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ks_dp_solvers_profiles.txt
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443 lines (382 loc) · 24.3 KB
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+++++++++++++++++++++++++++++++++++++++++++++++
Straightforward solver using nested `for` loops
+++++++++++++++++++++++++++++++++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 181.055 s
File: ks_dp_solvers.py
Function: solve_naive at line 39
Line # Hits Time Per Hit % Time Line Contents
==============================================================
39 def solve_naive(capacity, items, weights, values):
40
41 1 8171.0 8171.0 0.0 grid = [[0] * (capacity+1)]
42 101 170.0 1.7 0.0 for item in range(items):
43 100 1457275.0 14572.8 0.3 grid.append(grid[item].copy())
44 98387558 121134401.0 1.2 26.4 for k in range(weights[item], capacity+1):
45 98387458 336078747.0 3.4 73.3 grid[item + 1][k] = max(grid[item][k], grid[item][k-weights[item]] + values[item])
46
47 1 2.0 2.0 0.0 solution_value = grid[items][capacity]
48 1 2.0 2.0 0.0 solution_weight = 0
49 1 2.0 2.0 0.0 taken = []
50 1 1.0 1.0 0.0 k = capacity
51 101 130.0 1.3 0.0 for item in range(items, 0, -1):
52 100 489.0 4.9 0.0 if grid[item][k] != grid[item-1][k]:
53 80 164.0 2.0 0.0 taken.append(item - 1)
54 80 152.0 1.9 0.0 k -= weights[item - 1]
55 80 135.0 1.7 0.0 solution_weight +=weights[item-1]
56
57 1 2.0 2.0 0.0 return solution_value, solution_weight, taken
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Straightforward solver, inner loop broken down to individual operations
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 316.87 s
File: ks_dp_solvers.py
Function: solve_naive_detailed at line 64
Line # Hits Time Per Hit % Time Line Contents
==============================================================
64 def solve_naive_detailed(capacity, items, weights, values):
65
66 1 8822.0 8822.0 0.0 grid = [[0] * (capacity+1)]
67 101 196.0 1.9 0.0 for item in range(items):
68 100 1454886.0 14548.9 0.2 grid.append(grid[item].copy())
69 100 1463.0 14.6 0.0 wi = weights[item]
70 100 323.0 3.2 0.0 vi = values[item]
71 98387558 133663554.0 1.4 16.7 for k in range(wi, capacity+1):
72 98387458 156110242.0 1.6 19.4 a = grid[item][k]
73 98387458 194935490.0 2.0 24.3 b = grid[item][k-wi] + vi
74 98387458 138902753.0 1.4 17.3 if b > a:
75 60782758 109728042.0 1.8 13.7 grid[item + 1][k] = b
76 else:
77 37604700 67944391.0 1.8 8.5 grid[item + 1][k] = a
78
79
80 1 2.0 2.0 0.0 solution_value = grid[items][capacity]
81 1 2.0 2.0 0.0 solution_weight = 0
82 1 3.0 3.0 0.0 taken = []
83 1 1.0 1.0 0.0 k = capacity
84 101 162.0 1.6 0.0 for item in range(items, 0, -1):
85 100 558.0 5.6 0.0 if grid[item][k] != grid[item-1][k]:
86 80 190.0 2.4 0.0 taken.append(item - 1)
87 80 167.0 2.1 0.0 k -= weights[item - 1]
88 80 158.0 2.0 0.0 solution_weight += weights[item-1]
89
90 1 3.0 3.0 0.0 return solution_value, solution_weight, taken
+++++++++++++++++++++++++++++++++++++++++++++
Straightforward solver not using max function
+++++++++++++++++++++++++++++++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 253.933 s
File: ks_dp_solvers.py
Function: solve_naive_nomax at line 97
Line # Hits Time Per Hit % Time Line Contents
==============================================================
97 def solve_naive_nomax(capacity, items, weights, values):
98
99 1 8243.0 8243.0 0.0 grid = [[0] * (capacity+1)]
