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

#include "tests.h"

struct PHeapNode {
    int key;
    struct PHeapNode *parent;
    struct PHeapNode *left;
    struct PHeapNode *right;
    struct PHeapNode *children;
};

void phn_init(struct PHeapNode *phn, int key) {
    phn->key = key;
    phn->parent = NULL;
    phn->left = NULL;
    phn->right = NULL;
    phn->children = NULL;
}

static void phn_list_insert(struct PHeapNode **phn, struct PHeapNode *h) {
    if (*phn == NULL) {
        // list empty ==> h is only element now
        h->left = h;
        h->right = h;
        *phn = h;
    } else {
        // list not empty ==> insert at the end
        (*phn)->left->right = h;
        h->left = (*phn)->left;
        h->right = *phn;
        (*phn)->left = h;
    }
}

static void phn_list_remove(struct PHeapNode **phn, struct PHeapNode *h) {
    assert(*phn != NULL);

    if (h->left == h) {
        assert(h->right == h);
        // empty list
        *phn = NULL;
    } else {
        // rearrange pointers
        struct PHeapNode *tmp = h->left;
        h->left->right = h->right;
        h->right->left = tmp;

        if (*phn == h) {
            *phn = h->left;
        }
    }

    h->parent = NULL;
    h->left = NULL;
    h->right = NULL;
}

// returns a or b
struct PHeapNode *phn_union(struct PHeapNode *a, struct PHeapNode *b) {
    struct PHeapNode *min = a->key < b->key ? a : b;
    struct PHeapNode *max = a->key < b->key ? b : a;

    phn_list_insert(&min->children, max);
    return min;
}

struct PHeap {
    struct PHeapNode *roots;
    struct PHeapNode *min;
};

void ph_init(struct PHeap *ph) {
    ph->roots = NULL;
    ph->min = NULL;
}

void ph_print(struct PHeap *ph) {
    printf("roots: ");
    if (ph->roots != NULL) {
        struct PHeapNode *first = ph->roots;
        struct PHeapNode *curr = first;
        do {
            printf("--{%d}", curr->key);
            if (ph->min == curr) {
                printf("'");
            }
            curr = curr->right;
        } while (curr != first);
    }
    printf("--\n");
}

void ph_newtree(struct PHeap *ph, struct PHeapNode *h) {
    assert(h->parent == NULL);

    phn_list_insert(&ph->roots, h);
    if (ph->min == NULL || h->key < ph->min->key) {
        ph->min = h;
    }
}

void ph_insert_malloc(struct PHeap *ph, int key) {
    struct PHeapNode *h = malloc(sizeof(struct PHeapNode));
    phn_init(h, key);
    ph_newtree(ph, h);
}

struct PHeapNode *ph_deletemin(struct PHeap *ph) {
    if (ph->min == NULL) {
        return NULL;
    }

    struct PHeapNode *m = ph->min;

    // forest := forest \ {m}
    phn_list_remove(&ph->roots, m);
    ph->min = NULL;

    // foreach child h of m do newTree(h)
    while (m->children != NULL) {
        struct PHeapNode *curr = m->children;
        phn_list_remove(&m->children, m->children);
        ph_newtree(ph, curr);
    }

    // perform pair-wise union operations on the roots in forest
    // update minPtr
    if (ph->roots != NULL) {
        struct PHeapNode *new_roots = NULL;

        while (ph->roots != NULL && ph->roots->right != ph->roots) {
            // while two elements are available:
            struct PHeapNode *a = ph->roots;
            struct PHeapNode *b = ph->roots->right;
            phn_list_remove(&ph->roots, a);
            phn_list_remove(&ph->roots, b);

            a = phn_union(a, b);
            phn_list_insert(&new_roots, a);
            if (ph->min == NULL || a->key < ph->min->key) {
                ph->min = a;
            }
        }

        if (ph->roots != NULL) {
            // another element remains
            struct PHeapNode *last = ph->roots;
            phn_list_remove(&ph->roots, last);
            phn_list_insert(&new_roots, last);
            if (ph->min == NULL || last->key < ph->min->key) {
                ph->min = last;
            }
        }

        assert(ph->roots == NULL);
        ph->roots = new_roots;
    }

    return m;
}

void ph_deinit_free(struct PHeap *ph) {
    while (ph->min != NULL) {
        struct PHeapNode *h = ph_deletemin(ph);
        free(h);
    }
}

int cmp_int(const void *a, const void *b) {
    return *((int *) a) - *((int *) b);
}

int main() {
    TEST("consecutive deleteMin calls yield increasing results", {
        srand(2309);
    
        struct PHeap ph;
        ph_init(&ph);

        for (int i = 0; i < 1000; i++) {
            ph_insert_malloc(&ph, rand());
        }

        int max = INT_MIN;
        while (ph.min != NULL) {
            struct PHeapNode *h = ph_deletemin(&ph);
            ASSERT(h->key >= max);
            max = h->key;
            free(h);
        }

        ph_deinit_free(&ph);
    })

    TEST("deleteMin yields the same order as qsort", {
        srand(2309);

        struct PHeap ph;
        ph_init(&ph);

        int n = 1000;
        int xs[n];

        for (int i = 0; i < n; i++) {
            xs[i] = rand();
            ph_insert_malloc(&ph, xs[i]);
        }

        qsort(xs, n, sizeof(int), cmp_int);

        for (int i = 0; i < n; i++) {
            struct PHeapNode *h = ph_deletemin(&ph);
            ASSERT(h->key == xs[i]);
            free(h);
        }
        ASSERT(ph.min == NULL);

        ph_deinit_free(&ph);
    })

    DONE
}