动态编程中的真实代码与PHP中的背包问题[关闭]

Question

是否有任何资源可以找到真正的代码来解决动态编程中的问题，如 PHP 中的背包问题等？

我想自己分析代码，因为我不太懂理论。而且我在 Google 中找不到任何代码。

非常感谢。

Answer 1

这是使用 PHP (source) 解决的问题：

#########################################################
# 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
#
#It works uncorrectly! For examle if $aw=4. Max value is true, but no "Array Indices" and its parameters are displayed
#
#########################################################

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,$pickedItems);

        if ($w[$i] > $aW) { // Does it return too many?

            $m[$i][$aW] = $without_i; // Memo without including this one
            $m['picked'][$i][$aW] = array(); // and a blank array entry...
            return array($without_i,array()); // 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]),$m,$pickedItems);
            $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,$m,$pickedItems);

# 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>";
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>";

输出：

物品：地图、指南针、水、三明治、葡萄糖、锡、香蕉、苹果、奶酪、啤酒、防晒霜、相机、T恤、裤子、雨伞、防水长裤、防水外衣, 便签盒, 太阳镜, 毛巾, 袜子, 书

找到的最大值： 1030（在 8725 次调用中）

数组索引： 0,1,2,3,4,6,10,15,16,17,18,20

选择的物品：

Item                        Value             Weight
 map                         150                9
 compass                     35                 13
 water                       200                153
 sandwich                    160                50
 glucose                     60                 15
 banana                      60                 27
 suntan cream                70                 11
 waterproof trousers         70                 42
 waterproof overclothes      75                 43
 note-case                   80                 22
 sunglasses                  20                 7
 socks                       50                 4
 Totals                      1030               396