100 101 196.0 1.9 0.0 for item in range(items):
101 100 1477312.0 14773.1 0.2 grid.append(grid[item].copy())
102 100 1423.0 14.2 0.0 wi = weights[item]
103 100 269.0 2.7 0.0 vi = values[item]
104 98387558 140694071.0 1.4 21.9 for k in range(wi, capacity+1):
105 98387458 211324337.0 2.1 32.8 b = grid[item][k-wi] + vi
106 98387458 170748623.0 1.7 26.5 if b > grid[item][k]:
107 60782758 119051499.0 2.0 18.5 grid[item + 1][k] = b
108
109
110 1 2.0 2.0 0.0 solution_value = grid[items][capacity]
111 1 2.0 2.0 0.0 solution_weight = 0
112 1 3.0 3.0 0.0 taken = []
113 1 2.0 2.0 0.0 k = capacity
114 101 166.0 1.6 0.0 for item in range(items, 0, -1):
115 100 557.0 5.6 0.0 if grid[item][k] != grid[item-1][k]:
116 80 195.0 2.4 0.0 taken.append(item - 1)
117 80 185.0 2.3 0.0 k -= weights[item - 1]
118 80 166.0 2.1 0.0 solution_weight +=weights[item-1]
119
120 1 3.0 3.0 0.0 return solution_value, solution_weight, taken
++++++++++++++++++++++++++++++++++++++++++
Straightforward solver using Python arrays
++++++++++++++++++++++++++++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 207.48 s
File: ks_dp_solvers.py
Function: solve_naive_array at line 129
Line # Hits Time Per Hit % Time Line Contents
==============================================================
129 def solve_naive_array(capacity, items, weights, values):
130
131 1 7110.0 7110.0 0.0 weights = array('l', weights)
132 1 38.0 38.0 0.0 values = array('l', values)
133 1 111828.0 111828.0 0.0 grid = [array('l', [0] * (capacity+1))]
134 101 163.0 1.6 0.0 for item in range(items):
135 100 321591.0 3215.9 0.1 grid.append(array('l',grid[item]))
136 98387558 132526152.0 1.3 25.2 for k in range(weights[item], capacity+1):
137 98387458 392656647.0 4.0 74.7 grid[item + 1][k] = max(grid[item][k], grid[item][k-weights[item]] + values[item])
138
139 1 2.0 2.0 0.0 solution_value = grid[items][capacity]
140 1 1.0 1.0 0.0 solution_weight = 0
141 1 2.0 2.0 0.0 taken = []
142 1 1.0 1.0 0.0 k = capacity
143 101 130.0 1.3 0.0 for item in range(items, 0, -1):
144 100 361.0 3.6 0.0 if grid[item][k] != grid[item-1][k]:
145 80 166.0 2.1 0.0 taken.append(item - 1)
146 80 153.0 1.9 0.0 k -= weights[item - 1]
147 80 148.0 1.9 0.0 solution_weight += weights[item-1]
148
149 1 2.0 2.0 0.0 return solution_value, solution_weight, taken
++++++++++++++++++++++++++++++++++++++++++++++
Straightforward solver with flat Python arrays
++++++++++++++++++++++++++++++++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 337.543 s
File: ks_dp_solvers.py
Function: solve_naive_array_flat at line 157
Line # Hits Time Per Hit % Time Line Contents
==============================================================
157 def solve_naive_array_flat(capacity, items, weights, values):
158
159 1 31.0 31.0 0.0 weights = array('l', weights)
160 1 13.0 13.0 0.0 values = array('l', values)
161 1 109802810.0 109802810.0 12.8 grid = array('l', (0 for _ in range((capacity+1)*(items+1))))
162 101 221.0 2.2 0.0 for item in range(items):
163 100 561801.0 5618.0 0.1 grid[(item+1)*(capacity+1):(item+2)*(capacity+1)] = grid[item*(capacity+1):(item+1)*(capacity+1)]
164 98387558 181572084.0 1.8 21.2 for k in range(weights[item], capacity+1):
165 98387458 563185748.0 5.7 65.9 grid[(item+1)*(capacity+1)+k] = max(grid[item*(capacity+1)+k], grid[item*(capacity+1)+k-weights[item]] + values[item])
166
167 1 3.0 3.0 0.0 solution_value = grid[-1]
