A-M baby

Task/Knapsack-problem-Bounded/Python/knapsack-problem-bounded-1.py

@@ -0,0 +1,52 @@
+from itertools import groupby
+from collections import namedtuple
+from pprint import pprint as pp
+
+def anyvalidcomb(items,  val=0, wt=0):
+    ' All combinations below the maxwt '
+    if not items:
+        yield [], val, wt
+    else:
+        this, *items = items            # car, cdr
+        for n in range(this.number+1):
+            v = val + n*this.value
+            w = wt  + n*this.weight
+            if w > maxwt:
+                break
+            for c in anyvalidcomb(items, v, w):
+                yield [this]*n + c[COMB], c[VAL], c[WT]
+
+maxwt = 400
+COMB, VAL, WT = range(3)
+Item  = namedtuple('Items', 'name weight value number')
+items = [ Item(*x) for x in
+          (
+            ("map", 9, 150, 1),
+            ("compass", 13, 35, 1),
+            ("water", 153, 200, 3),
+            ("sandwich", 50, 60, 2),
+            ("glucose", 15, 60, 2),
+            ("tin", 68, 45, 3),
+            ("banana", 27, 60, 3),
+            ("apple", 39, 40, 3),
+            ("cheese", 23, 30, 1),
+            ("beer", 52, 10, 3),
+            ("suntan cream", 11, 70, 1),
+            ("camera", 32, 30, 1),
+            ("t-shirt", 24, 15, 2),
+            ("trousers", 48, 10, 2),
+            ("umbrella", 73, 40, 1),
+            ("waterproof trousers", 42, 70, 1),
+            ("waterproof overclothes", 43, 75, 1),
+            ("note-case", 22, 80, 1),
+            ("sunglasses", 7, 20, 1),
+            ("towel", 18, 12, 2),
+            ("socks", 4, 50, 1),
+            ("book", 30, 10, 2),
+           ) ]
+
+bagged = max( anyvalidcomb(items), key=lambda c: (c[VAL], -c[WT])) # max val or min wt if values equal
+print("Bagged the following %i items\n  " % len(bagged[COMB]) +
+      '\n  '.join('%i off: %s' % (len(list(grp)), item.name)
+                  for item,grp in groupby(sorted(bagged[COMB]))))
+print("for a total value of %i and a total weight of %i" % bagged[1:])

Task/Knapsack-problem-Bounded/Python/knapsack-problem-bounded-2.py

@@ -0,0 +1,66 @@
+from itertools import groupby
+
+try:
+    xrange
+except:
+    xrange = range
+
+maxwt = 400
+
+groupeditems = (
+            ("map", 9, 150, 1),
+            ("compass", 13, 35, 1),
+            ("water", 153, 200, 3),
+            ("sandwich", 50, 60, 2),
+            ("glucose", 15, 60, 2),
+            ("tin", 68, 45, 3),
+            ("banana", 27, 60, 3),
+            ("apple", 39, 40, 3),
+            ("cheese", 23, 30, 1),
+            ("beer", 52, 10, 3),
+            ("suntan cream", 11, 70, 1),
+            ("camera", 32, 30, 1),
+            ("t-shirt", 24, 15, 2),
+            ("trousers", 48, 10, 2),
+            ("umbrella", 73, 40, 1),
+            ("waterproof trousers", 42, 70, 1),
+            ("waterproof overclothes", 43, 75, 1),
+            ("note-case", 22, 80, 1),
+            ("sunglasses", 7, 20, 1),
+            ("towel", 18, 12, 2),
+            ("socks", 4, 50, 1),
+            ("book", 30, 10, 2),
+           )
+items = sum( ([(item, wt, val)]*n for item, wt, val,n in groupeditems), [])
+
+def knapsack01_dp(items, limit):
+    table = [[0 for w in range(limit + 1)] for j in xrange(len(items) + 1)]
+
+    for j in xrange(1, len(items) + 1):
+        item, wt, val = items[j-1]
+        for w in xrange(1, limit + 1):
+            if wt > w:
+                table[j][w] = table[j-1][w]
+            else:
+                table[j][w] = max(table[j-1][w],
+                                  table[j-1][w-wt] + val)
+
+    result = []
+    w = limit
+    for j in range(len(items), 0, -1):
+        was_added = table[j][w] != table[j-1][w]
+
+        if was_added:
+            item, wt, val = items[j-1]
+            result.append(items[j-1])
+            w -= wt
+
+    return result
+
+
+bagged = knapsack01_dp(items, maxwt)
+print("Bagged the following %i items\n  " % len(bagged) +
+      '\n  '.join('%i off: %s' % (len(list(grp)), item[0])
+                  for item,grp in groupby(sorted(bagged))))
+print("for a total value of %i and a total weight of %i" % (
+    sum(item[2] for item in bagged), sum(item[1] for item in bagged)))

Task/Knapsack-problem-Bounded/Python/knapsack-problem-bounded-3.py

@@ -0,0 +1,57 @@
+items = (
+	("map",		9,	150,	1),
+	("compass",	13,	35,	1),
+	("water",	153,	200,	3),
+	("sandwich",	50,	60,	2),
+	("glucose",	15,	60,	2),
+	("tin",		68,	45,	3),
+	("banana",	27,	60,	3),
+	("apple",	39,	40,	3),
+	("cheese",	23,	30,	1),
+	("beer",	52,	10,	3),
+	("suntan cream",11,	70,	1),
+	("camera",	32,	30,	1),
+	("t-shirt",	24,	15,	2),
+	("trousers",	48,	10,	2),
+	("umbrella",	73,	40,	1),
+	("w-trousers",	42,	70,	1),
+	("w-overcoat",	43,	75,	1),
+	("note-case",	22,	80,	1),
+	("sunglasses",	7,	20,	1),
+	("towel",	18,	12,	2),
+	("socks",	4,	50,	1),
+	("book",	30,	10,	2),
+)
+
+#cache: could just use memoize module, but explicit caching is clearer
+def choose_item(weight, idx, cache):
+    if idx < 0: return 0, []
+
+    k = (weight, idx)
+    if k in cache: return cache[k]
+
+    name, w, v, qty = items[idx]
+    best_v, best_list = 0, []
+
+    for i in range(0, qty + 1):
+        wlim = weight - i * w
+        if wlim < 0: break
+
+        val, taken = choose_item(wlim, idx - 1, cache)
+        if val + i * v > best_v:
+            best_v = val + i * v
+            best_list = taken[:]
+            best_list.append(i)
+
+    cache[k] = [best_v, best_list]
+    return best_v, best_list
+
+
+v, lst = choose_item(400, len(items) - 1, {})
+w = 0
+for i, cnt in enumerate(lst):
+    if cnt > 0:
+        print cnt, items[i][0]
+        w = w + items[i][1] * cnt
+
+print "Total weight:", w, "Value:", v