經典演算法——合併K個有序連結串列
阿新 • • 發佈：2019-01-02
一、題目要求：
將K個有序連結串列合併為一個有序連結串列
二、實現方法：
方法一：利用最小堆方法
用一個大小為K的最小堆（用優先佇列+自定義降序實現）(優先佇列就是大頂堆，隊頭元素最大,自定義為降序後，就變成小頂堆，隊頭元素最小)，先把K個連結串列的頭結點放入堆中，每次取堆頂元素，然後將堆頂元素所在連結串列的下一個結點加入堆中。
整體測試程式碼：
#include <vector> #include <iostream> #include<queue> #include<set> #include <functional> // std::greater using namespace std; struct ListNode { int val; ListNode* next; }; struct cmp { bool operator()(ListNode* a, ListNode* b) { return a->val > b->val; } }; //方法一：利用最小堆方法 //用一個大小為K的最小堆（用優先佇列+自定義降序實現）(優先佇列就是大頂堆，隊頭元素最大,自定義為降序後，就變成小頂堆，隊頭元素最小)， //先把K個連結串列的頭結點放入堆中，每次取堆頂元素，然後將堆頂元素所在連結串列的下一個結點加入堆中。 ListNode* mergeKLists2(vector<ListNode*> lists) { if (lists.size() == 0) return NULL; priority_queue<int, vector<ListNode*>, cmp> heap; for (int i = 0; i < lists.size(); ++i) { heap.push(lists[i]); } ListNode* newHead=NULL; ListNode* p=NULL; ListNode* q=NULL; while (!heap.empty()) { q = heap.top(); heap.pop(); if (q->next != NULL) heap.push(q->next); if (newHead == NULL) { newHead = q; p = q; } else { p->next = q; p = p->next; } } return newHead; } ListNode* CreateListNode(int value) { ListNode* pNode = new ListNode(); pNode->val = value; pNode->next = NULL; return pNode; } void DestroyList(ListNode* pHead) { ListNode* pNode = pHead; while (pNode != NULL) { pHead = pHead->next; delete pNode; pNode = pHead; } } void ConnectListNodes(ListNode* pCurrent, ListNode* pNext) { if (pCurrent == NULL) { printf("Error to connect two nodes.\n"); exit(1); } pCurrent->next = pNext; } int main() { vector<ListNode*> lists; ListNode* pNode1 = CreateListNode(1); ListNode* pNode2 = CreateListNode(2); ListNode* pNode3 = CreateListNode(3); ListNode* pNode4 = CreateListNode(4); ListNode* pNode5 = CreateListNode(2); ListNode* pNode6 = CreateListNode(3); ListNode* pNode7 = CreateListNode(4); ListNode* pNode8 = CreateListNode(5); ListNode* pNode9 = CreateListNode(6); ListNode* pNode10 = CreateListNode(7); ListNode* pNode11 = CreateListNode(8); ListNode* pNode12 = CreateListNode(9); ConnectListNodes(pNode1, pNode2); ConnectListNodes(pNode2, pNode3); ConnectListNodes(pNode3, pNode4); ConnectListNodes(pNode5, pNode6); ConnectListNodes(pNode6, pNode7); ConnectListNodes(pNode7, pNode8); ConnectListNodes(pNode9, pNode10); ConnectListNodes(pNode10, pNode11); ConnectListNodes(pNode11, pNode12); ListNode* L1 = pNode1; ListNode* L2 = pNode5; ListNode* L3 = pNode9; cout << "連結串列l1： "; while (L1) { cout << L1->val << " "; L1 = L1->next; } cout << endl; cout << "連結串列l2： "; while (L2) { cout << L2->val << " "; L2 = L2->next; } cout << endl; cout << "連結串列l3： "; while (L3) { cout << L3->val << " "; L3 = L3->next; } cout << endl; lists.push_back(pNode1); lists.push_back(pNode5); lists.push_back(pNode9); ListNode* res = mergeKLists2(lists); cout << "合併後連結串列： "; while (res) { cout << res->val << " "; res = res->next; } cout << endl; system("pause"); DestroyList(res); return 0; }
方法二：分治法
利用歸併排序的思想，利用遞迴和分治法將連結串列陣列劃分成為越來越小的半連結串列陣列，再對半連結串列陣列排序，最後再用遞迴步驟將排好序的半連結串列數組合併成為越來越大的有序連結串列。