168 1 2.0 2.0 0.0 solution_weight = 0
169 1 3.0 3.0 0.0 taken = []
170 1 2.0 2.0 0.0 k = capacity
171 101 191.0 1.9 0.0 for item in range(items, 0, -1):
172 100 548.0 5.5 0.0 if grid[item*(capacity+1)+k] != grid[(item-1)*(capacity+1)+k]:
173 80 223.0 2.8 0.0 taken.append(item - 1)
174 80 200.0 2.5 0.0 k -= weights[item - 1]
175 80 200.0 2.5 0.0 solution_weight += weights[item-1]
176
177 1 4.0 4.0 0.0 return solution_value, solution_weight, taken
++++++++++++++++
Map-based solver
++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 100.744 s
File: ks_dp_solvers.py
Function: solve_map at line 183
Line # Hits Time Per Hit % Time Line Contents
==============================================================
183 def solve_map(capacity, items,weights, values):
184 1 8221.0 8221.0 0.0 grid = [[0] * (capacity+1)]
185
186 101 1618.0 16.0 0.0 for item in range(items):
187 100 1450611.0 14506.1 0.6 grid.append(grid[item].copy())
188 100 1552.0 15.5 0.0 this_weight = weights[item]
189 100 281.0 2.8 0.0 this_value = values[item]
190
191 100 253757899.0 2537579.0 99.4 grid[item+1][this_weight:] = list(map(lambda k: max(grid[item][k], grid[item][k - this_weight] + this_value), range(this_weight, capacity+1)))
192
193
194 1 6.0 6.0 0.0 solution_value = grid[items][capacity]
195 1 3.0 3.0 0.0 solution_weight = 0
196 1 2.0 2.0 0.0 taken = []
197 1 2.0 2.0 0.0 k = capacity
198 101 215.0 2.1 0.0 for item in range(items, 0, -1):
199 100 501.0 5.0 0.0 if grid[item][k] != grid[item-1][k]:
200 80 213.0 2.7 0.0 taken.append(item - 1)
201 80 199.0 2.5 0.0 k -= weights[item - 1]
202 80 201.0 2.5 0.0 solution_weight += weights[item-1]
203
204 1 2.0 2.0 0.0 return solution_value, solution_weight, taken
+++++++++++++++++++++++++++++++
Map-based solver without lambda
+++++++++++++++++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 102.135 s
File: ks_dp_solvers.py
Function: solve_map_nolambda at line 211
Line # Hits Time Per Hit % Time Line Contents
==============================================================
211 def solve_map_nolambda(capacity, items, weights, values):
212
213 1 5.0 5.0 0.0 def selector(k):
214 nonlocal item, grid, this_weight, this_value
215 return max(grid[item][k], grid[item][k - this_weight] + this_value)
216
217 1 8339.0 8339.0 0.0 grid = [[0] * (capacity+1)]
218
219 101 1605.0 15.9 0.0 for item in range(items):
220 100 1450535.0 14505.4 0.6 grid.append(grid[item].copy())
221 100 1550.0 15.5 0.0 this_weight = weights[item]
222 100 305.0 3.0 0.0 this_value = values[item]
223
224 100 257283529.0 2572835.3 99.4 grid[item+1][this_weight:] = list(map(selector, range(this_weight, capacity+1)))
225
226
227 1 7.0 7.0 0.0 solution_value = grid[items][capacity]
228 1 4.0 4.0 0.0 solution_weight = 0
229 1 3.0 3.0 0.0 taken = []
230 1 2.0 2.0 0.0 k = capacity
231 101 196.0 1.9 0.0 for item in range(items, 0, -1):
232 100 486.0 4.9 0.0 if grid[item][k] != grid[item-1][k]:
233 80 215.0 2.7 0.0 taken.append(item - 1)
234 80 227.0 2.8 0.0 k -= weights[item - 1]
235 80 177.0 2.2 0.0 solution_weight += weights[item-1]
236
237 1 3.0 3.0 0.0 return solution_value, solution_weight, taken
+++++++++++++++++++++++++++++++
Solver using list comprehension
+++++++++++++++++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 80.5889 s
File: ks_dp_solvers.py
Function: solve_list_comp at line 243
Line # Hits Time Per Hit % Time Line Contents
