cKit/Graph/c_Bipartite.c

#include <c_Bipartite.h>

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


// Internal deep structural validation walker checking color partitions
static void c_Bipartite_DFS_Internal(c_Bipartite_t* self, const c_Graph_t* G, c_VertexId_t v) {
    self->marked[v] = C_TRUE;

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

    // 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];

        // Short-circuit search operations if an odd cycle has already been populated
        if (self->cycle.size > 0) return;

        if (!self->marked[w]) {
            self->edge_to[w] = v;
            self->color[w] = !self->color[v]; // Assign alternative inverted color mapping
            c_Bipartite_DFS_Internal(self, G, w);
        }
        // If neighbor w is already marked and shares the same color, an odd cycle is confirmed
        else if (self->color[w] == self->color[v]) {
            self->is_bipartite = C_FALSE;

            // Reconstruct the odd-length cycle path using back-tracing loops
            c_VertexIdList_t temp_stack;
            if (c_VertexIdList_Init(&temp_stack, 8, &self->allocator) != C_SUCCESS) return;

            c_size_t x = v;
            while (x != w && x != G->V) {
                c_VertexIdList_Append(&temp_stack, (c_uint_t)x);
                x = self->edge_to[x];
            }
            c_VertexIdList_Append(&temp_stack, (c_uint_t)w);
            c_VertexIdList_Append(&temp_stack, (c_uint_t)v); // Close cycle track frame

            // Invert elements to maintain correct chronological routing direction
            for (c_size_t j = temp_stack.size; j > 0; j--) {
                c_uint_t val;
                c_VertexIdList_Get(&temp_stack, j - 1, &val);
                c_VertexIdList_Append(&self->cycle, val);
            }

            c_VertexIdList_Destroy(&temp_stack);
            return;
        }
    }
}

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


c_err_t c_Bipartite_Init(c_Bipartite_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_UIntArray_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_Bipartite_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 definition

    // Scan all clusters within graph partitions sequentially
    for (c_VertexId_t v = 0; v < G->V; v++) {
        if (!self->marked[v]) {
            self->color[v] = C_FALSE; // Default baseline color option setting
            c_Bipartite_DFS_Internal(self, G, v);
        }
    }

    return C_SUCCESS;
}

void c_Bipartite_Destroy(c_Bipartite_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_UIntArray_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_Bipartite_IsBipartite(const c_Bipartite_t* self) {
    return self ? self->is_bipartite : C_FALSE;
}

c_bool_t c_Bipartite_Color(const c_Bipartite_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_Bipartite_Cycle(const c_Bipartite_t* self) {
    return self ? &self->cycle : NULL;
}