整體測試程式碼：
#include <iostream> #include <vector> using namespace std; struct ListNode { int val; ListNode* next; }; //方法二：分治法 //利用歸併排序的思想，利用遞迴和分治法將連結串列陣列劃分成為越來越小的半連結串列陣列， //再對半連結串列陣列排序，最後再用遞迴步驟將排好序的半連結串列數組合併成為越來越大的有序連結串列 ListNode* mergeKLists(vector<ListNode*> lists, int K) { return mergeLists(lists, 0, K); } ListNode* mergeLists(vector<ListNode*> listNodes, int low, int high) { if (low == high) return NULL; if (high - low == 1) return listNodes[low]; if (high - low == 2) return merge2(listNodes[low], listNodes[high - 1]); int mid = (high + low) / 2; ListNode* a = mergeLists(listNodes, low, mid); ListNode* b = mergeLists(listNodes, mid, high); return merge2(a, b); } ListNode* merge2(ListNode* L1, ListNode* L2) { if (L1 == NULL && L2 == NULL) return NULL; else if (L1 == NULL) return L2; else if (L2 == NULL) return L1; ListNode* newHead = NULL; ListNode* p = NULL; if (L1->val < L2->val){ newHead = L1; p = L1; L1 = L1->next; } else{ newHead = L2; p = L2; L2 = L2->next; } while (L1 != NULL && L2 != NULL) { if (L1->val < L2->val) { p->next = L1; L1 = L1->next; } else { p->next = L2; L2 = L2->next; } p = p->next; } p->next = L1 ? L1 : L2; return newHead; } ListNode* CreateListNode(int value) { ListNode* pNode = new ListNode(); pNode->val = value; pNode->next = NULL; return pNode; } void DestroyList(ListNode* pHead) { ListNode* pNode = pHead; while (pNode != NULL) { pHead = pHead->next; delete pNode; pNode = pHead; } } void ConnectListNodes(ListNode* pCurrent, ListNode* pNext) { if (pCurrent == NULL) { printf("Error to connect two nodes.\n"); exit(1); } pCurrent->next = pNext; } int main() { vector<ListNode*> lists; ListNode* pNode1 = CreateListNode(1); ListNode* pNode2 = CreateListNode(2); ListNode* pNode3 = CreateListNode(3); ListNode* pNode4 = CreateListNode(4); ListNode* pNode5 = CreateListNode(2); ListNode* pNode6 = CreateListNode(3); ListNode* pNode7 = CreateListNode(4); ListNode* pNode8 = CreateListNode(5); ListNode* pNode9 = CreateListNode(6); ListNode* pNode10 = CreateListNode(7); ListNode* pNode11 = CreateListNode(8); ListNode* pNode12 = CreateListNode(9); ConnectListNodes(pNode1, pNode2); ConnectListNodes(pNode2, pNode3); ConnectListNodes(pNode3, pNode4); ConnectListNodes(pNode5, pNode6); ConnectListNodes(pNode6, pNode7); ConnectListNodes(pNode7, pNode8); ConnectListNodes(pNode9, pNode10); ConnectListNodes(pNode10, pNode11); ConnectListNodes(pNode11, pNode12); ListNode* L1 = pNode1; ListNode* L2 = pNode5; ListNode* L3 = pNode9; cout << "連結串列l1： "; while (L1) { cout << L1->val << " "; L1 = L1->next; } cout << endl; cout << "連結串列l2： "; while (L2) { cout << L2->val << " "; L2 = L2->next; } cout << endl; cout << "連結串列l3： "; while (L3) { cout << L3->val << " "; L3 = L3->next; } cout << endl; lists.push_back(pNode1); lists.push_back(pNode5); lists.push_back(pNode9); ListNode* res = mergeKLists(lists, 3); cout << "合併後連結串列： "; while (res) { cout << res->val << " "; res = res->next; } cout << endl; system("pause"); DestroyList(res); return 0; }
