有一个 n×n 的方阵,第 1 列、对角线和第 n 列可以构成一个 “N”字,请编程求出这个 “N” 字上所有元素的和。
时间: 2024-11-17 12:28:54 浏览: 53
要解决这个问题,你可以使用两个嵌套的循环来遍历矩阵(二维数组)。首先,从左到右遍历第一列,然后从左上到右下的对角线,再从右到左遍历最后一列。对于每个位置,如果它的值为1(通常表示为白色),则将其添加到总和中。下面是用C++编写的示例代码:
```cpp
#include <iostream>
using namespace std;
int main() {
int n, sum = 0; // n is the size of the square matrix, and sum will store the total N shape sum
cout << "Enter the size of the matrix (n x n): ";
cin >> n;
// Create a boolean matrix representing an 'N' shape where 1 represents white (on the pattern) and 0 represents black (not on the pattern)
bool matrix[n][n];
for(int i = 0; i < n; ++i) {
if(i == 0 || i == n - 1) { // First column and last column are part of the 'N'
matrix[i][i] = true;
} else if(i % n == 0 || i + 1 == n) { // Diagonal from top-left to bottom-right
matrix[i][i] = true;
}
}
// Calculate the sum of all 'white' elements in the 'N' shape
for(int i = 0; i < n; ++i) {
for(int j = 0; j < n; ++j) {
if(matrix[i][j]) {
sum += matrix[i][j]; // Add 1 to the sum if the element is part of the 'N' shape
}
}
}
cout << "The sum of all elements in the 'N' shape is: " << sum << endl;
return 0;
}
```
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