分治：分解 解决 合并
快速排序
单向扫描分区法
java
public static void main(String[] args) {
// TODO Auto-generated method stub
int[] 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
java
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
java
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)）
java
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）
java
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
java
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
java
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
java
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
java
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