cKit/Graph/c_BipartiteBFS.c

#include <c_BipartiteBFS.h>

/* ------------------------------------------------------------------------------------------------------------------ */
/*  */

// Internal BFS helper routine to process a single connected component cluster
static void c_Bipartite_BFS_Internal(c_BipartiteBFS_t* self, const c_Graph_t* G, c_VertexId_t start) {
    // We will use your c_VertexIdList_t dynamic array as an explicit FIFO queue block.
    // To pop, we track a sliding 'head' cursor instead of physically shifting items.
    c_VertexIdList_t queue;
    if (c_VertexIdList_Init(&queue, 16, &self->allocator) != C_SUCCESS) return;

    self->marked[start] = C_TRUE;
    self->color[start] = C_FALSE; // Initialize base level color assignment
    if (c_VertexIdList_Append(&queue, (c_uint_t)start) != C_SUCCESS) {
        c_VertexIdList_Destroy(&queue);
        return;
    }

    c_size_t queue_head = 0;

    while (queue_head < queue.size) {
        // Dequeue structural element
        c_VertexId_t v = (c_VertexId_t)queue.array[queue_head++];

        c_AdjList_t* list = c_Graph_GetAdjList((c_Graph_t*)G, v);
        if (!list) continue;

        // Cache-friendly sequential sweep over flat neighbor array blocks
        for (c_size_t i = 0; i < list->size; i++) {
            c_VertexId_t w = (c_VertexId_t)list->array[i];

            if (!self->marked[w]) {
                self->marked[w] = C_TRUE;
                self->edge_to[w] = v;
                self->color[w] = !self->color[v]; // Assign opposite color inversion mapping
                if (c_VertexIdList_Append(&queue, (c_uint_t)w) != C_SUCCESS) {
                    c_VertexIdList_Destroy(&queue);
                    return;
                }
            }
            // If neighbor w is discovered and has the same color, we've found an odd-length cycle!
            else if (self->color[w] == self->color[v]) {
                self->is_bipartite = C_FALSE;

                // Reconstruct the shortest odd-length cycle by back-tracing paths from v and w
                // back to their lowest common ancestor (LCA) using edge_to coordinates.
                c_VertexIdList_t path_v;
                c_VertexIdList_t path_w;
                if (c_VertexIdList_Init(&path_v, 8, &self->allocator) != C_SUCCESS) goto cleanup;
                if (c_VertexIdList_Init(&path_w, 8, &self->allocator) != C_SUCCESS) {
                    c_VertexIdList_Destroy(&path_v);
                    goto cleanup;
                }

                // Trace back route frames from v
                c_size_t curr = v;
                while (curr != G->V) {
                    c_VertexIdList_Append(&path_v, (c_uint_t)curr);
                    curr = self->edge_to[curr];
                }

                // Trace back route frames from w
                curr = w;
                while (curr != G->V) {
                    c_VertexIdList_Append(&path_w, (c_uint_t)curr);
                    curr = self->edge_to[curr];
                }

                // Find lowest common ancestor intersection boundary index
                c_size_t p_v = path_v.size - 1;
                c_size_t p_w = path_w.size - 1;
                while (p_v > 0 && p_w > 0 && path_v.array[p_v - 1] == path_w.array[p_w - 1]) {
                    p_v--;
                    p_w--;
                }

                // Build output sequence path layout out to self->cycle container:
                // Format order flow: v -> ... -> LCA -> ... -> w -> v
                for (c_size_t j = 0; j <= p_v; j++) {
                    c_VertexIdList_Append(&self->cycle, path_v.array[j]);
                }
                for (c_size_t j = p_w; j > 0; j--) {
                    c_VertexIdList_Append(&self->cycle, path_w.array[j - 1]);
                }
                c_VertexIdList_Append(&self->cycle, (c_uint_t)v); // Close cycle loop boundary

                c_VertexIdList_Destroy(&path_v);
                c_VertexIdList_Destroy(&path_w);
                c_VertexIdList_Destroy(&queue);
                return;
            }
        }
    }

cleanup:
    c_VertexIdList_Destroy(&queue);
}

c_err_t c_BipartiteBFS_Init(c_BipartiteBFS_t* self, const c_Graph_t* G, c_Allocator_t* allocator) {
    if (!self || !G) return C_ERR_PARAM;

    self->allocator = allocator?*allocator:c_DefaultAllocator;
    self->is_bipartite = C_TRUE;
    self->V = G->V;
    self->marked = NULL;
    self->color = NULL;
    self->edge_to = NULL;

    if (c_VertexIdList_Init(&self->cycle, 0, &self->allocator) != C_SUCCESS) {
        return C_ERR_NOMEM;
    }

    if (G->V == 0) return C_SUCCESS;

    self->marked = (c_bool_t*)c_Allocator_Alloc(&self->allocator, G->V * sizeof(*self->marked));
    self->color = (c_bool_t*)c_Allocator_Alloc(&self->allocator, G->V * sizeof(*self->color));
    self->edge_to = (c_size_t*)c_Allocator_Alloc(&self->allocator, G->V * sizeof(*self->edge_to));

    if (!self->marked || !self->color || !self->edge_to) {
        c_BipartiteBFS_Destroy(self);
        return C_ERR_NOMEM;
    }

    memset(self->marked, 0, G->V * sizeof(*self->marked));
    memset(self->color, 0, G->V * sizeof(*self->color));
    for (c_size_t i = 0; i < G->V; i++) self->edge_to[i] = G->V; // Sentinel setting

    // Multi-component partition loop scanner sweeps
    for (c_VertexId_t v = 0; v < G->V; v++) {
        if (!self->marked[v]) {
            c_Bipartite_BFS_Internal(self, G, v);
            if (!self->is_bipartite) break; // Terminate early on odd cycle detection
        }
    }

    return C_SUCCESS;
}

void c_BipartiteBFS_Destroy(c_BipartiteBFS_t* self) {
    if (!self) return;

    if (self->marked) c_Allocator_Free(&self->allocator, self->marked);
    if (self->color)  c_Allocator_Free(&self->allocator, self->color);
    if (self->edge_to) c_Allocator_Free(&self->allocator, self->edge_to);

    c_VertexIdList_Destroy(&self->cycle);

    self->marked = NULL;
    self->color = NULL;
    self->edge_to = NULL;
    self->is_bipartite = C_FALSE;
    self->V = 0;
}

c_bool_t c_BipartiteBFS_IsBipartite(const c_BipartiteBFS_t* self) {
    return self ? self->is_bipartite : C_FALSE;
}

c_bool_t c_BipartiteBFS_Color(const c_BipartiteBFS_t* self, c_VertexId_t v) {
    if (!self || v >= self->V || !self->color) return C_FALSE;
    return self->color[v];
}

const c_VertexIdList_t* c_BipartiteBFS_Cycle(const c_BipartiteBFS_t* self) {
    return self ? &self->cycle : NULL;
}