歸并排序

特點：非原址排序，比較排序，時間復雜度O（nlgn）
穩定

// // Created by 許加權 on 2021/6/18. //#include <iostream> void merge_sort(int *arr,int start,int end) {if(start < end){int middle = (start + end)/2;merge_sort(arr,start,middle);merge_sort(arr,middle+1,end);int *left_arr = new int[middle - start + 2];int *right_arr = new int[end - start + 2];for (int i = start; i < middle+1; ++i) {left_arr[i-start] = arr[i];}left_arr[middle-start+1] = INT_MAX;for(int i = middle+1;i<end+1;i++){right_arr[i-middle-1]= arr[i];}right_arr[end - middle] = INT_MAX;int left =0,right = 0;for (int i = start; i < end+1; ++i) {if(left_arr[left]<right_arr[right]){arr[i] = left_arr[left];left++;}else{arr[i] = right_arr[right];right++;}}delete [] left_arr;delete [] right_arr;} }void show(int *arr,int length) {for(int i=0;i<length;i++){std::cout<<arr[i]<<" ";}std::cout<<std::endl; }int main() {int arr[] = {1,4,6,9,2,5,10,3,7};show(arr,sizeof(arr)/sizeof (int));merge_sort(arr,0,sizeof(arr)/sizeof (int)-1);show(arr,sizeof(arr)/sizeof (int)); }

內涵插入排序的歸并排序
時間復雜度
Θ(nk+nlg(n/k))
k取lgn

void merge(int *arr,int start,int end,int middle) {int *left_arr = new int[middle - start + 2];int *right_arr = new int[end - start + 2];for (int i = start; i < middle+1; ++i) {left_arr[i-start] = arr[i];}left_arr[middle-start+1] = INT_MAX;for(int i = middle+1;i<end+1;i++){right_arr[i-middle-1]= arr[i];}right_arr[end - middle] = INT_MAX;int left =0,right = 0;for (int i = start; i < end+1; ++i) {if(left_arr[left]<right_arr[right]){arr[i] = left_arr[left];left++;}else{arr[i] = right_arr[right];right++;}}delete [] left_arr;delete [] right_arr; } void merge_sort_internal_insertion(int *arr,int start,int end,int k) {if(end - start + 1> k){int middle = (start + end)/2;merge_sort_internal_insertion(arr,start,middle,k);merge_sort_internal_insertion(arr,middle+1,end,k);merge(arr,start,end,middle);}else{insertion_sort(arr,start,end);} }

內部插入排序代碼地址：插入排序

案例：利用歸并排序的原理，求逆序對的個數：
代碼地址

總結

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