Check if the maximum sum of visible faces of N dice is at least X

Efficiency and accuracy are often crucial when solving complex problems in programming. One particular challenge is to appropriately determine whether the maximum sum of the visible faces of N dice equals or exceeds X. In this paper, we evaluate various approaches to solving this difficulty in C coding, including syntactic explanations and step-by-step algorithms. Furthermore, we will provide two real, complete executable code examples based on the proposed approach. By the end, you will have a clear understanding of how to check in C whether the maximum sum of the visible faces of N dice is at least X.

grammar

Before we delve into these methods, let’s first understand the syntax of the methods we will use in the following code -

bool checkVisibleSum(int N, int X, vector<int>& dice);

method one

algorithm

• First, initialize a variable visibleSum to 0. This variable will store the sum of visible faces.

• Iterate through each element in the dice vector.

• For each die, arrange the faces in descending order.

• Add the largest face (the first element after sorting) to visibleSum.

• If at any time, visibleSum becomes greater than or equal to X, return true.

• If no visible sum greater than or equal to X is found after the iteration is completed, return false.

Example

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

bool checkVisibleSum(int N, int X, vector<vector<int>>& dice) {
   int visibleSum = 0;

   for (int i = 0; i < dice.size(); i++) {
      sort(dice[i].rbegin(), dice[i].rend());
      visibleSum += dice[i][0];

      if (visibleSum >= X)
         return true;
   }

   return false;
}

int main() {
   int N = 2; // Number of dice

   vector<vector<int>> dice(N);
   dice[0] = {6, 5, 4}; // Faces of dice 1
   dice[1] = {3, 2, 1}; // Faces of dice 2

   int X = 15; // Minimum sum (X)

   if (checkVisibleSum(N, X, dice))
      cout << "The maximum sum of visible faces of the dice is at least " << X << ".\n";
   else
      cout << "The maximum sum of visible faces of the dice is not at least " << X << ".\n";

   return 0;
}

Output

The maximum sum of visible faces of the dice is not at least 15.

Explanation

Explanation

In this code, we first define the function checkVisibleSum, which accepts three parameters: N (the number of dice), X (the minimum sum), and dice (a vector representing the vector of the dice face).

checkVisibleSum function implements method 1. It initializes a variable visibleSum to 0, which is used to store the sum of visible faces. It then iterates over each dice in the dice vector. For each dice, it sorts the faces in descending order using sort(dice[i].rbegin(), dice[i].rend()). This ensures that the largest face is at the beginning of the sorted vector.

Then, the code uses visibleSum = dice[i][0] to add the largest side of the current die to visibleSum. By using this function, one can better understand certain events that may occur in any given situation.

This can be seen by it analyzing whether a given visibleSum exceeds or equals X at various points during its analysis. If this possibility is discovered while conducting the study - usually indicated by a true output - then they can conclude with a certain degree of certainty that the maximum number of observable features is equal to or greater than their original intention of exceeding X.

Conversely, if they still can't find said statistics after some exploration with relevant iterations and calculations, then there are obviously more unanswered questions.

In the main function, we prompt the user to enter the number of dice (N). We create a vector of vectors called dice to store the faces of each die. We then iterate N times, and for each die, prompt the user for the number of faces and the faces themselves. We store these values ​​in the dice vector.

Next, we ask the user to enter the minimum sum (X). We pass N, X and dice to the checkVisibleSum function. We will accordingly convey a message that the maximum possible sum of visible die faces is equal to or greater than X. However, contrary to the positive outlook of this situation, we are likely to release knowledge as a result of learning that the function actually produces undesirable results related to X.

Method Two

algorithm

• First, initialize a variable visibleSum to 0. This variable will store the sum of visible faces.

• Iterate through each element in the dice vector.

• For each die, arrange the faces in descending order.

• Calculate the sum of the first N-1 faces (excluding the largest face) and add it to visibleSum.

• Return true if visibleSum becomes greater than or equal to X.

• If no visible sum greater than or equal to X is found after the iteration is completed, return false.

Example

#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>

using namespace std;

bool checkVisibleSum(int N, int X, vector<vector<int>>& dice) {
   int visibleSum = 0;

   for (int i = 0; i < dice.size(); i++) {
      sort(dice[i].rbegin(), dice[i].rend());
      int sum = accumulate(dice[i].begin(), dice[i].end() - 1, 0);
      visibleSum += sum;

      if (visibleSum >= X)
         return true;
   }

   return false;
}

int main() {
   int N = 2; // Number of dice

   vector<vector<int>> dice(N);
   dice[0] = {6, 5, 4}; // Faces of dice 1
   dice[1] = {3, 2, 1}; // Faces of dice 2

   int X = 15; // Minimum sum (X)

   if (checkVisibleSum(N, X, dice))
      cout << "The maximum sum of visible faces of the dice is at least " << X << ".\n";
   else
      cout << "The maximum sum of visible faces of the dice is not at least " << X << ".\n";

   return 0;
}

Output

The maximum sum of visible faces of the dice is at least 15.

Explanation

Explanation

In this code, we have the same checkVisibleSum function as in the first method. However, the main difference lies in the calculation of the visible sum.

Method 2 sums the first N-1 faces of each die, excluding the largest face. To achieve this, we use the accumulate function from the library. We pass dice[i].begin() and dice[i].begin() N - 1 as the range to accumulate, effectively summing over the required faces.

The rest of the code in the main function is the same as the previous example.

in conclusion

Through this article, our topic revolves around solving an important problem about C coding. How to tell exactly if the sum of the largest visible faces of a given set of dice (N) is at least X? In best answering this question, we found two practical solutions: first, ensure that the sum of the results of each die roll equals or exceeds X; second, only evaluate the sum of the first N-1 die rolls, and Determine whether they match or exceed X. In addition, we provide code setup for each method and detailed guidance for performing these procedures. Additionally, we provide two real, fully executable code examples based on these methods. By leveraging the knowledge and code provided in this article, you can now confidently solve the problem of determining whether the maximum visible sum of N dice is at least X in C programming.

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