mirror of
https://github.com/kuhyx/praca_magisterska.git
synced 2026-07-04 13:43:05 +02:00
382 lines
14 KiB
Python
382 lines
14 KiB
Python
|
#!/usr/bin/env python3
|
|||
|
|
"""
|
|||
|
|
Generate Bellman-Ford negative-weights & negative-cycle diagram for PYTANIE 2.
|
|||
|
|
|
|||
|
|
Two-part figure:
|
|||
|
|
Part 1: Graph with negative edge, Dijkstra WRONG vs Bellman-Ford CORRECT
|
|||
|
|
Part 2: Negative cycle detection (add C→B(−3))
|
|||
|
|
|
|||
|
|
A4-compatible, monochrome-friendly, 300 DPI.
|
|||
|
|
"""
|
|||
|
|
|
|||
|
|
import matplotlib
|
|||
|
|
matplotlib.use('Agg')
|
|||
|
|
import matplotlib.pyplot as plt
|
|||
|
|
import matplotlib.patches as mpatches
|
|||
|
|
import numpy as np
|
|||
|
|
import os
|
|||
|
|
|
|||
|
|
DPI = 300
|
|||
|
|
BG = 'white'
|
|||
|
|
LN = 'black'
|
|||
|
|
FS = 8
|
|||
|
|
FS_TITLE = 10
|
|||
|
|
FS_SMALL = 6.5
|
|||
|
|
FS_EDGE = 9
|
|||
|
|
OUTPUT_DIR = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'img')
|
|||
|
|
os.makedirs(OUTPUT_DIR, exist_ok=True)
|
|||
|
|
|
|||
|
|
GRAY1 = '#E8E8E8'
|
|||
|
|
GRAY2 = '#D0D0D0'
|
|||
|
|
GRAY3 = '#B8B8B8'
|
|||
|
|
GRAY4 = '#F5F5F5'
|
|||
|
|
LIGHT_GREEN = '#D5E8D4'
|
|||
|
|
LIGHT_RED = '#F8D7DA'
|
|||
|
|
LIGHT_YELLOW = '#FFF9C4'
|
|||
|
|
|
|||
|
|
# --- Graph layout for negative-weight example ---
|
|||
|
|
# S→A(2), A→C(3), S→B(5), B→A(−4)
|
|||
|
|
NEG_POS = {'S': (0.8, 2), 'A': (3.3, 3.2), 'B': (3.3, 0.8), 'C': (5.8, 2)}
|
|||
|
|
NEG_EDGES = [('S', 'A', 2), ('A', 'C', 3), ('S', 'B', 5), ('B', 'A', -4)]
|
|||
|
|
|
|||
|
|
|
|||
|
|
def draw_node(ax, name, pos, color='white', current=False, visited=False,
|
|||
|
|
dist_label=None, fontsize=12, error=False):
|
|||
|
|
x, y = pos
|
|||
|
|
r = 0.35
|
|||
|
|
lw = 2.5 if current else 1.5
|
|||
|
|
ec = '#D32F2F' if current else ('#D32F2F' if error else LN)
|
|||
|
|
fc = LIGHT_YELLOW if current else (LIGHT_GREEN if visited else color)
|
|||
|
|
if error:
|
|||
|
|
fc = LIGHT_RED
|
|||
|
|
|
|||
|
|
circle = plt.Circle((x, y), r, fill=True, facecolor=fc,
|
|||
|
|
edgecolor=ec, linewidth=lw, zorder=5)
|
|||
|
|
ax.add_patch(circle)
|
|||
|
|
ax.text(x, y, name, ha='center', va='center', fontsize=fontsize,
|
|||
|
|
fontweight='bold', zorder=6)
|
|||
|
|
|
|||
|
|
if dist_label is not None:
|
|||
|
|
bbox_ec = '#D32F2F' if error else GRAY3
|
|||
|
|
bbox_fc = LIGHT_RED if error else 'white'
|
|||
|
|
ax.text(x, y - 0.55, f'd={dist_label}', ha='center', va='center',
|
|||
|
|
fontsize=FS, zorder=6,
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.15', facecolor=bbox_fc,
|
|||
|
|
edgecolor=bbox_ec, alpha=0.95))
