Minimum operations required to remove an array in C++

Description

Given an array of N integers where N is an even number. There are two kinds of operations allowed on the array.

• Increase the value of any element of an array by 1.
• If two adjacent elements in the array are consecutive prime number, delete both the element.

The task is to find the minimum number of operations required to remove all the element of the array.

Example

If array is {10, 13} then minimum 2 operations are required

• Increment 1^st element of an array by 1. So new array becomes {11, 13}
• Delete 1^st and 2^nd element as both are consecutive prime numbers

Algorithm

1. To remove numbers, we must transform two numbers to two consecutive primes.
2. Let us suppose a and b are the consecutive prime numbers then we use sieve of Eratosthenes to precompute prime numbers and then find the first prime p not greater than a and the first greater than p using array
3. Once this computation is done use dynamic programming to solve the problem

Example

 Live Demo

#include <iostream>
#include <algorithm>
#include <queue>
using namespace std;
int minimumPrefixReversals(int *a, int n) {
   string start = "";
   string destination = "", t, r;
   for (int i = 0; i < n; i++) {
      start += to_string(a[i]);
   }
   sort(a, a + n);
   for (int i = 0; i < n; i++) {
      destination += to_string(a[i]);
   }
   queue<pair<string, int> > qu;
   pair<string, int> p;
   qu.push(make_pair(start, 0));
   if (start == destination) {
      return 0;
   }
   while (!qu.empty()) {
      p = qu.front();
      t = p.first;
      qu.pop();
      for (int j = 2; j <= n; j++) {
         r = t;
         reverse(r.begin(), r.begin() + j);
         if (r == destination) {
            return p.second + 1;
         }
         qu.push(make_pair(r, p.second + 1));
      }
   }
}
int main() {
   int a[] = { 1, 2, 4, 3 };
   int n = sizeof(a) / sizeof(a[0]);
   cout << "Minimum reversal: " <<
   minimumPrefixReversals(a, n) << endl;
   return 0;
}

When you compile and execute above program. It generates following output:

Output

Minimum reversal: 3

Narendra Kumar

Published on 23-Dec-2019 05:21:11

• Related Questions & Answers
• Minimum operations required to make all the array elements equal in C++
• Minimum number of operations required to delete all elements of the array using C++.
• Minimum number of swaps required to sort an array in C++
• Find minimum operations needed to make an Array beautiful in C++
• Minimum operations required to set all elements of binary matrix in C++
• Program to find number of operations required to remove palindromic sublists in C++
• Minimum number of operations required to sum to binary string S using C++.
• Find minimum number of merge operations to make an array palindrome in C++
• Minimum number of given operations required to make two strings equal using C++.
• Minimum operations to make XOR of array zero in C++
• Minimum positive integer required to split the array equally in C++
• Minimum number of operations on an array to make all elements 0 using C++.
• Finding minimum number of required operations to reach n from m in JavaScript
• Minimum delete operations to make all elements of array same in C++.
• Program to count minimum number of operations required to make numbers non coprime in Python?