/*    netflow.c

      Network flow implementation -- Ford-Fulkerson augmenting path algorithm.
*/

/* Copyright 2003-2020 by Steven S. Skiena; all rights reserved.
Permission is granted for use in non-commerical applications
provided this copyright notice remains intact and unchanged.

These programs appear in my books:

"The Algorithm Design Manual" by Steven Skiena, second edition, Springer,
London 2008.  See out website www.algorist.com for additional information
or https://www.amazon.com/exec/obidos/ASIN/1848000693/thealgorith01-20

"Programming Challenges: The Programming Contest Training Manual"
by Steven Skiena and Miguel Revilla, Springer-Verlag, New York 2003.
See our website www.programming-challenges.com for additional information,
or https://www.amazon.com/exec/obidos/ASIN/0387001638/thealgorithmrepo/
*/



#include <stdio.h>
#include <stdlib.h>

#include <stdbool.h>
#include "geometry.h"
#include "queue.h"

#define MAXV         100    /* maximum number of vertices */
#define MAXDEGREE    50     /* maximum outdegree of a vertex */

/* [[[ netflow_edgenode_cut */
typedef struct {
    int v;                  /* neighboring vertex */
    int capacity;           /* capacity of edge */
    int flow;               /* flow through edge */
    int residual;           /* residual capacity of edge */
    struct edgenode *next;  /* next edge in list */
} edgenode;
/* ]]] */

typedef struct {
    edgenode *edges[MAXV+1];    /* adjacency info */
    int degree[MAXV+1];         /* outdegree of each vertex */
    int nvertices;              /* number of vertices in the graph */
    int nedges;                 /* number of edges in the graph */
} flow_graph;

void initialize_graph(flow_graph *g) { /* graph to initialize */
    int i;    /* counter */

    g->nvertices = 0;
    g->nedges = 0;

    for (i = 0; i < MAXV; i++) {
        g->degree[i] = 0;
    }

    for (i = 0; i < MAXV; i++) {
        g->edges[i] = NULL;
    }
}

void insert_flow_edge(flow_graph *g, int x, int y, bool directed, int w) {
    edgenode *p;    /* temporary pointer */

    p = malloc(sizeof(edgenode));   /* allocate storage for edgenode */

    p->v = y;
    p->capacity = w;
    p->flow = 0;
    p->residual = w;
    p->next = (struct edgenode*)g->edges[x];

    g->edges[x] = p;                /* insert at head of list */
    g->degree[x] ++;

    if (!directed) {
        insert_flow_edge(g, y, x, true, w);
    } else {
        g->nedges++;
    }
}

void read_flow_graph(flow_graph *g, bool directed) { /* graph to initialize */    /* is this graph directed? */
    int i;        /* counter */
    int m;        /* number of edges */
    int x, y, w;  /* placeholder for edge and weight */

    initialize_graph(g);

    scanf("%d %d\n", &(g->nvertices), &m);

    for (i = 1; i <= m; i++) {
        scanf("%d %d %d\n", &x, &y, &w);
        insert_flow_edge(g, x, y, directed, w);
    }
}

/* [[[ netflow_fedge_cut */
edgenode *find_edge(flow_graph *g, int x, int y) {
    edgenode *p;    /* temporary pointer */

    p = g->edges[x];

    while (p != NULL) {
        if (p->v == y) {
            return(p);
        }
        p = (edgenode*)p->next;
    }

    return(NULL);
}
/* ]]] */

void add_residual_edges(flow_graph *g) {
    int i;       /* counter */
    edgenode *p; /* temporary pointer */

    for (i = 1; i <= g->nvertices; i++) {
        p = g->edges[i];
        while (p != NULL) {
            if (find_edge(g, p->v, i) == NULL) {
                insert_flow_edge(g, p->v, i, true, 0);
            }
            p = (edgenode*)p->next;
        }
    }
}

void print_flow_graph(flow_graph *g) {
    int i;                          /* counter */
    edgenode *p;                    /* temporary pointer */

