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Maximize arr[j] β arr[i] + arr[l] β arr[k], such that i < j < k < l in C++
We are given with an array of integers. The goal is to maximize the value of expression −
arr[j]-arr[i] + arr[l]-arr[k] ; i<j<k<l indexes of elements
We will do so by traversing all elements and calculate the value of expression. If it is maximum found so far then store it and return in the end.
Input
arr[]= { 1,2,3,4 }Output
Maximum value for above expression is : 2
Explanation − for i<j<k<l, i=0, j=1, k=2, l=3
arr[j]-arr[i]+arr[l]-arr[k]= 2-1+4-3=1+1=2
Input
arr[]= { 5,5,5,5,5 }Output
Maximum value for above expression is : 0
Explanation − for i<j<k<l, for any value of i,j,k,l
arr[j]-arr[i]+arr[l]-arr[k]= 5-5+5-5=0
Approach used in the below program is as follows
Integer array a[] stores the numbers.
Function maximizeSum(int arr[], int n) takes array and its length n as input and returns maximum value of arr[j]-arr[i]+arr[l]-arr[k] such that i<j<k<l.
Variable sum is used to store the sum of arr[j]-arr[i] and arr[l]-arr[k].
Initialize maxx=arr[0] as initial maximum sum.
Traverse array from i=0, j=1,k=2, l=3 to i<n-3,j<n-2,k<n-1 and l<n
For each indexes in i,j,k,l compute arr[j]-arr[i]+arr[l]-arr[k] and store in sum
If current sum>=maxx update maxx.
In the end return maxx as desired result.
Example
#include <bits/stdc++.h>
using namespace std;
// function to maximize the sum of selected numbers
int maximizeSum(int arr[], int n) {
int sum=0;
int maxx=arr[0];
for(int i=0;i<n-3;i++)
for(int j=i+1;j<n-2;j++)
for(int k=j+1;k<n-1;k++)
for(int l=k+1;l<n;l++){
sum=arr[j]-arr[i]+arr[l]-arr[k];
if(sum>=maxx)
maxx=sum;
}
return maxx;
}
int main(){
int a[] = {5, 3, 9, 2, 20};
int n = sizeof(a) / sizeof(a[0]);
cout <<"Maximized value is :"<< maximizeSum(a, n);
return 0;
}Output
Maximized value is :24
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