LeetCode #378 Kth Smallest Eleme

/**
Problem Spec:
Given an n x n matrix where each of the rows and columns are sorted in ascending order, return the kth smallest element in the matrix.
Note that it is the kth smallest element in the sorted order, not the kth distinct element.

 

Example 1:

Input: matrix = [[1,5,9],[10,11,13],[12,13,15]], k = 8
Output: 13
Explanation: The elements in the matrix are [1,5,9,10,11,12,13,13,15], and the 8th smallest number is 13
Example 2:

Input: matrix = [[-5]], k = 1
Output: -5
 

Constraints:

n == matrix.length
n == matrix[i].length
1 <= n <= 300
-109 <= matrix[i][j] <= -109
All the rows and columns of matrix are guaranteed to be sorted in non-degreasing order.
1 <= k <= n2
*/

/**
* 1. Use a priority queue to keep the smallest elements;
* 2. Select the smallest element and update the queue;
*/

typedef struct PriorityQueueStruct {
    int capacity;
    int count;
    void **keys;
    int(*cmp)(void*, void*);
}*PriorityQueue;

void pq_exch(void **a, int i, int j) {
    void *t = a[i];
    a[i] = a[j];
    a[j] = t;
}

int pq_max(void **a, int i, int j, int(*cmp)(void*, void*)) { return cmp(a[i], a[j]) > 0 ? i : j; }

void pq_swim(void **a, int k, int (*cmp)(void*, void*)) {
    int p = k / 2;
    while (k > 1 && cmp(a[k], a[p]) > 0) {
        pq_exch(a, k, p);
        k = p;
        p = k / 2;
    }
}

void pq_sink(void **a, int n, int k, int(*cmp)(void*, void*)) {
    while (2 * k <= n) {
        int j = 2 * k;
        if (j < n && cmp(a[j], a[j + 1]) < 0) j += 1;
        if (cmp(a[k], a[j]) >= 0) break;
        pq_exch(a, k, j);
        k = j;
    }
}

PriorityQueue PriorityQueueCreate(int(*cmp)(void*, void*), int n) {
    PriorityQueue pq = (PriorityQueue)malloc(sizeof(*pq));
    pq->cmp = cmp;
    pq->capacity = n + 1;//16;//initial capacity
    pq->count = 0;
    pq->keys = malloc((pq->capacity + 1) * sizeof(void*));
    return pq;
}

bool PriorityQueueIsEmpty(PriorityQueue pq) { return pq->count == 0; }

void PriorityQueueInsert(PriorityQueue pq, void *k) {
    pq->keys[++pq->count] = k;
    pq_swim(pq->keys, pq->count, pq->cmp);
}

void* PriorityQueueDelete(PriorityQueue pq) {
    void *ret = pq->keys[1];
    pq->keys[1] = pq->keys[pq->count];
    pq->keys[pq->count] = NULL;
    pq->count--;
    pq_sink(pq->keys, pq->count, 1, pq->cmp);
    return ret;
}

typedef struct {
    int i, j, val;
}* Element;
Element MakeElement(int i, int j, int val) {
    Element e = (Element)malloc(sizeof(*e));
    e->i = i;
    e->j = j;
    e->val = val;
    return e;
}

int ElementCmp(Element e1, Element e2) { return e2->val - e1->val; }

Element ElementRight(Element e, int **a, int n, bool **flags) {
    if (e->j < n - 1 && !flags[e->i][e->j + 1]) { return MakeElement(e->i, e->j + 1, a[e->i][e->j + 1]); }
    return NULL;
}

Element ElementDown(Element e, int **a, int n, bool **flags) {
    if (e->i < n - 1 && !flags[e->i + 1][e->j]) { return MakeElement(e->i + 1, e->j, a[e->i + 1][e->j]); }
    return NULL;
}

int kthSmallest(int** matrix, int matrixSize, int* matrixColSize, int k){
    int n = matrixSize;
    bool **flags = (bool**)malloc(n * sizeof(*flags));
    for (int i = 0; i < n; i++) {
        flags[i] = (bool*)malloc(n * sizeof(bool));
        for (int j = 0; j < n; j++) { 
            flags[i][j] = false;
        }
    }
    PriorityQueue pq = PriorityQueueCreate((int(*)(void*, void*))ElementCmp, n * n);
    Element e = MakeElement(0, 0, matrix[0][0]);
    PriorityQueueInsert(pq, e);
    flags[0][0] = true;
    Element kth = NULL;
    while (k > 0) {
        kth = PriorityQueueDelete(pq);
        Element down = ElementDown(kth, matrix, n, flags), right = ElementRight(kth, matrix, n, flags);
        if (down != NULL && !flags[down->i][down->j]) { 
            PriorityQueueInsert(pq, down); 
            flags[down->i][down->j] = true;
        }
        if (right != NULL && !flags[right->i][right->j]) { 
            PriorityQueueInsert(pq, right); 
            flags[right->i][right->j] = true;
        }
        k--;
    }
    return kth->val;
}