    for (i = 1; i <= g->nvertices; i++) {
        printf("%d: ", i);
        p = g->edges[i];
        while (p != NULL) {
            printf(" %d(%d,%d,%d)",p->v, p->capacity, p->flow, p->residual);
            p = (edgenode*)p->next;
        }
        printf("\n");
    }
}

bool processed[MAXV+1];    /* which vertices have been processed */
bool discovered[MAXV+1];   /* which vertices have been found */
int parent[MAXV+1];        /* discovery relation */

bool finished = false;     /* if true, cut off search immediately */

void initialize_search(flow_graph *g) {  /* graph to traverse */
    int i;                               /* counter */

    for (i = 1; i <= g->nvertices; i++) {
        processed[i] = false;
        discovered[i] = false;
        parent[i] = -1;
    }
}

void process_vertex_early(int v) {  /* vertex to process */

}

void process_vertex_late(int v) {   /* vertex to process */

}

void process_edge(int x, int y) {   /* edge to process */

}

/* [[[ netflow_vedge_cut */
bool valid_edge(edgenode *e) {
    return (e->residual > 0);
}
/* ]]] */

void bfs(flow_graph *g, int start) {
    queue q;                        /* queue of vertices to visit */
    int v;                          /* current vertex */
    int y;                          /* successor vertex */
    edgenode *p;                    /* temporary pointer */

    init_queue(&q);
    enqueue(&q, start);
    discovered[start] = true;

    while (!empty_queue(&q)) {
        v = dequeue(&q);
        process_vertex_early(v);
        processed[v] = true;
        p = g->edges[v];
        while (p != NULL) {
            y = p->v;
            if (valid_edge(p)) {
                if (!processed[y]) {
                    process_edge(v, y);
                }

                if (!discovered[y]) {
                    enqueue(&q, y);
                    discovered[y] = true;
                    parent[y] = v;
                }
            }
            p = (edgenode*)p->next;
        }
        process_vertex_late(v);
    }
}

void find_path(int start, int end, int parents[]) {
    if ((start == end) || (end == -1)) {
        printf("\n%d",start);
    } else {
        find_path(start, parents[end], parents);
        printf(" %d", end);
    }
}

/* [[[ path_volume_cut */
int path_volume(flow_graph *g, int start, int end) {
    edgenode *e;    /* edge in question */

    if (parent[end] == -1) {
        return(0);
    }

    e = find_edge(g, parent[end], end);

    if (start == parent[end]) {
        return(e->residual);
    } else {
        return(min(path_volume(g, start, parent[end]), e->residual));
    }
}
/* ]]] */

/* [[[ augment_path_cut */
void augment_path(flow_graph *g, int start, int end, int volume) {
    edgenode *e;    /* edge in question */

    if (start == end) {
        return;
    }

    e = find_edge(g, parent[end], end);
    e->flow += volume;
    e->residual -= volume;
    
    e = find_edge(g, end, parent[end]);
    e->residual += volume;

    augment_path(g, start, parent[end], volume);
}
/* ]]] */

/* [[[ netflow_cut */
void netflow(flow_graph *g, int source, int sink) {
    int volume;    /* weight of the augmenting path */

    add_residual_edges(g);

    initialize_search(g);
    bfs(g, source);

    volume = path_volume(g, source, sink);

    while (volume > 0) {
        augment_path(g, source, sink, volume);
        initialize_search(g);
        bfs(g, source);
        volume = path_volume(g, source, sink);
    }
}
/* ]]] */

int main(void) {
    flow_graph g;        /* graph to analyze */
    int source, sink;    /* source and sink vertices */
    int flow;            /* total flow */
    edgenode *p;         /* temporary pointer */

    scanf("%d %d", &source, &sink);
    read_flow_graph(&g, true);

    netflow(&g, source, sink);

    print_flow_graph(&g);

    flow = 0;
    p = g.edges[source];
    while (p != NULL) {
        flow += p->flow;
        p = (edgenode*)p->next;
    }

    printf("total flow = %d\n", flow);

    return 0;
}