|
|||
|
|
|
|||
|
|
|
|||
|
|
def draw_edge(ax, pos1, pos2, weight, highlighted=False, relaxed=False,
|
|||
|
|
negative=False, cycle_edge=False, offset=0.0):
|
|||
|
|
x1, y1 = pos1
|
|||
|
|
x2, y2 = pos2
|
|||
|
|
|
|||
|
|
dx, dy = x2 - x1, y2 - y1
|
|||
|
|
length = np.sqrt(dx**2 + dy**2)
|
|||
|
|
r = 0.38
|
|||
|
|
sx = x1 + r * dx / length
|
|||
|
|
sy = y1 + r * dy / length
|
|||
|
|
ex = x2 - r * dx / length
|
|||
|
|
ey = y2 - r * dy / length
|
|||
|
|
|
|||
|
|
# Offset perpendicular for parallel edges
|
|||
|
|
if offset != 0:
|
|||
|
|
perp_x = -dy / length * offset
|
|||
|
|
perp_y = dx / length * offset
|
|||
|
|
sx += perp_x; sy += perp_y
|
|||
|
|
ex += perp_x; ey += perp_y
|
|||
|
|
|
|||
|
|
if cycle_edge:
|
|||
|
|
color = '#D32F2F'
|
|||
|
|
lw = 2.5
|
|||
|
|
ls = '--'
|
|||
|
|
elif negative:
|
|||
|
|
color = '#D32F2F'
|
|||
|
|
lw = 2.5
|
|||
|
|
ls = '-'
|
|||
|
|
elif relaxed:
|
|||
|
|
color = '#D32F2F'
|
|||
|
|
lw = 2.5
|
|||
|
|
ls = '-'
|
|||
|
|
elif highlighted:
|
|||
|
|
color = '#1565C0'
|
|||
|
|
lw = 2.0
|
|||
|
|
ls = '-'
|
|||
|
|
else:
|
|||
|
|
color = GRAY3
|
|||
|
|
lw = 1.5
|
|||
|
|
ls = '-'
|
|||
|
|
|
|||
|
|
# Arrow
|
|||
|
|
ax.annotate('', xy=(ex, ey), xytext=(sx, sy),
|
|||
|
|
arrowprops=dict(arrowstyle='->', color=color, lw=lw,
|
|||
|
|
linestyle=ls, shrinkA=0, shrinkB=0),
|
|||
|
|
zorder=2)
|
|||
|
|
|
|||
|
|
# Weight label
|
|||
|
|
mx = (sx + ex) / 2
|
|||
|
|
my = (sy + ey) / 2
|
|||
|
|
perp_x = -dy / length * 0.22
|
|||
|
|
perp_y = dx / length * 0.22
|
|||
|
|
if offset != 0:
|
|||
|
|
perp_x *= 0.5
|
|||
|
|
perp_y *= 0.5
|
|||
|
|
|
|||
|
|
weight_str = str(weight)
|
|||
|
|
edge_fc = LIGHT_RED if negative or cycle_edge else 'white'
|
|||
|
|
edge_ec = '#D32F2F' if negative or cycle_edge else GRAY3
|
|||
|
|
ax.text(mx + perp_x, my + perp_y, weight_str, ha='center', va='center',
|
|||
|
|
fontsize=FS_EDGE, fontweight='bold',
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.15', facecolor=edge_fc,
|
|||
|
|
edgecolor=edge_ec, alpha=0.95),
|
|||
|
|
zorder=4)
|
|||
|
|
|
|||
|
|
|
|||
|
|
def draw_neg_graph(ax, edges, title="", dist=None, current=None, visited=None,
|
|||
|
|
relaxed_edges=None, error_nodes=None, extra_edges=None,
|
|||
|
|
node_positions=None):
|
|||
|
|
if visited is None:
|
|||
|
|
visited = set()
|
|||
|
|
if relaxed_edges is None:
|
|||
|
|
relaxed_edges = set()
|
|||
|
|
if dist is None:
|
|||
|
|
dist = {}
|
|||
|
|
if error_nodes is None:
|
|||
|
|
error_nodes = set()
|
|||
|
|
if node_positions is None:
|
|||
|
|
node_positions = NEG_POS
|
|||
|
|
|
|||
|
|
ax.set_xlim(-0.5, 7.0)
