package algs64; // section 6.4
import stdlib.*;
import algs13.Queue;
/* ***********************************************************************
 *  Compilation:  javac FordFulkerson.java
 *  Execution:    java FordFulkerson V E
 *  Dependencies: FlowNetwork.java FlowEdge.java Queue.java
 *
 *  Ford-Fulkerson algorithm for computing a max flow and
 *  a min cut using shortest augmenthing path rule.
 *
 *********************************************************************/

public class FordFulkerson {
	private boolean[] marked;     // marked[v] = true iff s->v path in residual graph
	private FlowEdge[] edgeTo;    // edgeTo[v] = last edge on shortest residual s->v path
	private double value;         // current value of max flow

	// max flow in flow network G from s to t
	public FordFulkerson(FlowNetwork G, int s, int t) {
		if (s < 0 || s >= G.V()) {
			throw new IndexOutOfBoundsException("Source s is invalid: " + s);
		}
		if (t < 0 || t >= G.V()) {
			throw new IndexOutOfBoundsException("Sink t is invalid: " + t);
		}
		if (s == t) {
			throw new IllegalArgumentException("Source equals sink");
		}
		value = excess(G, t);
		if (!isFeasible(G, s, t)) {
			throw new Error("Initial flow is infeasible");
		}

		// while there exists an augmenting path, use it
		while (hasAugmentingPath(G, s, t)) {

			// compute bottleneck capacity
			double bottle = Double.POSITIVE_INFINITY;
			for (int v = t; v != s; v = edgeTo[v].other(v)) {
				bottle = Math.min(bottle, edgeTo[v].residualCapacityTo(v));
			}

			// augment flow
			for (int v = t; v != s; v = edgeTo[v].other(v)) {
				edgeTo[v].addResidualFlowTo(v, bottle);
			}

			value += bottle;
		}

		// check optimality conditions
		assert check(G, s, t);
	}

	// return value of max flow
	public double value()  {
		return value;
	}

	// is v in the s side of the min s-t cut?
	public boolean inCut(int v)  {
		return marked[v];
	}


	// return an augmenting path if one exists, otherwise return null
	private boolean hasAugmentingPath(FlowNetwork G, int s, int t) {
		edgeTo = new FlowEdge[G.V()];
		marked = new boolean[G.V()];

		// breadth-first search
		Queue<Integer> q = new Queue<>();
		q.enqueue(s);
		marked[s] = true;
		while (!q.isEmpty()) {
			int v = q.dequeue();

			for (FlowEdge e : G.adj(v)) {
				int w = e.other(v);

				// if residual capacity from v to w
				if (e.residualCapacityTo(w) > 0) {
					if (!marked[w]) {
						edgeTo[w] = e;
						marked[w] = true;
						q.enqueue(w);
					}
				}
			}
		}

		// is there an augmenting path?
		return marked[t];
	}



	// return excess flow at vertex v
	private double excess(FlowNetwork G, int v) {
		double excess = 0.0;
		for (FlowEdge e : G.adj(v)) {
			if (v == e.from()) excess -= e.flow();
			else               excess += e.flow();
		}
		return excess;
	}

	// return excess flow at vertex v
	private boolean isFeasible(FlowNetwork G, int s, int t) {
		double EPSILON = 1E-11;

		// check that capacity constraints are satisfied
		for (int v = 0; v < G.V(); v++) {
			for (FlowEdge e : G.adj(v)) {
				if (e.flow() < -EPSILON || e.flow() > e.capacity() + EPSILON) {
					System.err.println("Edge does not satisfy capacity constraints: " + e);
					return false;
				}
			}
		}

		// check that net flow into a vertex equals zero, except at source and sink
		if (Math.abs(value + excess(G, s)) > EPSILON) {
			System.err.println("Excess at source = " + excess(G, s));
			System.err.println("Max flow         = " + value);
			return false;
		}
		if (Math.abs(value - excess(G, t)) > EPSILON) {
			System.err.println("Excess at sink   = " + excess(G, t));
			System.err.println("Max flow         = " + value);
			return false;
		}
		for (int v = 0; v < G.V(); v++) {
			if (v == s || v == t) continue;
			else if (Math.abs(excess(G, v)) > EPSILON) {
				System.err.println("Net flow out of " + v + " doesn't equal zero");
				return false;
			}
		}
		return true;
	}



	// check optimality conditions
	private boolean check(FlowNetwork G, int s, int t) {

		// check that flow is feasible
		if (!isFeasible(G, s, t)) {
			System.err.println("Flow is infeasible");
			return false;
		}

		// check that s is on the source side of min cut and that t is not on source side
		if (!inCut(s)) {
			System.err.println("source " + s + " is not on source side of min cut");
			return false;
		}
		if (inCut(t)) {
			System.err.println("sink " + t + " is on source side of min cut");
			return false;
		}

		// check that value of min cut = value of max flow
		double mincutValue = 0.0;
		for (int v = 0; v < G.V(); v++) {
			for (FlowEdge e : G.adj(v)) {
				if ((v == e.from()) && inCut(e.from()) && !inCut(e.to()))
					mincutValue += e.capacity();
			}
		}

		double EPSILON = 1E-11;
		if (Math.abs(mincutValue - value) > EPSILON) {
			System.err.println("Max flow value = " + value + ", min cut value = " + mincutValue);
			return false;
		}

		return true;
	}


	// test client that creates random network, solves max flow, and prints results
	public static void main(String[] args) {

		// create flow network with V vertices and E edges
		int V = Integer.parseInt(args[0]);
		int E = Integer.parseInt(args[1]);
		int s = 0, t = V-1;
		FlowNetwork G = new FlowNetwork(V, E);
		StdOut.println(G);

		// compute maximum flow and minimum cut
		FordFulkerson maxflow = new FordFulkerson(G, s, t);
		StdOut.println("Max flow from " + s + " to " + t);
		for (int v = 0; v < G.V(); v++) {
			for (FlowEdge e : G.adj(v)) {
				if ((v == e.from()) && e.flow() > 0)
					StdOut.println("   " + e);
			}
		}

		// print min-cut
		StdOut.print("Min cut: ");
		for (int v = 0; v < G.V(); v++) {
			if (maxflow.inCut(v)) StdOut.print(v + " ");
		}
		StdOut.println();

		StdOut.println("Max flow value = " +  maxflow.value());
	}

}