==============================================================
243 def solve_list_comp(capacity, items, weights, values):
244
245 1 8212.0 8212.0 0.0 grid = [[0] * (capacity+1)]
246
247 101 1654.0 16.4 0.0 for item in range(items):
248 100 1452204.0 14522.0 0.7 grid.append(grid[item].copy())
249 100 1603.0 16.0 0.0 this_weight = weights[item]
250 100 272.0 2.7 0.0 this_value = values[item]
251
252 100 202696910.0 2026969.1 99.3 grid[item+1][this_weight:] = [max(grid[item][k], grid[item][k - this_weight] + this_value) for k in range(this_weight, capacity+1)]
253
254 1 8.0 8.0 0.0 solution_value = grid[items][capacity]
255 1 2.0 2.0 0.0 solution_weight = 0
256 1 2.0 2.0 0.0 taken = []
257 1 1.0 1.0 0.0 k = capacity
258 101 199.0 2.0 0.0 for item in range(items, 0, -1):
259 100 463.0 4.6 0.0 if grid[item][k] != grid[item-1][k]:
260 80 221.0 2.8 0.0 taken.append(item - 1)
261 80 189.0 2.4 0.0 k -= weights[item - 1]
262 80 178.0 2.2 0.0 solution_weight += weights[item-1]
263
264 1 2.0 2.0 0.0 return solution_value, solution_weight, taken
++++++++++++++++++++++++++++++++++++++++++++++++
List comprehension-based solver with numpy array
++++++++++++++++++++++++++++++++++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 122.988 s
File: ks_dp_solvers.py
Function: solve_list_comp_numpy at line 271
Line # Hits Time Per Hit % Time Line Contents
==============================================================
271 def solve_list_comp_numpy(capacity, items, weights, values):
272
273 1 42.0 42.0 0.0 grid = np.empty((items + 1, capacity + 1), dtype=int)
274 1 2527.0 2527.0 0.0 grid[0] = 0
275 101 1427.0 14.1 0.0 for item in range(items):
276 100 322952.0 3229.5 0.1 grid[item+1] = grid[item]
277 100 1341.0 13.4 0.0 this_weight = weights[item]
278 100 266.0 2.7 0.0 this_value = values[item]
279 100 311244493.0 3112444.9 99.9 grid[item+1, this_weight:] = [max(grid[item, k], grid[item, k - this_weight] + this_value) for k in range(this_weight, capacity+1)]
280
281 1 14.0 14.0 0.0 solution_value = grid[items, capacity]
282 1 3.0 3.0 0.0 solution_weight = 0
283 1 2.0 2.0 0.0 taken = []
284 1 1.0 1.0 0.0 k = capacity
285 101 219.0 2.2 0.0 for item in range(items, 0, -1):
286 100 477.0 4.8 0.0 if grid[item, k] != grid[item-1, k]:
287 80 219.0 2.7 0.0 taken.append(item - 1)
288 80 217.0 2.7 0.0 k -= weights[item - 1]
289 80 195.0 2.4 0.0 solution_weight += weights[item-1]
290
291 1 2.0 2.0 0.0 return solution_value, solution_weight, taken
++++++++++++++++++++++++++++++++
Numpy arrays built in `for` loop
++++++++++++++++++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 295.277 s
File: ks_dp_solvers.py
Function: solve_naive_numpy at line 298
Line # Hits Time Per Hit % Time Line Contents
==============================================================
298 def solve_naive_numpy(capacity, items, weights, values):
299
300 1 43.0 43.0 0.0 grid = np.empty((items + 1, capacity + 1), dtype=int)
301 1 3008.0 3008.0 0.0 grid[0] = 0
302 101 174.0 1.7 0.0 for item in range(items):
303 100 335658.0 3356.6 0.0 grid[item+1] = grid[item]
304 100 1210.0 12.1 0.0 this_weight = weights[item]
305 100 259.0 2.6 0.0 this_value = values[item]
306
307 98387558 177357543.0 1.8 23.7 for k in range(this_weight, capacity+1):
308 98387458 570347915.0 5.8 76.2 grid[item + 1, k] = max(grid[item, k], grid[item, k - this_weight] + this_value)
309
