凸多边形最优三角剖分python代码和伪代码

以下是凸多边形最优三角剖分的 Python 代码和伪代码：

Python 代码：

import math

# 计算三角形面积
def triangle_area(p1, p2, p3):
    return abs(0.5 * ((p2[0] - p1[0]) * (p3[1] - p1[1]) - (p2[1] - p1[1]) * (p3[0] - p1[0])))

# 计算最优三角剖分
def optimal_triangulation(points):
    n = len(points)
    dp = [[0 for j in range(n)] for i in range(n)]

    for i in range(n - 2, -1, -1):
        for j in range(i + 2, n):
            dp[i][j] = math.inf
            for k in range(i + 1, j):
                dp[i][j] = min(dp[i][j], dp[i][k] + dp[k][j] + triangle_area(points[i], points[j], points[k]))

    return dp[0][n - 1]

# 测试
points = [(0, 0), (1, 0), (2, 1), (1, 2), (0, 2)]
print(optimal_triangulation(points))

伪代码：

function triangle_area(p1, p2, p3):
    return abs(0.5 * ((p2[0] - p1[0]) * (p3[1] - p1[1]) - (p2[1] - p1[1]) * (p3[0] - p1[0])))

function optimal_triangulation(points):
    n = length(points)
    dp = array(n, n)

    for i = n - 2 to 0 step -1:
        for j = i + 2 to n - 1:
            dp[i][j] = infinity
            for k = i + 1 to j - 1:
                dp[i][j] = min(dp[i][j], dp[i][k] + dp[k][j] + triangle_area(points[i], points[j], points[k]))

    return dp[0][n - 1]

# 测试
points = [(0, 0), (1, 0), (2, 1), (1, 2), (0, 2)]
print(optimal_triangulation(points))