From c96f6aa6992b97cd5d607da99803bd2c09fafbfe Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Tomasz=20P=C3=B3=C5=82grabia?=
 <tomasz.polgrabia@protonmail.com>
Date: Sat, 5 Mar 2022 17:10:14 +0100
Subject: [PATCH] Adding algorithms max flow.

---
 2022/03/algorithms/maxflow1.js     | 226 +++++++++++++++++++++++++++++
 2022/03/algorithms/maxflow1_01.txt |   8 +
 2 files changed, 234 insertions(+)
 create mode 100644 2022/03/algorithms/maxflow1.js
 create mode 100644 2022/03/algorithms/maxflow1_01.txt

diff --git a/2022/03/algorithms/maxflow1.js b/2022/03/algorithms/maxflow1.js
new file mode 100644
index 0000000..353b5da
--- /dev/null
+++ b/2022/03/algorithms/maxflow1.js
@@ -0,0 +1,226 @@
+"use strict";
+
+const fs = require('fs');
+const {EOL} = require('os');
+const eps = 1e-6;
+
+function increasingFlowPath(c, s, t) {
+	console.log(`Look for increasing flow path ${s} -> ${t}`);
+	let queue = [];
+	let processed = new Set();
+
+	queue.unshift(s);
+	processed.add(s);
+	let precedessor = {vi: null}; // i -> precedessor
+
+	while (queue.length) {
+		let vi = queue.pop();
+		if (vi === t) {
+			break;
+		}
+
+		for (let i = 0; i < c.length; i++) {
+			if (Math.abs(c[vi][i]) > eps && !processed.has(i)) {
+				precedessor[i] = vi;
+				queue.unshift(i);
+				processed.add(i);
+			}
+		}
+	}
+
+	if (!precedessor[t]) {
+		return {path: [], flow: 0};
+	}
+
+	let path = [];
+	let i = t;
+	path.push(t);
+	let flow = Infinity;
+	while (typeof(precedessor[i]) === 'number') {
+		console.log(`Precedessor ${i} is ${precedessor[i]}`);
+		flow = Math.min(flow, c[precedessor[i]][i]);
+		path.unshift(precedessor[i]);
+		i = precedessor[i];
+	}
+
+	return {path, flow};
+
+}
+
+function findMaximumFlow(graph) {
+	let nodes = [];
+	let m = {};
+	for (let el of graph.nodes) {
+		nodes.push(el);
+	}
+
+	for (let i = 0; i < nodes.length; i++) {
+		m[nodes[i]] = i;
+	}
+
+	const n = nodes.length;
+	let c = new Array(n);
+	let f = new Array(n);
+	for (let i = 0; i < n; i++) {
+		c[i] = new Array(n);
+		f[i] = new Array(n);
+	}
+
+	for (let i = 0; i < n; i++) {
+		for (let j = 0; j < n; j++) {
+			c[i][j] = 0;
+			f[i][j] = 0;
+		}
+	}
+
+	for (let v in graph.edges) {
+		for (let {node, weight} of graph.edges[v]) {
+			let vi = m[v]
+			let nodei = m[node];
+			c[vi][nodei] = weight;
+		}
+	}
+
+	console.log('C weights', c);
+
+	// let's find increasing flow path
+	let p, fl;
+	do {
+		let {path, flow} = increasingFlowPath(c, m[graph.source], m[graph.target]);
+		p = path;
+		fl = flow;
+		console.log(`Increasing flow ${flow} path ${path}`);	
+		if (path) {
+			// new increasing flow path
+			// f increase
+			// c decrease
+
+			for (let i = 1; i < path.length; i++) {
+				c[path[i-1]][path[i]] -= flow;
+				f[path[i-1]][path[i]] += flow;
+			}
+
+		}
+	} while (fl);
+
+	console.log(`Flow`, c);
+
+	let flow = 0;
+	for (let i = 0; i < nodes.length; i++) {
+		flow += f[m[graph.source]][i];
+	}
+
+	return flow;
+}
+
+function sourceCmdLine(ctx, cmdLine) {
