Question

我正在寻找PHP中的算法示例，以获取一组大小不同的项目（数字），并打印出可以容纳特定更大数字的每种可能组合，排除不适合的数字。

最好是该算法示例能够随着特定大数的缩小而进行调整。

例如输入：

$timeleft = 160;
$times = array("wash dishes"=>"25", "vacuum"=>"45", "Laundry"=>"120");
//Output after processing:
Echo $combo1;
"Laundry, wash dishes"
Echo $combo2;
"Wash dishes, vacuum"

预先感谢

Answer 1

答案类似于0-1背包问题。

这是PHP中的解决方案：

#########################################################
# 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>"

;

找到范围内可能的金额组合

1 个答案: