蛇形填数 C++代码

蛇形填数，也被称为帕斯卡三角形(Pascal's Triangle)，是一个经典的数学图形，每一行都是前一行的两倍加当前行数减一。在C++中，我们可以使用动态规划的方式来生成它。下面是一个简单的C++代码示例：

#include<iostream>
using namespace std;

vector<vector<int>> generateSpiral(int n) {
    vector<vector<int>> pascal(n, vector<int>(n, 0));
    for (int i = 0; i < n; ++i) {
        pascal[i][0] = pascal[i][i] = 1;
    }

    int top = 0, bottom = n - 1, left = 0, right = n - 1;
    while (top <= bottom && left <= right) {
        // Fill the current row from left to right
        for (int i = left; i <= right; ++i) {
            pascal[top][i] = pascal[top][i - 1] + pascal[top + 1][i];
        }
        top++;

        // Fill the current column from top to bottom
        for (int i = top; i <= bottom; ++i) {
            pascal[i][right] = pascal[i - 1][right] + pascal[i][right - 1];
        }
        right--;

        // If there are remaining elements at the bottom row, fill them
        if (top <= bottom) {
            for (int i = right; i >= left; --i) {
                pascal[bottom][i] = pascal[bottom][i + 1] + pascal[bottom - 1][i];
            }
            bottom--;
        }

        // If there are remaining elements at the rightmost column, fill them
        if (left <= right) {
            for (int i = bottom; i >= top; --i) {
                pascal[i][left] = pascal[i + 1][left] + pascal[i][left - 1];
            }
            left++;
        }
    }

    return pascal;
}

int main() {
    int n = 5;
    vector<vector<int>> spiralTriangle = generateSpiral(n);
    for (const auto& row : spiralTriangle) {
        for (int num : row) {
            cout << num << " ";
        }
        cout << "\n";
    }
    return 0;
}

上述代码首先初始化一个二维向量`pascal`，并设置边界条件。接着在一个循环中处理每一层的填充，按照左->右，上->下，右->上，下->左的顺序。通过这种方式，我们能够生成帕斯卡三角形的每一层，并存储在`pascal`矩阵中。