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Heap(힙) a.k.a Priority Queue(우선순위 큐)

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Heap(힙)이란?

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왜 a.k.a Priority Queue(우선순위 큐)?

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linked list 구현 vs. linear list(array) 구현

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Heap(힙) 구현

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    insert(data) = 삽입 : data를 heap의 마지막에 삽입 후 부모 노드와 대소 비교를 한다. 부모 노드보다 크면 (min heap : 작으면) data를 swap을 하고 부모 노드보다 작으면 (min heap : 크면) 현재 위치를 유지한다. root까지 반복한다.

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    withdraw() = 삭제 : root 노드의 data를 꺼내고, heap의 마지막 원소를 root로 올린 후 자식 노드와 대소 비교를 한다. 자식 노드보다 작으면 (혹은 min heap : 크면) swap을 하고 자식 노드보다 크면 (min heap : 작으면) 현재 위치를 유지한다. leaf node(단말 노드)까지 반복한다. 자식 노드가 2개일 시 두 노드의 대소 비교 후 큰 (min heap : 작은) 자식 노드를 대소 비교에 쓴다.

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    현재 위치 = idx
    \n부모 노드 = idx / 2
    \n왼쪽 자식 노드 = idx * 2
    \n오른쪽 자식 노드 = idx * 2 + 1

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Max Heap 구현 코드 (C++)

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#include <iostream>\n\ntemplate <typename T>\nclass Max_Heap {\nprivate:\n\tT* data_arr;\n\tint size;\n\tint num_data;\n\t\npublic:\n\tMax_Heap(int size = 1000) : data_arr(new T[size]), size(size), num_data(0) {}\n\t\n\t~Max_Heap() {delete[] data_arr;}\n\t\n\tvoid insert(T data) {\n\t\t++num_data;\n\t\t\n\t\tif (num_data == 1) // no data before\n\t\t\tdata_arr[1] = data;\n\t\telse { // at least one data exist\n\t\t\tdata_arr[num_data] = data;\n\t\t\tint parent_idx = num_data / 2;\n\t\t\tint child_idx = num_data;\n\t\t\t\n\t\t\tdo {\n\t\t\t\tif (data_arr[child_idx] < data_arr[parent_idx])\n\t\t\t\t\tbreak;\n\t\t\t\telse {\n\t\t\t\t\tstd::swap(data_arr[child_idx], data_arr[parent_idx]);\n\t\t\t\t\tchild_idx = parent_idx;\n\t\t\t\t\tparent_idx = child_idx / 2;\n\t\t\t\t}\n\t\t\t} while (parent_idx >= 1);\n\t\t}\n\t}\n\t\n\tT withdraw() {\n\t\tif (num_data == 0) // no data before\n\t\t\treturn -1; // error code (up to data-type)\n\t\telse { // at least one data exist\n\t\t\tT return_data = data_arr[1];\n\t\t\t\n\t\t\tif (num_data == 1) // only root data exists\n\t\t\t\tdata_arr[1] = 0;\n\t\t\telse {\n\t\t\t\tdata_arr[1] = data_arr[num_data];\n\t\t\t\tdata_arr[num_data] = 0;\n\t\t\t\t\n\t\t\t\tint idx = 1; // root\n\t\t\t\t\n\t\t\t\twhile (data_arr[idx*2] != 0 || data_arr[idx*2+1] != 0) { // until leaf node\n\t\t\t\t\tif (data_arr[idx*2] == 