
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};
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// Returns the final Residual Graph
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this.fordFulkerson = (s, t) => {
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// Net flow must be a directed graph
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if (!this.directed)
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return false;
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const flow = new Map();
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// Initially f(e)=0 for all e in G
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// for each edge of G f(u,v) = 0
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// Initially f(e)=0
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// for each edge(u,v) of G f(e) = 0
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for (let [u, vertexList] of this.list) {
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flow.set(u, new Map());
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for (let v of vertexList) {
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flow.get(u).set(v.node, 0);
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}
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}
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let residualGraph = this.createResidualGraph();
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residualGraph.print();
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let { exists, path } = this.augmentingPath(s, t, residualGraph);
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// if there is no path between s - t return false
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if (!exists || !path)
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return false;
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// min val of flow that still can pass through
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const bottleneck = this.bottleneck(path, residualGraph);
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// while exists a path do augmenting path in Gr
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while (exists) {

‎data-structures/graph/graph.ts

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Original file line numberDiff line numberDiff line change
@@ -205,6 +205,8 @@ class Graph<T> {
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return min;
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};
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// Returns the initial Residual Graph (Gr)
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// with original edges, and residual edges with zero capacity
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createResidualGraph = () => {
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const rg = new Graph<T>(true);
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for (let [u, vertexList] of this.list) {
@@ -218,39 +220,47 @@ class Graph<T> {
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return rg;
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};
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223+
// Update the edeges (orignal and residual) of Gr that are used in this path
224+
// using the bottleneck value
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updateResidualGraph = (g: Graph<T>, path: Array<T>, bottleneck: number) => {
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// for each edge of this path
223227
for (let i = 0; i < path.length - 1; i++) {
224-
// we need to check if edge(u,v) is from the original Graph or from the Residual Graph
225-
// let isResidual = true;
228+
// nodes u,v from the edge (u,v)
226229
const u = path[i];
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const v = path[i + 1];
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// ajd list (capacity of each edge that remains) of u and v
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const listU = g.list.get(u)!;
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const listV = g.list.get(v)!;
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// values that will be updated
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let updatedEdgeUV: Vertex<T>;
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let updatedEdgeVU: Vertex<T>;
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// search for edge(u,v) in residual graph
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// serach for v in adj list of u
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for (let i = 0; i < listU.length; i++) {
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const t = listU[i];
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if (v == t.node) {
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// remove <bottleneck> from the remaining capacity of the edge (u,v)
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updatedEdgeUV = {
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node: t.node,
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weight: t.weight - bottleneck,
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};
246+
// updated adj list of u and set in Gr's map
240247
const updatedList = [...listU];
241248
updatedList[i] = updatedEdgeUV;
242249
g.list.set(u, updatedList);
243250
break;
244251
}
245252
}
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// search for edge(v,v) in residual graph
253+
// search for u in the adj list of v
247254
for (let i = 0; i < listV.length; i++) {
248255
const t = listV[i];
249256
if (u == t.node) {
257+
// add <bottleneck> from the remaining capacity of the edge (v,u)
258+
// edges (u,v) and (v,u) are complementary, residual and original
250259
updatedEdgeVU = {
251260
node: t.node,
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weight: t.weight + bottleneck,
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};
263+
// update adj list of v and set to Gr's map
254264
const updatedList = [...listV];
255265
updatedList[i] = updatedEdgeVU;
256266
g.list.set(v, updatedList);
@@ -1052,22 +1062,22 @@ class Graph<T> {
10521062

10531063
// Returns the final Residual Graph
10541064
fordFulkerson = (s: T, t: T) => {
1065+
// Net flow must be a directed graph
10551066
if (!this.directed) return false;
10561067
const flow = new Map<T, Map<T, number>>();
1057-
// Initially f(e)=0 for all e in G
1058-
// for each edge of G f(u,v) = 0
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// Initially f(e)=0
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// for each edge(u,v) of G f(e) = 0
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for (let [u, vertexList] of this.list) {
10601071
flow.set(u, new Map<T, number>());
10611072
for (let v of vertexList) {
10621073
flow.get(u)!.set(v.node, 0);
10631074
}
10641075
}
10651076
let residualGraph: Graph<T> = this.createResidualGraph();
1066-
residualGraph.print();
10671077
let { exists, path } = this.augmentingPath(s, t, residualGraph);
10681078
// if there is no path between s - t return false
10691079
if (!exists || !path) return false;
1070-
1080+
// min val of flow that still can pass through
10711081
const bottleneck = this.bottleneck(path, residualGraph);
10721082
// while exists a path do augmenting path in Gr
10731083
while (exists) {

‎greedy/README.md

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@@ -19,3 +19,7 @@ I used a lot of references for each problem, in this section I will try to point
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- [Huffman coding Lecture](https://www.coursera.org/learn/algorithms-greedy/lecture/Jo6gK/a-greedy-algorithm)
2020
- [Algorithm Design 1st Edition](https://www.amazon.com/Algorithm-Design-Jon-Kleinberg/dp/0321295358)
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- [Introduction to Algorithms, 3rd Edition](https://www.amazon.com/Introduction-Algorithms-3rd-MIT-Press/dp/0262033844)
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- Ford-Fulkerson
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- [Ford-Fulkerson Algorithm Lectures](https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-046j-design-and-analysis-of-algorithms-spring-2015/lecture-videos/lecture-13-incremental-improvement-max-flow-min-cut/)
24+
- [Introduction to Algorithms, 3rd Edition](https://en.wikipedia.org/wiki/Introduction_to_Algorithms)
25+
- [Algorithm Design 1st Edition](https://www.amazon.com/Algorithm-Design-Jon-Kleinberg/dp/0321295358)

‎greedy/ford-fulkerson/exe.js

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@@ -8,8 +8,7 @@ const test = (file) => {
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const g = graph_1.default.createDirected(file, true, false);
99
const rg = g.fordFulkerson("s", "t");
1010
if (rg) {
11-
// console.log("LALALALALALALLA");
12-
// rg.print();
11+
rg.print();
1312
}
1413
};
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test("test.txt");

‎greedy/ford-fulkerson/exe.ts

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Original file line numberDiff line numberDiff line change
@@ -4,8 +4,7 @@ const test = (file: string) => {
44
const g = Graph.createDirected(file, true, false);
55
const rg = g.fordFulkerson("s", "t");
66
if (rg) {
7-
// console.log("LALALALALALALLA");
8-
// rg.print();
7+
rg.print();
98
}
109
};
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