import numpy as np

# Sample data points

data$\_$points $=\{$

$\text{'}$P$1\text{'}$: $[5\mathrm{.}1,3\mathrm{.}5],$

$\text{'}$P$2\text{'}$: $[4\mathrm{.}9,3\mathrm{.}0],$

$\text{'}$P$3\text{'}$: $[4\mathrm{.}7,3\mathrm{.}2],$

$\text{'}$P$4\text{'}$: $[4\mathrm{.}6,3\mathrm{.}1],$

$\text{'}$P$5\text{'}$: $[5\mathrm{.}0,3\mathrm{.}6],$

$\text{'}$P$6\text{'}$: $[5\mathrm{.}4,3\mathrm{.}9]\}$

# Calculate Euclidean distance between two points

def euclidean$\_$distance$($point$1,$ point$2)$:

return np$.$sqrt$($np$.$sum$(($np$.$array$($point$1)-$ np$.$array$($point$2))**2))$

# Create initial distance matrix

labels $=$ list$($data$\_$points.keys$())$

num$\_$points $=$ len$($labels$)$

distance$\_$matrix $=$ np$.$zeros$(($num$\_$points, num$\_$points$))$

for i in range$($num$\_$points$)$:

for j in range$($i $+1,$ num$\_$points$)$:

distance$\_$matrix$[$i$,$ j$]=$ euclidean$\_$distance$($data$\_$points$[$labels$[$i$]],$ data$\_$points$[$labels$[$j$]])$

distance$\_$matrix$[$j$,$ i$]=$ distance$\_$matrix$[$i$,$ j$]$ # Distance matrix is symmetric

# Display initial distance matrix

print$("$Initial Distance Matrix:"$)$

print$($distance$\_$matrix$)$

# Single linkage clustering and updating distance matrix

clusters $=\{$label: $[$label$]$ for label in labels$\}$

while len$($clusters$)>1$:

# Find the minimum distance in the current matrix

min$\_$distance $=$ np$.$min$($distance$\_$matrix$[$np$.$nonzero$($distance$\_$matrix$)])$

# Find indices of the minimum distance

indices $=$ np$.$where$($distance$\_$matrix $==$ min$\_$distance$)$

idx$1,$ idx$2=$ indices$[0][0],$ indices$[1][0]$

# Merge the clusters by updating the distance matrix

new$\_$cluster $=($labels$[$idx$1],$ labels$[$idx$2])$

clusters$[$new$\_$cluster$]=$ clusters.pop$($labels$[$idx$1])+$ clusters.pop$($labels$[$idx$2])$

# Update the distance matrix for merged clusters

for i in range$($num$\_$points$)$:

if labels$[$i$]$ in clusters$[$new$\_$cluster$]$:

for j in range$($num$\_$points$)$:

if labels$[$j$]$ not in clusters$[$new$\_$cluster$]$:

min$\_$dist $=$ min$($distance$\_$matrix$[$i$,$ j$],$ distance$\_$matrix$[$idx$1,$ j$],$ distance$\_$matrix$[$idx$2,$ j$])$

distance$\_$matrix$[$i$,$ j$]=$ min$\_$dist

distance$\_$matrix$[$j$,$ i$]=$ min$\_$dist

# Display updated distance matrix

print$($f$"$

Clusters Formed: $\{$list$($clusters$.$keys$())\}")$

print$("$Updated Distance Matrix:"$)$

print$($distance$\_$matrix$)$

# Print the final cluster

print$($f$"$

Final Cluster: $\{$list$($clusters$.$keys$())\}")$