0 || data_arr[idx*2+1] == 0) { // only one child exists\n\t\t\t\t\t\tif(data_arr[idx*2]) { // left child exists\n\t\t\t\t\t\t\tif (data_arr[idx] < data_arr[idx*2]) { // current node < left child\n\t\t\t\t\t\t\t\tstd::swap(data_arr[idx], data_arr[idx*2]);\n\t\t\t\t\t\t\t\tidx *= 2;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse if(data_arr[idx*2+1]) { // right child exists\n\t\t\t\t\t\t\tif (data_arr[idx] < data_arr[idx*2+1]) { // current node < right child\n\t\t\t\t\t\t\t\tstd::swap(data_arr[idx], data_arr[idx*2+1]);\n\t\t\t\t\t\t\t\tidx = idx * 2 + 1;\n\t\t\t\t\t\t\t} \n\t\t\t\t\t\t\telse\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t\telse { // both children exist\n\t\t\t\t\t\tif (data_arr[idx*2] > data_arr[idx*2+1] && data_arr[idx] < data_arr[idx*2]) { // left child > right child && current node < left child\n\t\t\t\t\t\t\tstd::swap(data_arr[idx], data_arr[idx*2]);\n\t\t\t\t\t\t\tidx *= 2;\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse if (data_arr[idx*2] < data_arr[idx*2+1] && data_arr[idx] < data_arr[idx*2+1]) { // left child < right child && current node < right child\n\t\t\t\t\t\t\tstd::swap(data_arr[idx], data_arr[idx*2+1]);\n\t\t\t\t\t\t\tidx = idx * 2 + 1;\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t\t\n\t\t\t--num_data;\n\t\t\t\n\t\t\treturn return_data;\n\t\t}\n\t}\n\n\tfriend std::ostream& operator <<(std::ostream &out, Max_Heap &heap){\n\t\tT *temp = heap.data_arr;\n\t\tint power = 1;\n\t\t\n\t\t\n\t\tout << \"──────────────────────────────────\" << std::endl;\n\t\t\n\t\tfor (int i = 1; i <= heap.num_data; ++i) {\n\t\t\tstd::cout << temp[i];\n\t\t\tif (i == std::pow(2, power) - 1) {\n\t\t\t\tstd::cout << '\\n';\n\t\t\t\t++power;\n\t\t\t}\n\t\t}\n\t\tif (heap.num_data != std::pow(2, power-1) - 1)\n\t\t\tstd::cout << '\\n';\n\t\t\n\t\tout << \"──────────────────────────────────\" << std::endl;\n\t\t\n\t\treturn out;\n\t}\n};\n\nint main() {\n\tstd::ios::sync_with_stdio(false);\n\tstd::cin.tie(NULL); \n\tstd::cout.tie(NULL);\n\t\n\tMax_Heap<int> heap(1000);\n\t\n\theap.insert(9);\n\tstd::cout << heap << std::endl;\n\t\n\theap.insert(5);\n\tstd::cout << heap << std::endl;\n\t\n\theap.insert(1);\n\tstd::cout << heap << std::endl;\n\t\n\tstd::cout << heap.withdraw() << std::endl;\n\tstd::cout << heap << std::endl;\n\tstd::cout << heap.withdraw() << std::endl;\n\tstd::cout << heap << std::endl;\n\tstd::cout << heap.withdraw() << std::endl;\n\tstd::cout << heap << std::endl;\n\n\treturn 0;\n}
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Min Heap 구현 코드 (C++)

