#include<bits/stdc++.h>
using namespace std;
int merge(int a[],int st,int mid,int end)
{
int inv=0;
int temp[end-st+1];
int l=0;
int i=st;
int j=mid+1;
while(i<=mid && j<=end)
{
if(a[i]<a[j])
{
temp[l++]=a[i++];
}
else
{
temp[l++]=a[j++];
inv+=(mid-i+1);
}
}
while(i<=mid)
temp[l++]=a[i++];
while(j<=end)
temp[l++]=a[j++];
for(i=0;i<l;i++)
a[st+i]=temp[i];
return inv;
}
int countInversions(int a[],int st,int end)
{
int inv=0;
if(st<end)
{
int mid=(st+end)/2;
inv=countInversions(a,st,mid);
inv+=countInversions(a,mid+1,end);
inv+=merge(a,st,mid,end);
}
return inv;
}
int main()
{
int n,i;
cin>>n;
int a[n];
for(i=0;i<n;i++)
cin>>a[i];
cout<<countInversions(a,0,n-1);
}
Time Complexity:- O(nlogn)
Please upvote if you found this solution useful and comment for any doubts.
Can i please get help with problem 3? please, if possible, answer in a text format....
Recall the problem of ¯nding the number of inversions. As in the text, we are given asequence of numbers a1; : : : ; an, which we assume are all distinct, and we de¯ne an inversionto be a pair i < j such that ai > aj .We motivated the problem of counting inversions as a good measure of how di®erent twoorderings are. However, one might feel that this measure is two sensitive. Let's call a pair asigni¯cant inversion if...
ALGORITHM PROBLEM: A) Significant Inversions: We are given a sequence of n arbitrary but distinct real numbers <a1 , a2 ,..., an>. We define a significant inversion to be a pair i < j such that ai > 2 aj . Design and analyze an O(n log n) time algorithm to count the number of significant inversions in the given sequence. [Hint: Use divide-&-conquer. Do the “combine” step carefully] B) The Maximum-Sum Monotone Sub-Array Problem: Input: An array A[1..n] of...
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Recall the problem of finding the number of inversions. As in the test, we are given a sequence of n numbers a1, …, an, which we assume are all distinct, and we define an inversion to be a pair of i < j such that a1 >aj.We motivated the problem of counting inversion as a good measure of how difference two orderings are. However, one might feel that this measure is too sensitive. Let’s call a pair a significant inversion if i...
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Can someone please help me in solving question in attached image. Thanks Suppose that an array A of n 1 numbers is given. We want to create a n x n matrix B such that, for 0 i<j<n, Bli.j] AIk] = Ali]Ali+1] for n ij 0, B[i.j] 0 +Aljl k-i I need to write a program where it accepts A as array and return B as matrix defined above, for O(n 2) algorithm
maybe use induction to prove? Problem 2: Let p-p.Pn be a permutation considered in its one-line notation. An inversion in p is a pair 1 i<jS n such that j appears to the left of i in p (i.e., an out-of-order pair). Let inv(p) be the total number of inversions in p. Prove that PES where z is a variable. Problem 2: Let p-p.Pn be a permutation considered in its one-line notation. An inversion in p is a pair 1...