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Copy pathCount Inversion Sort
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Count Inversion Sort
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//count the inversion in a given array while sorting
#include<iostream>
using namespace std;
long long merge (int arr[],int l, int mid,int r){
long long inv =0;
int n1=mid-l+1;
int n2=r-mid;
int a[n1];
int b[n2]; //we are making two temporary array as we have to compare two values and then inputing the lower value
for(int i=0;i<n1;i++){
a[i]=arr[l+i]; //as our indexing start with leftmost value of original array
}
for(int i=0;i<n2;i++){
b[i]=arr[mid+1+i]; //as our indexing start with mid+1 value of original array
}
int i=0;
int j=0;
int k=l;//our indexinging will start with leftmost value
while(i<n1 && j<n2){
if(a[i]<b[j]){
arr[k]=a[i];
k++;
i++; //no inversion as a[i]<b[j]
}
else{
arr[k]=b[j];
inv = inv + n1-i; //n1-i as a[i+1],a[i+2]... and so on are greater than b[j] //major catch
k++;
j++; //inversion as a[i]>b[j]
}
}
while(i<n1){
arr[k]=a[i];
k++;
i++;
}
while(j<n2){
arr[k]=b[j];
k++;
j++;
}
return inv;
}
long long mergeSort(int arr[],int l,int r){
long long inv =0;
if(r>l){
int mid=(l+r)/2;
inv += mergeSort(arr,l,mid); //inversion in left side
inv += mergeSort(arr,mid+1,r); //inversion in right side
inv += merge(arr,l,mid,r); //inversion while merging
}
return inv;
}
int main(){
int n ;
cout<<"Enter size of array ";
cin>>n;
int arr[n];
cout<<"Enter values of array ";
for(int i=0;i<n;i++){
cin>>arr[i];
}
//brut force approach
int inv=0;
for(int i=0;i<n;i++){
for(int j=i+1;j<n;j++){
if(arr[i]>arr[j]){
inv++;
}
}
}
cout<<inv<<endl;//time complexity of order o(n^2)
//optimise approach
cout<<(mergeSort(arr,0,n));
return 0;
}