# 创建原始数据点
x = range(0, 2π, length=10)  # 稀疏采样点
y = sin.(x)

# 手动实现线性插值函数
function linear_interpolate(x_points, y_points, x_query)
    n = length(x_points)
    # 找到x_query所在的区间
    for i in 1:n-1
        if x_query >= x_points[i] && x_query <= x_points[i+1]
            # 线性插值公式: y = y1 + (y2-y1)*(x-x1)/(x2-x1)
            return y_points[i] + (y_points[i+1] - y_points[i]) * 
                   (x_query - x_points[i]) / (x_points[i+1] - x_points[i])
        end
    end
    return 0.0  # 超出范围返回0
end

# 生成密集的插值点用于绘图
x_dense = range(0, 2π, length=100)
y_dense = [linear_interpolate(x, y, xi) for xi in x_dense]
y_true = sin.(x_dense)

# 创建简单的ASCII艺术图形
println("\n生成sin函数插值对比图...")

# 创建图形数据
height = 20
width = 60
graph = fill(' ', (height, width))

# 绘制坐标轴
mid_y = height ÷ 2
for i in 1:width
    graph[mid_y, i] = '─'
end
for i in 1:height
    graph[i, 1] = '│'
end
graph[mid_y, 1] = '┼'

# 绘制真实sin函数
for i in 1:length(x_dense)
    x_pos = round(Int, (x_dense[i] / (2π)) * (width-2)) + 1
    y_pos = round(Int, (1 - (y_true[i] + 1)/2) * (height-2)) + 1
    if 1 <= y_pos <= height && 1 <= x_pos <= width
        graph[y_pos, x_pos] = '•'
    end
end

# 绘制插值点
for i in 1:length(x_dense)
    x_pos = round(Int, (x_dense[i] / (2π)) * (width-2)) + 1
    y_pos = round(Int, (1 - (y_dense[i] + 1)/2) * (height-2)) + 1
    if 1 <= y_pos <= height && 1 <= x_pos <= width
        graph[y_pos, x_pos] = '+'
    end
end

# 绘制采样点
for i in 1:length(x)
    x_pos = round(Int, (x[i] / (2π)) * (width-2)) + 1
    y_pos = round(Int, (1 - (y[i] + 1)/2) * (height-2)) + 1
    if 1 <= y_pos <= height && 1 <= x_pos <= width
        graph[y_pos, x_pos] = '○'
    end
end

# 输出图形
println("\nsin函数线性插值对比图:")
for i in 1:height
    println(join(graph[i, :]))
end

# 添加图例
println("\n图例:")
println("• 真实sin函数")
println("+ 线性插值结果")
println("○ 采样点")

# 计算并输出插值误差
error = maximum(abs.(y_dense - y_true))
println("\n最大插值误差: $(round(error, digits=4))")
println("插值完成!")

# 计算数字各位之和的函数
function digit_sum(num)
    sum = 0
    while num > 0
        sum += num % 10
        num ÷= 10
    end
    return sum
end

# 查找满足条件的数字
while true
    if n % 7 == 0
        d_sum = digit_sum(n)
        if d_sum > 20
            return n, d_sum
        end
    end
    n += 1
end