+	ctx.source = cmdLine.slice(
+		'source'.length,
+		cmdLine.indexOf(';')
+	).trim();
+}
+
+function targetCmdLine(ctx, cmdLine) {
+	ctx.target = cmdLine.slice(
+		'target'.length,
+		cmdLine.indexOf(';')
+	).trim();
+}
+
+function edgeCmdLine(ctx, cmdLine) {
+	let edgeLine = cmdLine.slice(
+		'edge'.length,
+		cmdLine.indexOf(';')
+	).trim();
+	console.log(`Edge line ${edgeLine}`);
+
+	const matches = edgeLine.match(/^([a-zA-Z]*) -> ([a-zA-Z]*): ([0-9.]*)$/);
+	// console.log('Matches', matches);
+	const v = matches[1];
+	const z = matches[2];
+	const weight = Number.parseFloat(matches[3]);
+
+	console.log(`Parsed ${v} ->  ${z} : ${weight}`);
+
+	ctx.nodes.add(v);
+	ctx.nodes.add(z);
+	let targetEdges = ctx.edges[v] || [];
+	targetEdges.push({node: z, weight});
+	ctx.edges[v] = targetEdges;
+
+}
+
+function processCmdLine(ctx, cmdLine) {
+	console.log(`Processing command line ${cmdLine}`);
+	if (cmdLine.startsWith('source')) {
+		sourceCmdLine(ctx, cmdLine);
+	} else if (cmdLine.startsWith('target')) {
+		targetCmdLine(ctx, cmdLine);
+	} else if (cmdLine.startsWith('edge')) {
+		edgeCmdLine(ctx, cmdLine);
+	}
+}
+
+console.log(`Process argv: ${process.argv}`);
+
+const inputPath  = process.argv.length > 2 ? process.argv[2] : '-';
+const outputPath = process.argv.length > 3 ? process.argv[3] : '-';
+
+console.log(`Input path ${inputPath}, output path: ${outputPath}`);
+
+const inputStream = inputPath === '-' 
+	? process.stdin
+	: fs.createReadStream(inputPath);
+
+// const outputStream = outputPath === '-' 
+// 	? process.stdout
+//	: fs.createWriteStream(outputStream);
+
+let inputBuffer = "";
+let ctx = {
+	source: '',
+	target: '',
+	edges: {},
+	nodes: new Set()
+};
+
+function processChunk(chunk) {
+	inputBuffer += chunk;
+	console.log(`Chunk: ${chunk}`);
+	let eolIdx;
+	do {
+		eolIdx = inputBuffer.indexOf(EOL);
+		if (eolIdx < 0 && !chunk) {
+			eolIdx = inputBuffer.length;
+		}
+
+		let cmdLine = null;
+		if (eolIdx >= 0) {
+			console.log(`We got new line ${eolIdx}`);
+			cmdLine = inputBuffer.slice(0, eolIdx);
+			processCmdLine(ctx, cmdLine);
+			inputBuffer = inputBuffer.slice(eolIdx+EOL.length);
+		}
+	} while (eolIdx >= 0 && inputBuffer.length);
+}
+
+inputStream.on('data', (chunk) => {
+	processChunk(chunk);
+});
+
+inputStream.on('end', (chunk) => {
+	console.log(`end chunk ${chunk}`);
+	processChunk(chunk);
+	console.log('Got following graph', ctx);
+
+	for (let v in ctx.edges) {
+		for (let {node, weight} of ctx.edges[v]) {
+			console.log(`${v} ${node} : ${weight}`);
+		}
+	}
+
+	let mflow = findMaximumFlow(ctx);
+
+	console.log(`Maximum flow is ${mflow}`);
+
+});
diff --git a/2022/03/algorithms/maxflow1_01.txt b/2022/03/algorithms/maxflow1_01.txt
new file mode 100644
index 0000000..8ce4a48
--- /dev/null
+++ b/2022/03/algorithms/maxflow1_01.txt
@@ -0,0 +1,8 @@
+source s;
+target t;
+
+edge s -> u: 10;
+edge u -> t: 5;
+edge s -> v: 5;
+edge v -> t: 10;
+edge u -> v: 15;
\ No newline at end of file