#!/bin/bash

# Function to convert a node number to its grid coordinates
get_coordinates() {
    local node=$1
    echo "$((node / 5)) $((node % 5))"
}

# Function to calculate the Chebyshev distance between two nodes
chebyshev_distance() {
    local x1=$1
    local y1=$2
    local x2=$3
    local y2=$4
    # Calculate absolute values of differences
    local dx=$((x1 - x2))
    local dy=$((y1 - y2))
    dx=${dx#-}  # Remove negative sign to get absolute value
    dy=${dy#-}  # Remove negative sign to get absolute value
    # Return the maximum of the two distances
    echo $((dx > dy ? dx : dy))
}

# Function to calculate the Manhattan distance between two nodes
manhattan_distance() {
    local x1=$1
    local y1=$2
    local x2=$3
    local y2=$4
    # Calculate absolute values of differences and sum them
    local dx=$((x1 - x2))
    local dy=$((y1 - y2))
    dx=${dx#-}  # Remove negative sign to get absolute value
    dy=${dy#-}  # Remove negative sign to get absolute value
    echo $((dx + dy))
}

# Function to calculate absolute value
abs() {
    echo ${1#-}
}

# Check if exactly one argument is provided and it is in the range 1 to 4
if [[ $# -ne 1 || $1 -lt 1 || $1 -gt 4 ]]; then
    echo "Usage: $0 <hops (1-4)>"
    exit 1
fi

hops=$1

# Iterate over all pairs of nodes
for start in {0..24}; do
    read x1 y1 <<< $(get_coordinates $start)
    
    for end in {0..24}; do
        if [[ $start -ne $end ]]; then
            read x2 y2 <<< $(get_coordinates $end)
            
            # Calculate Manhattan distance
            # distance=$(manhattan_distance $x1 $y1 $x2 $y2)
            distance=$(chebyshev_distance $x1 $y1 $x2 $y2)
            
            # If distance matches the given hops, print the pair
            if [[ $distance -eq $hops ]]; then
                echo "($start, $end)"
            fi
        fi
    done
done