|
|||
|
|
ax.set_ylim(-0.8, 4.5)
|
|||
|
|
ax.set_aspect('equal')
|
|||
|
|
ax.axis('off')
|
|||
|
|
if title:
|
|||
|
|
ax.set_title(title, fontsize=FS, fontweight='bold', pad=5)
|
|||
|
|
|
|||
|
|
all_edges = list(edges)
|
|||
|
|
if extra_edges:
|
|||
|
|
all_edges += extra_edges
|
|||
|
|
|
|||
|
|
for u, v, w in all_edges:
|
|||
|
|
rl = (u, v) in relaxed_edges
|
|||
|
|
neg = w < 0
|
|||
|
|
cycle = extra_edges and (u, v, w) in extra_edges
|
|||
|
|
# If B→A and A→B both exist, offset them
|
|||
|
|
off = 0.0
|
|||
|
|
draw_edge(ax, node_positions[u], node_positions[v], w,
|
|||
|
|
relaxed=rl, negative=neg, cycle_edge=cycle, offset=off)
|
|||
|
|
|
|||
|
|
for name, pos in node_positions.items():
|
|||
|
|
is_current = (name == current)
|
|||
|
|
is_visited = (name in visited)
|
|||
|
|
d_label = dist.get(name, None)
|
|||
|
|
is_error = (name in error_nodes)
|
|||
|
|
draw_node(ax, name, pos, current=is_current, visited=is_visited,
|
|||
|
|
dist_label=d_label, error=is_error)
|
|||
|
|
|
|||
|
|
|
|||
|
|
def generate_bf_negative_weights():
|
|||
|
|
"""
|
|||
|
|
Two-row figure:
|
|||
|
|
Row 1: Graph structure + Dijkstra WRONG + Bellman-Ford CORRECT
|
|||
|
|
Row 2: B-F iterations 1-3 step by step
|
|||
|
|
"""
|
|||
|
|
fig = plt.figure(figsize=(14, 10))
|
|||
|
|
fig.suptitle('Bellman-Ford — ujemne wagi vs Dijkstra\n'
|
|||
|
|
'Graf: S→A(2), A→C(3), S→B(5), B→A(−4). Start = S',
|
|||
|
|
fontsize=FS_TITLE + 1, fontweight='bold', y=0.99)
|
|||
|
|
|
|||
|
|
# ---- Row 1: Graph + Dijkstra wrong + BF correct ----
|
|||
|
|
|
|||
|
|
# Panel 1: The graph structure
|
|||
|
|
ax1 = fig.add_subplot(2, 3, 1)
|
|||
|
|
draw_neg_graph(ax1, NEG_EDGES,
|
|||
|
|
title='Graf z ujemną wagą\n(B→A = −4, zaznaczona na czerwono)',
|
|||
|
|
dist={'S': '0', 'A': '?', 'B': '?', 'C': '?'})
|
|||
|
|
# START label
|
|||
|
|
ax1.annotate("START", xy=(NEG_POS['S'][0] - 0.35, NEG_POS['S'][1]),
|
|||
|
|
xytext=(NEG_POS['S'][0] - 1.2, NEG_POS['S'][1]),
|
|||
|
|
fontsize=FS, fontweight='bold', color='#D32F2F',
|
|||
|
|
arrowprops=dict(arrowstyle='->', color='#D32F2F', lw=2),
|
|||
|
|
va='center')
|
|||
|
|
|
|||
|
|
# Panel 2: Dijkstra — WRONG
|
|||
|
|
ax2 = fig.add_subplot(2, 3, 2)
|
|||
|
|
draw_neg_graph(ax2, NEG_EDGES,
|
|||
|
|
title='Dijkstra — BŁĘDNY wynik\nA zamknięty z d=2, nie poprawia przy B→A',
|
|||
|
|
dist={'S': '0', 'A': '2', 'B': '5', 'C': '5'},
|
|||
|
|
visited={'S', 'A', 'B', 'C'},
|
|||
|
|
error_nodes={'A', 'C'})
|
|||
|
|
# Add "WRONG" annotations
|
|||
|
|
ax2.text(NEG_POS['A'][0] + 0.6, NEG_POS['A'][1] + 0.3, '✗ powinno 1',
|
|||
|
|
