归并排序
思想是分治
将排序好的两部分进行合并
注意：最后需要将temp[]数组重新赋值回arr
import java.util.*;
public class Main{
static Scanner sc = new Scanner(System.in);
static int N = 100010;
static int[] arr = new int[N];
static int[] temp = new int[N];
public static void merge_sort(int[] arr, int l, int r){
if(l >= r) return;
int mid = (l+r) >> 1;
merge_sort(arr,l,mid);
merge_sort(arr,mid+1,r);
int i = l, j = mid+1;
int k = 0;
while(i <= mid && j <= r){
if(arr[i] <= arr[j]) temp[k++] = arr[i++];
else temp[k++] = arr[j++];
}
while(i <= mid) temp[k++] = arr[i++];
while(j <= r) temp[k++] = arr[j++];
for(i = l, j = 0; i <= r; i++,j++) arr[i] = temp[j];
}
public static void main(String[] args){
int n = sc.nextInt();
for(int i = 0; i < n; i++) arr[i] = sc.nextInt();
merge_sort(arr,0,n-1);
for(int i = 0; i < n; i++) System.out.print(arr[i] + " ");
}
}
求逆序对板子
关键在于合并的时候统计逆序对
while(i <= mid && j <= r){
if(arr[i] <= arr[j]) temp[k++] = arr[i++];
else{
res += mid - i + 1;
temp[k++] = arr[j++];
}
}
import java.util.*;
public class Main{
static Scanner sc = new Scanner(System.in);
static int N = 100010;
static int[] arr = new int[N];
static int[] temp = new int[N];
public static void main(String[] args){
int n = sc.nextInt();
for(int i = 0; i < n; i++) arr[i] = sc.nextInt();
System.out.print(merge_sort(0,n-1));
}
public static long merge_sort(int l ,int r){
if(l >= r) return 0;
int mid = l + r >> 1;
long res = merge_sort(l,mid) + merge_sort(mid+1,r);
int k = 0, i = l, j = mid + 1;
while(i <= mid && j <= r){
if(arr[i] <= arr[j]) temp[k++] = arr[i++];
else{
res += mid - i + 1;
temp[k++] = arr[j++];
}
}
while(i <= mid) temp[k++] = arr[i++];
while(j <= r) temp[k++] = arr[j++];
//恢复
for(i = l, j = 0; i <= r; i++,j++) arr[i] = temp[j];
return res;
}
}