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#include <iostream>\n\ntemplate <typename T>\nclass Min_Heap {\nprivate:\n\tT* data_arr;\n\tint size;\n\tint num_data;\n\t\npublic:\n\tMin_Heap(int size = 1000) : data_arr(new T[size]), size(size), num_data(0) {}\n\t\n\t~Min_Heap() {delete[] data_arr;}\n\t\n\tvoid insert(T data) {\n\t\t++num_data;\n\t\t\n\t\tif (num_data == 1) // no data before\n\t\t\tdata_arr[1] = data;\n\t\telse { // at least one data exist\n\t\t\tdata_arr[num_data] = data;\n\t\t\tint parent_idx = num_data / 2;\n\t\t\tint child_idx = num_data;\n\t\t\t\n\t\t\tdo {\n\t\t\t\tif (data_arr[child_idx] > data_arr[parent_idx])\n\t\t\t\t\tbreak;\n\t\t\t\telse {\n\t\t\t\t\tstd::swap(data_arr[child_idx], data_arr[parent_idx]);\n\t\t\t\t\tchild_idx = parent_idx;\n\t\t\t\t\tparent_idx = child_idx / 2;\n\t\t\t\t}\n\t\t\t} while (parent_idx >= 1);\n\t\t}\n\t}\n\t\n\tT withdraw() {\n\t\tif (num_data == 0) // no data before\n\t\t\treturn -1; // error code (up to data-type)\n\t\telse { // at least one data exist\n\t\t\tT return_data = data_arr[1];\n\t\t\t\n\t\t\tif (num_data == 1) // only root exists\n\t\t\t\tdata_arr[1] = 0;\n\t\t\telse {\n\t\t\t\tdata_arr[1] = data_arr[num_data];\n\t\t\t\tdata_arr[num_data] = 0;\n\t\t\t\t\n\t\t\t\tint idx = 1; // root index\n\t\t\t\t\n\t\t\t\twhile (data_arr[idx*2] != 0 || data_arr[idx*2+1] != 0) { // until leaf node\n\t\t\t\t\tif (data_arr[idx*2] == 0 || data_arr[idx*2+1] == 0) { // only one child exists\n\t\t\t\t\t\tif(data_arr[idx*2]) { // left child exists\n\t\t\t\t\t\t\tif (data_arr[idx] > data_arr[idx*2]) { // current node > left child\n\t\t\t\t\t\t\t\tstd::swap(data_arr[idx], data_arr[idx*2]);\n\t\t\t\t\t\t\t\tidx *= 2;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse if(data_arr[idx*2+1]) { // right child exists\n\t\t\t\t\t\t\tif (data_arr[idx] < data_arr[idx*2+1]) { // current node > right child\n\t\t\t\t\t\t\t\tstd::swap(data_arr[idx], data_arr[idx*2+1]);\n\t\t\t\t\t\t\t\tidx = idx * 2 + 1;\n\t\t\t\t\t\t\t} \n\t\t\t\t\t\t\telse\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t\telse { // both children exist\n\t\t\t\t\t\tif (data_arr[idx*2] < data_arr[idx*2+1] && data_arr[idx] > data_arr[idx*2]) { // left child < right child && current node > left child\n\t\t\t\t\t\t\tstd::swap(data_arr[idx], data_arr[idx*2]);\n\t\t\t\t\t\t\tidx *= 2;\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse if (data_arr[idx*2] > data_arr[idx*2+1] && data_arr[idx] > data_arr[idx*2+1]) { // left child > right child && current node > right child\n\t\t\t\t\t\t\tstd::swap(data_arr[idx], data_arr[idx*2+1]);\n\t\t\t\t\t\t\tidx = idx * 2 + 1;\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t\t\n\t\t\t--num_data;\n\t\t\t\n\t\t\treturn return_data;\n\t\t}\n\t}\n\n\tfriend std::ostream& operator <<(std::ostream &out, Min_Heap &heap){\n\t\tT *temp = heap.data_arr;\n\t\tint power = 1;\n\t\t\n\t\t\n\t\tout << \"──────────────────────────────────\" << std::endl;\n\t\t\n\t\tfor (int i = 1; i <= heap.num_data; ++i) {\n\t\t\tstd::cout << temp[i];\n\t\t\tif (i == std::pow(2, power) - 1) {\n\t\t\t\tstd::cout << '\\n';\n\t\t\t\t++power;\n\t\t\t}\n\t\t}\n\t\tif (heap.num_data != std::pow(2, power-1) - 1)\n\t\t\tstd::cout << '\\n';\n\t\t\n\t\tout << \"──────────────────────────────────\" << std::endl;\n\t\t\n\t\treturn out;\n\t}\n};\n\n\nint main() {\n\tstd::ios::sync_with_stdio(false);\n\tstd::cin.tie(NULL); \n\tstd::cout.tie(NULL);\n\t\n\tMin_Heap<int> heap(1000);\n\t\n\theap.insert(9);\n\tstd::cout << heap << std::endl;\n\t\n\theap.insert(5);\n\tstd::cout << heap << std::endl;\n\t\n\theap.insert(1);\n\tstd::cout << heap << std::endl;\n\t\n\tstd::cout << heap.withdraw() << std::endl;\n\tstd::cout << heap << std::endl;\n\tstd::cout << heap.withdraw() << std::endl;\n\tstd::cout << heap << std::endl;\n\tstd::cout << heap.withdraw() << std::endl;\n\tstd::cout << heap << std::endl;\n\n\treturn 0;\n}
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References

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https://velog.io/@pa324/%EC%9A%B0%EC%84%A0%EC%88%9C%EC%9C%84-%ED%81%90-1xk1cw46t2
\nhttps://www.crocus.co.kr/379
\nhttps://medium.com/jiwon-bae/data-structure-%EC%9A%B0%EC%84%A0%EC%88%9C%EC%9C%84-%ED%81%90%EC%99%80-%ED%9E%99-c01947539d3d
\nhttps://ohdumak.tistory.com/75

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