fontsize=FS_SMALL, color='#D32F2F', fontweight='bold',
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.1', facecolor=LIGHT_RED,
|
|||
|
|
edgecolor='#D32F2F', alpha=0.9, lw=0.5))
|
|||
|
|
ax2.text(NEG_POS['C'][0] + 0.05, NEG_POS['C'][1] + 0.55, '✗ powinno 4',
|
|||
|
|
fontsize=FS_SMALL, color='#D32F2F', fontweight='bold',
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.1', facecolor=LIGHT_RED,
|
|||
|
|
edgecolor='#D32F2F', alpha=0.9, lw=0.5))
|
|||
|
|
|
|||
|
|
# Panel 3: Bellman-Ford — CORRECT
|
|||
|
|
ax3 = fig.add_subplot(2, 3, 3)
|
|||
|
|
draw_neg_graph(ax3, NEG_EDGES,
|
|||
|
|
title='Bellman-Ford — POPRAWNY wynik\nUjemna waga B→A poprawnie propagowana',
|
|||
|
|
dist={'S': '0', 'A': '1', 'B': '5', 'C': '4'},
|
|||
|
|
visited={'S', 'A', 'B', 'C'},
|
|||
|
|
relaxed_edges={('B', 'A')})
|
|||
|
|
ax3.text(NEG_POS['A'][0] + 0.6, NEG_POS['A'][1] + 0.3, '✓ poprawne!',
|
|||
|
|
fontsize=FS_SMALL, color='#006400', fontweight='bold',
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.1', facecolor=LIGHT_GREEN,
|
|||
|
|
edgecolor='#006400', alpha=0.9, lw=0.5))
|
|||
|
|
ax3.text(NEG_POS['C'][0] + 0.05, NEG_POS['C'][1] + 0.55, '✓ poprawne!',
|
|||
|
|
fontsize=FS_SMALL, color='#006400', fontweight='bold',
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.1', facecolor=LIGHT_GREEN,
|
|||
|
|
edgecolor='#006400', alpha=0.9, lw=0.5))
|
|||
|
|
|
|||
|
|
# ---- Row 2: B-F iterations step by step ----
|
|||
|
|
iterations = [
|
|||
|
|
{
|
|||
|
|
'title': 'B-F Iteracja 1\nRelaksuj WSZYSTKIE krawędzie',
|
|||
|
|
'dist': {'S': '0', 'A': '1', 'B': '5', 'C': '5'},
|
|||
|
|
'relaxed': {('S', 'A'), ('A', 'C'), ('S', 'B'), ('B', 'A')},
|
|||
|
|
'detail': ('S→A: 0+2=2<∞ → A=2\n'
|
|||
|
|
'A→C: 2+3=5<∞ → C=5\n'
|
|||
|
|
'S→B: 0+5=5<∞ → B=5\n'
|
|||
|
|
'B→A: 5−4=1<2 → A=1 ✓'),
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
'title': 'B-F Iteracja 2\nPropagacja poprawionego A',
|
|||
|
|
'dist': {'S': '0', 'A': '1', 'B': '5', 'C': '4'},
|
|||
|
|
'relaxed': {('A', 'C')},
|
|||
|
|
'detail': ('S→A: 0+2=2>1 ✗\n'
|
|||
|
|
'A→C: 1+3=4<5 → C=4 ✓\n'
|
|||
|
|
'S→B: 0+5=5=5 ✗\n'
|
|||
|
|
'B→A: 5−4=1=1 ✗'),
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
'title': 'B-F Iteracja 3\nBrak zmian → stabilne!',
|
|||
|
|
'dist': {'S': '0', 'A': '1', 'B': '5', 'C': '4'},
|
|||
|
|
'relaxed': set(),
|
|||
|
|
'detail': ('Wszystkie krawędzie:\n'
|
|||
|
|
'brak poprawy ✗\n'
|
|||
|
|
'→ wynik stabilny\n'
|
|||
|
|
'→ BRAK cyklu ujemnego'),
|
|||
|
|
},
|
|||
|
|
]
|
|||
|
|
|
|||
|
|
for i, it in enumerate(iterations):
|
|||
|
|
ax = fig.add_subplot(2, 3, i + 4)
|
