Task: Knapsack problem_0-1






PHP: #########################################################
# 0-1 Knapsack Problem Solve with memoization optimize and index returns
# $w = weight of item
# $v = value of item
# $i = index
# $aW = Available Weight
# $m = Memo items array
# PHP Translation from Python, Memoization,
# and index return functionality added by Brian Berneker
#
#########################################################

function knapSolveFast2($w, $v, $i, $aW, &$m) {

	global $numcalls;
	$numcalls ++;


	if (isset($m[$i][$aW])) {
		return array( $m[$i][$aW], $m['picked'][$i][$aW] );
	} else {

		if ($i == 0) {
			if ($w[$i] <= $aW) { // Will this item fit?
				$m[$i][$aW] = $v[$i]; // Memo this item
				$m['picked'][$i][$aW] = array($i); // and the picked item
				return array($v[$i],array($i)); // Return the value of this item and add it to the picked list

			} else {

				$m[$i][$aW] = 0; // Memo zero
				$m['picked'][$i][$aW] = array(); // and a blank array entry...
				return array(0,array()); // Return nothing
			}
		}	


		list ($without_i, $without_PI) = knapSolveFast2($w, $v, $i-1, $aW, $m);

		if ($w[$i] > $aW) { // Does it return too many?
			
			$m[$i][$aW] = $without_i; // Memo without including this one
			$m['picked'][$i][$aW] = $without_PI; // and a blank array entry...
			return array($without_i, $without_PI); // and return it

		} else {

			list ($with_i,$with_PI) = knapSolveFast2($w, $v, ($i-1), ($aW - $w[$i]), $m);
			$with_i += $v[$i];  // ..and add the value of this one..

			if ($with_i > $without_i) {
				$res = $with_i;
				$picked = $with_PI;
				array_push($picked,$i);
			} else {
				$res = $without_i;
				$picked = $without_PI;
			}
						
			$m[$i][$aW] = $res; // Store it in the memo
			$m['picked'][$i][$aW] = $picked; // and store the picked item
			return array ($res,$picked); // and then return it
		}	
	}
}



$items4 = array("map","compass","water","sandwich","glucose","tin","banana","apple","cheese","beer","suntan cream","camera","t-shirt","trousers","umbrella","waterproof trousers","waterproof overclothes","note-case","sunglasses","towel","socks","book");
$w4 = array(9,13,153,50,15,68,27,39,23,52,11,32,24,48,73,42,43,22,7,18,4,30);
$v4 = array(150,35,200,160,60,45,60,40,30,10,70,30,15,10,40,70,75,80,20,12,50,10);

## Initialize
$numcalls = 0; $m = array(); $pickedItems = array();

## Solve
list ($m4,$pickedItems) = knapSolveFast2($w4, $v4, sizeof($v4) -1, 400, $m);

# Display Result 
echo "<b>Items:</b><br>".join(", ",$items4)."<br>";
echo "<b>Max Value Found:</b><br>$m4 (in $numcalls calls)<br>";
echo "<b>Array Indices:</b><br>".join(",",$pickedItems)."<br>";


echo "<b>Chosen Items:</b><br>";
echo "<table border cellspacing=0>";
echo "<tr><td>Item</td><td>Value</td><td>Weight</td></tr>";
$totalVal = $totalWt = 0;
foreach($pickedItems as $key) {
	$totalVal += $v4[$key];
	$totalWt += $w4[$key];
	echo "<tr><td>".$items4[$key]."</td><td>".$v4[$key]."</td><td>".$w4[$key]."</td></tr>";
}
echo "<tr><td align=right><b>Totals</b></td><td>$totalVal</td><td>$totalWt</td></tr>";
echo "</table><hr>";


Python: from itertools import combinations

def anycomb(items):
    ' return combinations of any length from the items '
    return ( comb
             for r in range(1, len(items)+1)
             for comb in combinations(items, r)
             )

def totalvalue(comb):
    ' Totalise a particular combination of items'
    totwt = totval = 0
    for item, wt, val in comb:
        totwt  += wt
        totval += val
    return (totval, -totwt) if totwt <= 400 else (0, 0)

items = (
    ("map", 9, 150), ("compass", 13, 35), ("water", 153, 200), ("sandwich", 50, 160),
    ("glucose", 15, 60), ("tin", 68, 45), ("banana", 27, 60), ("apple", 39, 40),
    ("cheese", 23, 30), ("beer", 52, 10), ("suntan cream", 11, 70), ("camera", 32, 30),
    ("t-shirt", 24, 15), ("trousers", 48, 10), ("umbrella", 73, 40),
    ("waterproof trousers", 42, 70), ("waterproof overclothes", 43, 75),
    ("note-case", 22, 80), ("sunglasses", 7, 20), ("towel", 18, 12),
    ("socks", 4, 50), ("book", 30, 10),
    )
bagged = max( anycomb(items), key=totalvalue) 
print("Bagged the following items\n  " +
      '\n  '.join(sorted(item for item,_,_ in bagged)))
val, wt = totalvalue(bagged)
print("for a total value of %i and a total weight of %i" % (val, -wt))