310 1 10.0 10.0 0.0 solution_value = grid[items][capacity]
311 1 2.0 2.0 0.0 solution_weight = 0
312 1 2.0 2.0 0.0 taken = []
313 1 2.0 2.0 0.0 k = capacity
314 101 164.0 1.6 0.0 for item in range(items, 0, -1):
315 100 523.0 5.2 0.0 if grid[item][k] != grid[item-1][k]:
316 80 223.0 2.8 0.0 taken.append(item - 1)
317 80 181.0 2.3 0.0 k -= weights[item - 1]
318 80 166.0 2.1 0.0 solution_weight += weights[item-1]
319
320 1 3.0 3.0 0.0 return solution_value, solution_weight, taken
+++++++++++++++++++++++++
Proper numpy-based solver
+++++++++++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 0.553634 s
File: ks_dp_solvers.py
Function: solve_numpy_func at line 327
Line # Hits Time Per Hit % Time Line Contents
==============================================================
327 def solve_numpy_func(capacity,items, weights, values):
328
329 1 40.0 40.0 0.0 grid = np.empty((items + 1, capacity + 1), dtype=int)
330 1 2441.0 2441.0 0.2 grid[0] = 0
331
332 101 1123.0 11.1 0.1 for item in range(items):
333 100 463.0 4.6 0.0 this_weight = weights[item]
334 100 254.0 2.5 0.0 this_value = values[item]
335 100 7500.0 75.0 0.5 grid[item+1, :this_weight] = grid[item, :this_weight]
336 100 374943.0 3749.4 26.7 temp = grid[item, :-this_weight] + this_value
337 100 1014621.0 10146.2 72.3 grid[item + 1, this_weight:] = np.where(temp > grid[item, this_weight:], temp, grid[item, this_weight:])
338
339 1 10.0 10.0 0.0 solution_value = grid[items, capacity]
340 1 2.0 2.0 0.0 solution_weight = 0
341 1 2.0 2.0 0.0 taken = []
342 1 2.0 2.0 0.0 k = capacity
343 101 170.0 1.7 0.0 for item in range(items, 0, -1):
344 100 465.0 4.7 0.0 if grid[item][k] != grid[item - 1][k]:
345 80 184.0 2.3 0.0 taken.append(item - 1)
346 80 178.0 2.2 0.0 k -= weights[item - 1]
347 80 165.0 2.1 0.0 solution_weight += weights[item-1]
348
349 1 2.0 2.0 0.0 return solution_value, solution_weight, taken
++++++++++++++++++++++++
Numpy solver with buffer
++++++++++++++++++++++++
Timer unit: 3.9473e-07 s
Total time: 0.657976 s
File: ks_dp_solvers.py
Function: solve_numpy_func_buffer at line 355
Line # Hits Time Per Hit % Time Line Contents
==============================================================
355 def solve_numpy_func_buffer(capacity, items, weights, values):
356
357 1 40.0 40.0 0.0 grid = np.empty((items + 1, capacity + 1), dtype=int)
358 1 2463.0 2463.0 0.1 grid[0] = 0
359 1 68.0 68.0 0.0 temp = np.zeros(capacity+1, dtype=int)
360
361 101 1283.0 12.7 0.1 for item in range(items):
362 100 495.0 5.0 0.0 this_weight = weights[item]
363 100 243.0 2.4 0.0 this_value = values[item]
364 100 8189.0 81.9 0.5 grid[item+1, :this_weight] = grid[item, :this_weight]
365 100 546527.0 5465.3 32.8 temp[:capacity+1-this_weight] = grid[item, :-this_weight] + this_value
366 100 1106355.0 11063.5 66.4 grid[item + 1, this_weight:] = np.where(temp[:-this_weight] > grid[item, this_weight:], temp[:-this_weight], grid[item, this_weight:])
367
368 1 11.0 11.0 0.0 solution_value = grid[items, capacity]
369 1 2.0 2.0 0.0 solution_weight = 0
370 1 2.0 2.0 0.0 taken = []
371 1 2.0 2.0 0.0 k = capacity
372 101 172.0 1.7 0.0 for item in range(items, 0, -1):
373 100 490.0 4.9 0.0 if grid[item][k] != grid[item - 1][k]:
374 80 201.0 2.5 0.0 taken.append(item - 1)
375 80 186.0 2.3 0.0 k -= weights[item - 1]
376 80 170.0 2.1 0.0 solution_weight += weights[item-1]
377
378 1 3.0 3.0 0.0 return solution_value, solution_weight, taken