配列のすべての要素をC++で4で割り切れるようにするための最小手順

問題の説明

サイズnの配列が与えられた場合、タスクは、配列のすべての要素を4で割り切れるのに必要な最小ステップ数を見つけることです。ステップは、配列から任意の2つの要素を削除し、これらの要素の合計を加算することとして定義されます。アレイへ

例

入力配列が{1、2、0、2、4、3}の場合、3つの操作が必要です-

1 + 3 = 4
2 + 2 = 4
0 + 4 = 4

アルゴリズム

1. Sum of all the elements of the array should be divisible by If not, this task is not possible
2. Initialize an array namely modulus of size 4 to 0
3. Initialize a counter to 0. It will keep track of number of steps done
4. Traverse through the input array and take modulus 4 of each element
5. Increment the value of the mod 4 value in the modulus array by 1
6. modulus[0] is the count of elements that are already divisible by 4. So no need to pair them with any other element
7. modulus[1] and modulus[3] elements can be combined to get a number divisible by 4. So, increment count to the minimum value of the both
8. Every 2 elements of modulus[2] can be combined to get an element divisible to 4.
9. For the remaining elements, increment value modulus[2] by half of modulus[1] and modulus[3].
10. Now, increment count by half modulus[2]. We take half because every two elements are combined as one
11. The final value of count is the number of steps required to convert the all the elements of the input array divisible by 4

例

#include <bits/stdc++.h>
using namespace std;
int getMinRequiredSteps(int arr[], int n) {
   int count = 0;
   int modulus[4] = {0};
   int sum = 0;
   for (int i = 0; i < n; i++) {
      int mod = arr[i] % 4;
      sum += mod;
      modulus[mod]++;
   }
   if (sum % 4 != 0) {
      return -1;
   } else {
      if (modulus[1] > modulus[3]) {
         count += modulus[3];
      }
      else {
         count += modulus[1];
      }
      modulus[1] -= count;
      modulus[3] -= count;
      modulus[2] += modulus[1] / 2;
      modulus[2] += modulus[3] / 2;
      count += modulus[1] / 2;
      count += modulus[3] / 2;
      count += modulus[2] / 2;
      return count;
   }
}
int main() {
   int arr[] = {1, 2, 0, 2, 4, 3};
   int n = sizeof(arr) / sizeof(arr[0]);
   cout << "Minimum required steps = " << getMinRequiredSteps(arr, n) << endl;
   return 0;
}

上記のプログラムをコンパイルして実行する場合。次の出力を生成します

出力

Minimum required steps = 2