I have a program which searches for the largest and smallest number in an array of n elements in the C ++ language. What I want to do is to decrease the complexity of the algorithm a (3n / 2) - 2
, which currently does not meet this complexity.
This complexity is in the worst case
My question is how can I leave this algorithm to the aforementioned complexity formula? Or what can I modify, delete and add to comply with that condition?
Thank you. The comparison algorithm is as follows:
#include <iostream>
using namespace std;
int main(){
int arreglo[10] = {9,8,7,6,5,4,3,2,1,0};
int menor =0, mayor =0, comparaciones=0;
menor = arreglo[0], mayor = arreglo[0];
for(int i=1;i<10;i++){
if(arreglo[i]>mayor){
mayor = arreglo[i];
}
comparaciones++;
if(arreglo[i]<menor){
menor = arreglo[i];
}
comparaciones++;
}
cout<<"Mayor: "<<mayor<<" Menor: "<<menor<<" Comparaciones: "<<comparaciones;
}
UPDATE: The algorithm has a complexity equation of 5n-2
, I must lower its complexity to (3n / 2) - 2
This solution uses the Divide and Conquer
paradigm.
I based this answer from this website and there you can see the explanation of why this will take (3n / 2) - 2
comparisons.
To understand how it works, I suggest getting a pen and paper and follow the code, using a smaller input (eg: {3,2,1,0}).
#include <iostream>
using namespace std;
int* maxMin(int* values, int begin, int end) {
int partialSmallest, partialLargest;
int mid, max1, min1, max2, min2;
//Here we store Largest/Smallest
int* result = new int[2];
//When there's only one element
if (begin == end) {
partialSmallest = values[begin];
partialLargest = values[begin];
}
else {
//There is not only one element, therefore
//We will split into two parts, and call the function recursively
mid = (begin + end) / 2;
// Solve both "sides"
int* result1 = maxMin(values, begin, mid);
int* result2 = maxMin(values, mid+1, end);
max1 = result1[0];
min1 = result1[1];
max2 = result2[0];
min2 = result2[1];
//Combine the solutions.
if (max1 < max2)
partialLargest = max2;
else
partialLargest = max1;
if (min1 < min2)
partialSmallest = min1;
else
partialSmallest = min2;
}
result[0] = partialLargest;
result[1] = partialSmallest;
return result;
}
int main(){
int values[10] = {9,8,7,6,5,4,3,2,1,0};
int* finalResult = maxMin(values, 0, 9);
cout << "Largest: " << finalResult[0] << " Smallest: " << finalResult[1];
}
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