3.1 分治法介绍及关键点解析_哔哩哔哩_bilibili

分治：分解 解决 合并

快速排序

        单向扫描分区法

public static void main(String[] args) {// TODO Auto-generated method stubint[] arr = {1,6,3,6,2,8,6,1,0,7};quickSort1(arr,0,arr.length-1);for(int i:arr) {System.out.println(i);}}public static void quickSort1(int[] arr,int idx1,int idx2) {if(idx1<idx2) {int q = partition(arr,idx1,idx2);quickSort1(arr,idx1,q-1);quickSort1(arr,q+1,idx2);}	}public static int partition(int[] arr,int idx1,int idx2) {int pivot = arr[idx1];int l = idx1+1;int r = idx2;int temp;while(l<=r) {if(arr[l]<pivot)l++;else{temp = arr[l];arr[l]=arr[r];arr[r]=temp;r--;}			}temp = arr[idx1];arr[idx1] = arr[r];arr[r] = temp;return r;}

        双向扫描分区法

public static int partition2(int[] arr,int idx1,int idx2) {int pivot = arr[idx1];int l = idx1+1;int r = idx2;int temp;while(l<=r) {while(l<=r&&arr[l]<=pivot)l++;while(l<=r&&arr[r]>pivot)r--;if(l<r) {temp = arr[l];arr[l] = arr[r];arr[r] = temp;}			}temp = arr[idx1];arr[idx1] = arr[r];arr[r] = temp;return r;}

快速排序的优化

        三点中值法 （在p r mid之间，选一个中间值作为pivot）

        绝对中值法

        待排序列表较短时，用插入排序

归并排序 Merge Sort

public class Solution3_1 {private static int[] helper;public static void main(String[] args) {int[] arr = {10,2,7,3,19,11,1,6,8,4,13};sort(arr);for(int i=0;i<arr.length;i++){System.out.println(arr[i]);}}public static void sort(int[] arr){helper = new int[arr.length];mergeSort(arr,0,arr.length-1);}private static void mergeSort(int[] arr,int low, int high){if(low<high){int mid = low + ((high - low)>>1);mergeSort(arr,low,mid);mergeSort(arr,mid+1,high);merge(arr,low,mid,high);}}public static void merge(int[] arr, int low,int mid,int high){System.arraycopy(arr,low,helper,low,high-low+1);int left = low,right = mid +1;int cur = low;while(left<=mid&&right<=high){if(helper[left]<=helper[right]){arr[cur++]=helper[left++];}else{arr[cur++]=helper[right++];}}while(left<=mid){arr[cur++]=helper[left++];}}
}

题1：调整数组顺序使奇数位于偶数前面（O(n)）

public static void main(String[] args) {int[] arr={1,2,3,4,5,6,7,8,9,10};int[] helper = new int[arr.length];System.arraycopy(arr,0,helper,0,arr.length-1);int p=0;for(int i=0;i<arr.length;i++){if(helper[i]%2==1){arr[p++]=helper[i];}}for(int i=0;i<arr.length;i++){if(helper[i]%2==0){arr[p++]=helper[i];}}for(int i=0;i<arr.length;i++){System.out.println(arr[i]);}}

  题2：第k个元素（第k大的元素）

public class Solution3_3 {public static void main(String[] args) {int[] arr = {1,5,2,4,3,6,9,8,7};int k = 7;System.out.println(getK(arr,k,0,arr.length-1));}public static int getK(int[] arr,int k,int idx1,int idx2){int q = partition(arr,idx1,idx2);int qK = q-idx1+1;//pivot是第几个元素if(qK==k) {return arr[q];}else if(qK>k){return getK(arr,k,idx1,q-1);}else{return getK(arr,k-qK,q+1,idx2);}}public static int partition(int[] arr,int idx1,int idx2){int pivot = arr[idx1];int l = idx1+1;int r = idx2;int temp;while(l<=r) {while(l<=r&&arr[l]<=pivot)l++;while(l<=r&&arr[r]>pivot)r--;if(l<r) {temp = arr[l];arr[l] = arr[r];arr[r] = temp;}}temp = arr[idx1];arr[idx1] = arr[r];arr[r] = temp;return r;}
}

题3：超过一半的数字

        排序后位置在下标n/2的元素

public static void main(String[] args) {int[] arr = {6,7,7,7,8,8,8,8,8,8};Arrays.sort(arr);System.out.println(arr[arr.length/2]);}

题3扩展：寻找发帖水王

public static int getCandidate(int[] arr){int candidate = arr[0];int nTimes = 1;for(int i=0;i<arr.length;i++){if(nTimes==0){candidate = arr[i];nTimes = 1;continue;}if(arr[i]==candidate){nTimes++;}else{nTimes--;}}return candidate;}

  题4：最小可用id

public class Solution3_5 {public static void main(String[] args) {int[] arr = {10,2,3,4,6,7,8,1};System.out.println(getMinId(arr,0,arr.length-1));}public static int getMinId(int[] arr,int low,int high){if(low>=high)return Math.max(low,high)+1;int q = partition(arr,low,high);if(arr[q]==q+1){return getMinId(arr,q+1,high);}else{return getMinId(arr,low,q);}}public static int partition(int[] arr,int low,int high){int pivot = arr[low];int l = low+1;int r = high;int temp;while(l<=r){if(arr[l]<pivot){l++;}else{temp = arr[l];arr[l] = arr[r];arr[r--] = temp;}}temp = arr[low];arr[low] = arr[r];arr[r] = temp;return r;}
}

题5：合并有序数组

题6：逆序对个数

树和二叉树

        树的遍历 先序遍历 中序遍历 后序遍历

        数组的先序遍历

    public static void preOrder(int[] arr,int i){if(i>=arr.length){return;}System.out.println(arr[i]);preOrder(arr,i*2+1);preOrder(arr,i*2+2);}

堆 

        完全二叉树 近似完全二叉树

        大顶堆 小顶堆

堆排序

        堆化 反向调整使得每个子树都是大顶堆或者小顶堆

        按序输出元素 把堆顶和最末元素对调 然后调整堆顶元素

计数排序

        用辅助数组对数组中出现的数字计数 元素转下标 下标转元素