|||
|
|
draw_neg_graph(ax, NEG_EDGES, title=it['title'],
|
|||
|
|
dist=it['dist'],
|
|||
|
|
visited={'S', 'A', 'B', 'C'},
|
|||
|
|
relaxed_edges=it['relaxed'])
|
|||
|
|
# Detail text below graph
|
|||
|
|
ax.text(3.2, -0.5, it['detail'], ha='center', va='top',
|
|||
|
|
fontsize=FS_SMALL, family='monospace',
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.3', facecolor=GRAY4,
|
|||
|
|
edgecolor=GRAY3))
|
|||
|
|
|
|||
|
|
# Bottom note
|
|||
|
|
fig.text(0.5, 0.01,
|
|||
|
|
'Dijkstra zamyka wierzchołki na stałe (zachłanność) → ujemna waga B→A(−4) nie może poprawić zamkniętego A.\n'
|
|||
|
|
'Bellman-Ford relaksuje WSZYSTKIE krawędzie w każdej iteracji → ujemne wagi propagują się poprawnie.',
|
|||
|
|
ha='center', fontsize=FS, fontweight='bold',
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.3', facecolor=LIGHT_YELLOW, edgecolor=LN))
|
|||
|
|
|
|||
|
|
plt.tight_layout(rect=[0, 0.05, 1, 0.95])
|
|||
|
|
plt.savefig(os.path.join(OUTPUT_DIR, 'bellman_ford_negative_weights.png'),
|
|||
|
|
dpi=DPI, bbox_inches='tight', facecolor=BG)
|
|||
|
|
plt.close()
|
|||
|
|
print(" ✓ bellman_ford_negative_weights.png")
|
|||
|
|
|
|||
|
|
|
|||
|
|
def generate_bf_negative_cycle():
|
|||
|
|
"""
|
|||
|
|
Figure showing negative cycle detection.
|
|||
|
|
Graph: S→A(2), A→C(3), S→B(5), B→A(−4), C→B(−3) [added edge]
|
|||
|
|
Cycle: B→A→C→B = −4+3+(−3) = −4 < 0
|
|||
|
|
"""
|
|||
|
|
cycle_edges = NEG_EDGES + [('C', 'B', -3)]
|
|||
|
|
|
|||
|
|
fig = plt.figure(figsize=(14, 5.5))
|
|||
|
|
fig.suptitle('Bellman-Ford — wykrywanie cyklu ujemnego\n'
|
|||
|
|
'Dodano krawędź C→B(−3). Cykl: B→A→C→B = −4+3+(−3) = −4 < 0',
|
|||
|
|
fontsize=FS_TITLE + 1, fontweight='bold', y=0.99)
|
|||
|
|
|
|||
|
|
# Panel 1: Graph with cycle highlighted
|
|||
|
|
ax1 = fig.add_subplot(1, 3, 1)
|
|||
|
|
draw_neg_graph(ax1, NEG_EDGES,
|
|||
|
|
title='Graf z cyklem ujemnym\nDodana krawędź C→B(−3) — przerywana',
|
|||
|
|
dist={'S': '0', 'A': '?', 'B': '?', 'C': '?'},
|
|||
|
|
extra_edges=[('C', 'B', -3)])
|
|||
|
|
# Mark cycle
|
|||
|
|
ax1.annotate("CYKL\n−4+3+(−3)=−4<0",
|
|||
|
|
xy=(3.3, 2.0),
|
|||
|
|
fontsize=FS, fontweight='bold', color='#D32F2F',
|
|||
|
|
ha='center', va='center',
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.3', facecolor=LIGHT_RED,
|
|||
|
|
edgecolor='#D32F2F', alpha=0.9))
|
|||
|
|
|
|||
|
|
# Panel 2: After V−1 iterations — still changing
|
|||
|
|
ax2 = fig.add_subplot(1, 3, 2)
|
|||
|
|
draw_neg_graph(ax2, NEG_EDGES,
|
|||
|
|
title='Po V−1=3 iteracjach\ndist wciąż maleje (niestabilne!)',
|
|||
|
|
dist={'S': '0', 'A': '−7', 'B': '−4', 'C': '−4'},
