如何使用Python为生成的随机坐标点计算并构建欧氏距离矩阵

纯Python无依赖实现方案 #

无需安装额外第三方库，直接在你现有代码基础上补充距离计算和表格输出逻辑即可：

import random
import math

npoints = int(input("Type the npoints:"))
width = float(input("Enter the Width you want:"))
height = float(input("Enter the Height you want:"))

# 生成随机点，保留你原有逻辑
sample = []
for _ in range(npoints):
    sample.append((width * random.random(), height * random.random()))
print("生成的随机点：", *[f"({w:.2f}, {h:.2f})" for w, h in sample], sep=', ')

# 初始化n*n距离矩阵，对角线默认值为0（点到自身的距离）
dist_matrix = [[0.0 for _ in range(npoints)] for _ in range(npoints)]

# 利用矩阵对称性计算上三角和下三角，减少一半计算量
for i in range(npoints):
    x1, y1 = sample[i]
    for j in range(i + 1, npoints):
        x2, y2 = sample[j]
        # 欧氏距离计算
        dist = math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
        dist_matrix[i][j] = dist_matrix[j][i] = round(dist, 2)

# 表格格式输出
print("\n欧氏距离矩阵：")
# 打印表头
print(f"{'':<5}", end="")
for col in range(npoints):
    print(f"P{col:<6}", end="")
print()
# 打印每行数据
for row in range(npoints):
    print(f"P{row:<4}", end="")
    for val in dist_matrix[row]:
        print(f"{val:<7.2f}", end="")
    print()

运行示例

对应你给出的4个点输入，输出效果如下：

Type the npoints:4
Enter the Width you want:10
Enter the Height you want:10
生成的随机点：, (8.52, 3.73), (9.69, 6.87), (8.20, 6.14), (4.18, 0.76)

欧氏距离矩阵：
     P0     P1     P2     P3     
P0   0.00   3.33   2.42   5.19   
P1   3.33   0.00   1.63   8.24   
P2   2.42   1.63   0.00   6.72   
P3   5.19   8.24   6.72   0.00   

高效实现方案（适合点数量较多的场景） #

如果需要处理大量点，可使用scipy的内置距离计算接口，性能远高于纯Python循环，使用前先执行pip install scipy安装依赖：

import random
from scipy.spatial.distance import pdist, squareform

npoints = int(input("Type the npoints:"))
width = float(input("Enter the Width you want:"))
height = float(input("Enter the Height you want:"))

sample = []
for _ in range(npoints):
    sample.append((width * random.random(), height * random.random()))
print("生成的随机点：", *[f"({w:.2f}, {h:.2f})" for w, h in sample], sep=', ')

# 一行代码生成距离矩阵
dist_matrix = squareform(pdist(sample, metric="euclidean")).round(2)

# 输出逻辑和纯Python版本一致
print("\n欧氏距离矩阵：")
print(f"{'':<5}", end="")
for col in range(npoints):
    print(f"P{col:<6}", end="")
print()
for row in range(npoints):
    print(f"P{row:<4}", end="")
    for val in dist_matrix[row]:
        print(f"{val:<7.2f}", end="")
    print()

内容的提问来源于stack exchange，提问作者user16726326