Data commit

Task/Knapsack-problem-0-1/PHP/knapsack-problem-0-1-1.php

@@ -0,0 +1,100 @@
+#########################################################
+# 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;
+	$numcalls ++;
+	// echo "Called with i=$i, aW=$aW<br>";
+
+	// Return memo if we have one
+	if (isset($m[$i][$aW])) {
+		return array( $m[$i][$aW], $m['picked'][$i][$aW] );
+	} else {
+
+		// At end of decision branch
+		if ($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 {
+				// Won't fit
+				$m[$i][$aW] = 0; // Memo zero
+				$m['picked'][$i][$aW] = array(); // and a blank array entry...
+				return array(0,array()); // Return nothing
+			}
+		}	
+	
+		// Not at end of decision branch..
+		// Get the result of the next branch (without this one)
+		list ($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, $without_PI); // and return it
+
+		} else {
+		
+			// Get the result of the next branch (WITH this one picked, so available weight is reduced)
+			list ($with_i,$with_PI) = knapSolveFast2($w, $v, ($i-1), ($aW - $w[$i]), $m);
+			$with_i += $v[$i];  // ..and add the value of this one..
+			
+			// Get the greater of WITH or WITHOUT
+			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>";

Task/Knapsack-problem-0-1/PHP/knapsack-problem-0-1-2.php

@@ -0,0 +1,94 @@
+#########################################################
+# 0-1 Knapsack Problem Solve
+# $w = weight of item
+# $v = value of item
+# $i = index
+# $aW = Available Weight
+# PHP Translation by Brian Berneker
+#########################################################
+
+function knapSolve($w,$v,$i,$aW) {
+
+	global $numcalls;
+	$numcalls ++;
+	// echo "Called with i=$i, aW=$aW<br>";
+
+	if ($i == 0) {
+		if ($w[$i] <= $aW) {
+			return $v[$i];
+		} else {
+			return 0;
+		}
+	}	
+	
+	$without_i = knapSolve($w, $v, $i-1, $aW);
+	if ($w[$i] > $aW) {
+		return $without_i;
+	} else {
+		$with_i = $v[$i] + knapSolve($w, $v, ($i-1), ($aW - $w[$i]));
+		return max($with_i, $without_i);
+	}	
+
+}
+
+
+#########################################################
+# 0-1 Knapsack Problem Solve (with "memo"-ization optimization)
+# $w = weight of item
+# $v = value of item
+# $i = index
+# $aW = Available Weight
+# $m = 'memo' array
+# PHP Translation by Brian Berneker
+#########################################################
+
+function knapSolveFast($w,$v,$i,$aW,&$m) { // Note: We use &$m because the function writes to the $m array
+
+	global $numcalls;
+	$numcalls ++;
+	// echo "Called with i=$i, aW=$aW<br>";
+
+	// Return memo if we have one
+	if (isset($m[$i][$aW])) {
+		return $m[$i][$aW];
+	} else {
+
+		if ($i == 0) {
+			if ($w[$i] <= $aW) {
+				$m[$i][$aW] = $v[$i]; // save memo
+				return $v[$i];
+			} else {
+				$m[$i][$aW] = 0; // save memo
+				return 0;
+			}
+		}	
+	
+		$without_i = knapSolveFast($w, $v, $i-1, $aW,$m);
+		if ($w[$i] > $aW) {
+			$m[$i][$aW] = $without_i; // save memo
+			return $without_i;
+		} else {
+			$with_i = $v[$i] + knapSolveFast($w, $v, ($i-1), ($aW - $w[$i]),$m);
+			$res = max($with_i, $without_i);
+			$m[$i][$aW] = $res; // save memo
+			return $res;
+		}	
+	}
+}
+
+
+$w3 = array(1, 1, 1, 2, 2, 2, 4, 4, 4, 44, 96, 96, 96);
+$v3 = array(1, 1, 1, 2, 2, 2, 4, 4, 4, 44, 96, 96, 96);
+
+$numcalls = 0;
+$m = array();
+$m3 = knapSolveFast($w3, $v3, sizeof($v3) -1, 54,$m);
+print_r($w3); echo "<br>FAST: ";
+echo "<b>Max: $m3</b> ($numcalls calls)<br><br>";
+
+
+$numcalls = 0;
+$m = array();
+$m3 = knapSolve($w3, $v3, sizeof($v3) -1, 54 );
+print_r($w3); echo "<br>";
+echo "<b>Max: $m3</b> ($numcalls calls)<br><br>";