八大排序算法总结（2）
归并排序；
如下图所示，为数组 [7, 3, 2, 6, 0, 1, 5, 4][7,3,2,6,0,1,5,4] 的归并排序过程。
1 //merge sort 2 public static void merge(int[] a,int aux[],int lo ,int mid,int hi ){ 3 int i = lo; 4 int j = mid+1; 5 //copy a 6 for (int k = lo; k <= hi; k++) 7 aux[k] = a[k]; 8 //merge 9 for(int k = lo;k<=hi;k++){ 10 //先判断是否越界 11 if(i>mid) a[k]=aux[j++]; 12 else if(j>hi) a[k]=aux[i++]; 13 // merge 14 else if(aux[j]<=aux[i]) a[k]=aux[j++]; 15 else a[k]=aux[i++]; 16 } 17 } 18 public static void mergesort(int[] a,int aux[],int lo,int hi) { 19 //边界条件 20 if(lo>=hi) return ; 21 int mid = (hi-lo)/2+lo; 22 mergesort(a,aux, lo, mid); 23 mergesort(a,aux, mid+1, hi); 24 merge(a,aux, lo, mid, hi); 25 26 } 27 public static void mergeSort(int[] a){ 28 int aux[] = new int[a.length]; 29 mergesort(a,aux, 0, a.length-1); 30 }
class Solution: def sortArray(self, nums: List[int]) -> List[int]: def merge(nums,aux,l,m,r): i = l j = m k = l while i < m and j < r : if aux[i] < aux[j]: nums[k] = aux[i] i+=1 k+=1 else: nums[k] = aux[j] j+=1 k+=1 while i < m : nums[k] = aux[i] i+=1 k+=1 while j < r : nums[k] = aux[j] j+=1 k+=1 aux[l:r] = nums[l:r] def merge_sort(nums,aux,l,r): if l>=r-1 : return m = l + int((r-l)/2) merge_sort(nums,aux,l,m) merge_sort(nums,aux,m,r) merge(nums,aux,l,m,r) aux = nums.copy() merge_sort(nums,aux,0,len(nums)) return aux
void merge(vector<int>& nums,int low, int mid, int high){ int l_start = low; int l_end = mid; int r_start = mid + 1; int r_end = high; int k = low; vector<int> aux = vector<int>(nums); while(l_start <= l_end && r_start <= r_end) aux[k++] = nums[l_start]<nums[r_start]?nums[l_start++]:nums[r_start++]; while(l_start <= l_end) aux[k++] = nums[l_start++]; while(r_start <= r_end) aux[k++] = nums[r_start++]; //把数据复制回原数组 for(int i = low; i <= high; ++i) { nums[i] = aux[i]; } }; void merge_and_sort(vector<int>& nums,int low,int high) { if (low>=high) return; int mid = low + (high - low) / 2; merge_and_sort(nums,low,mid); merge_and_sort(nums,mid+1,high); merge(nums,low,mid,high); }; void mergeSort(vector<int>& nums) { merge_and_sort(nums,0,nums.size()-1); };
快速排序
class Solution: def sortArray(self, nums: List[int]) -> List[int]: def partition(nums,l,r): pivot = nums[l] i = l+1 j = r while i <= j: if nums[i] < pivot < nums[j]: nums[i],nums[j] = nums[j],nums[i] i+=1 j-=1 if nums[i] >= pivot: i+=1 if nums[j] <= pivot: j-=1 nums[j],nums[l] = nums[l],nums[j] return j def quick_sort(nums,l,r): if l>r : return j = partition(nums,l,r) quick_sort(nums,l,j-1) quick_sort(nums,j+1,r) random.shuffle(nums) quick_sort(nums,0,len(nums)-1) return nums[::-1]
215. 数组中的第K个最大元素(快排，堆排序)
int partition(vector<int>& nums, int left, int right) { int pivot = nums[left], i = left + 1, j = right; while (i <= j) { if (nums[i] < pivot && pivot < nums[j] ) { swap(nums[i++], nums[j--]); } if (nums[i] >= pivot) { i++; } if (pivot >= nums[j]) { j--; } } swap(nums[left], nums[j]); return j; } void partation_and_sort(vector<int>& nums, int low ,int high) { if (low>=high) return; int j = partation(nums,low,high); cout << j << endl; partation_and_sort(nums,low,j); partation_and_sort(nums,j+1,high); } void quickSort(vector<int>& nums) { partation_and_sort(nums,0,nums.size()-1); }
堆排序
215. 数组中的第K个最大元素(快排，堆排序)
class Solution: def sortArray(self, nums: List[int]) -> List[int]: def max_heapfiy(nums,l,r): dad = l son = dad*2+1 while son <= r: if son+1 <= r and nums[son] > nums[son+1]: son+=1 if nums[dad] < nums[son]: return else: nums[son],nums[dad] = nums[dad],nums[son] dad = son son = dad*2+1 n = len(nums) for i in range(0,n//2)[::-1]: max_heapfiy(nums,i,n-1) for i in range(1,n)[::-1]: nums[i],nums[0] = nums[0],nums[i] max_heapfiy(nums,0,i-1) return nums[::-1]
#include <iostream> #include <algorithm> using namespace std; void max_heapify(int arr[], int start, int end) { //建立父节点指标和子节点指标 int dad = start; int son = dad * 2 + 1; while (son <= end) //若子节点指标在范围内才做比较 { if (son + 1 <= end && arr[son] < arr[son + 1]) //先比较两个子节点大小，选择最大的 son++; if (arr[dad] > arr[son]) //如果父节点大於子节点代表调整完毕，直接跳出函数 return; else //否则交换父子内容再继续子节点和孙节点比较 { swap(arr[dad], arr[son]); dad = son; son = dad * 2 + 1; } } } void heap_sort(int arr[], int len) { //初始化，i从最後一个父节点开始调整 for (int i = len / 2 - 1; i >= 0; i--) max_heapify(arr, i, len - 1); //先将第一个元素和已经排好的元素前一位做交换，再从新调整(刚调整的元素之前的元素)，直到排序完毕 for (int i = len - 1; i > 0; i--) { swap(arr[0], arr[i]); max_heapify(arr, 0, i - 1); } } void main() { int arr[] = { 3, 5, 3, 0, 8, 6, 1, 5, 8, 6, 2, 4, 9, 4, 7, 0, 1, 8, 9, 7, 3, 1, 2, 5, 9, 7, 4, 0, 2, 6 }; int len = (int) sizeof(arr) / sizeof(*arr); heap_sort(arr, len); for (int i = 0; i < len; i++) cout << arr[i] << ' '; cout << endl; system("pause"); }