|
|||
|
|
visited={'S', 'A', 'B', 'C'},
|
|||
|
|
error_nodes={'A', 'B', 'C'},
|
|||
|
|
extra_edges=[('C', 'B', -3)])
|
|||
|
|
ax2.text(3.2, -0.4,
|
|||
|
|
'Każde okrążenie cyklu\nzmniejsza dist o 4.\n'
|
|||
|
|
'Dist → −∞ (brak minimum!)',
|
|||
|
|
ha='center', va='top', fontsize=FS_SMALL, fontweight='bold',
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.3', facecolor=LIGHT_RED,
|
|||
|
|
edgecolor='#D32F2F'))
|
|||
|
|
|
|||
|
|
# Panel 3: V-th iteration detects
|
|||
|
|
ax3 = fig.add_subplot(1, 3, 3)
|
|||
|
|
ax3.axis('off')
|
|||
|
|
ax3.set_xlim(0, 10)
|
|||
|
|
ax3.set_ylim(0, 10)
|
|||
|
|
|
|||
|
|
detection_text = (
|
|||
|
|
"V-ta iteracja (sprawdzenie):\n"
|
|||
|
|
"━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\n\n"
|
|||
|
|
"for (src, dst, w) in edges:\n"
|
|||
|
|
" if dist[src]+w < dist[dst]:\n"
|
|||
|
|
" return None # CYKL!\n\n"
|
|||
|
|
"━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\n\n"
|
|||
|
|
"Sprawdzamy np. krawędź B→A:\n"
|
|||
|
|
" dist[B] + (−4) = −4 + (−4) = −8\n"
|
|||
|
|
" −8 < dist[A] = −7\n"
|
|||
|
|
" → NADAL SIĘ POPRAWIA!\n"
|
|||
|
|
" → CYKL UJEMNY WYKRYTY!\n\n"
|
|||
|
|
"━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\n\n"
|
|||
|
|
"Wynik: return None\n"
|
|||
|
|
"(najkrótsza ścieżka nie istnieje)"
|
|||
|
|
)
|
|||
|
|
ax3.text(5, 5, detection_text, ha='center', va='center',
|
|||
|
|
fontsize=FS + 0.5, family='monospace',
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.6', facecolor=LIGHT_RED,
|
|||
|
|
edgecolor='#D32F2F', lw=2))
|
|||
|
|
ax3.set_title('Wykrywanie — V-ta iteracja\nJeśli cokolwiek się poprawia → cykl ujemny!',
|
|||
|
|
fontsize=FS, fontweight='bold', pad=5)
|
|||
|
|
|
|||
|
|
# Bottom note
|
|||
|
|
fig.text(0.5, 0.01,
|
|||
|
|
'Bez cyklu ujemnego: po V−1 iteracjach dist jest stabilne. '
|
|||
|
|
'Z cyklem ujemnym: dist maleje w nieskończoność → V-ta iteracja to wykrywa.',
|
|||
|
|
ha='center', fontsize=FS, fontweight='bold',
|
|||
|
|
bbox=dict(boxstyle='round,pad=0.3', facecolor=LIGHT_YELLOW, edgecolor=LN))
|
|||
|
|
|
|||
|
|
plt.tight_layout(rect=[0, 0.06, 1, 0.94])
|
|||
|
|
plt.savefig(os.path.join(OUTPUT_DIR, 'bellman_ford_negative_cycle.png'),
|
|||
|
|
dpi=DPI, bbox_inches='tight', facecolor=BG)
|
|||
|
|
plt.close()
|
|||
|
|
print(" ✓ bellman_ford_negative_cycle.png")
|
|||
|
|
|
|||
|
|
|
|||
|
|
if __name__ == '__main__':
|
|||
|
|
print("Generating Bellman-Ford negative weight diagrams...")
|
|||
|
|
generate_bf_negative_weights()
|
|||
|
|
generate_bf_negative_cycle()
|
|||
|
|
print(f"\nAll diagrams saved to {OUTPUT_DIR}/")
|