knapsack graph algorithm

knapsack.cpp

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+// http://www.cplusplus.com/forum/general/75356/
+
+// I've got this code from the pseudo-code here:
+// http://books.google.com/books?id=QrvsNy9paOYC&pg=PA235&lpg=PA235&dq=knapsack+problem+branch+and+bound+C%2B%2B&source=bl&ots=e6ok2kODMN&sig=Yh5__d3iAFa5rEkaCoBJ2JAWybk&hl=en&sa=X&ei=k1EDULDrHIfKqgHqtYyxDA&ved=0CEsQ6AEwAA#v=onepage&q=knapsack%20problem%20branch%20and%20bound%20C%2B%2B&f=false
+
+#include <queue>
+#include <iostream>
+using namespace std;
+
+struct node
+{
+  int level;
+  int profit;
+  int weight;
+  float bound;
+
+  bool operator<(const node& right) const
+  {
+    return bound < right.bound;
+  }
+};
+
+float bound(node u, int n, int W, int p[], int w[])
+{
+  int j, k;
+  int totweight;
+  float result;
+
+  if (u.weight >= W)
+  {
+    return 0;
+  }
+  else
+  {
+    result = u.profit;
+    j = u.level + 1;
+    totweight = u.weight;
+    while (j <= n && totweight + w[j] <= W)
+    {
+      totweight = totweight + w[j];
+      result = result + p[j];
+      j++;
+    }
+    k = j;
+    if (k <= n)
+    {
+      result = result + (W - totweight) * p[k]/w[k];
+    }
+    return result;
+  }
+}
+
+
+void knapsack(int n, int p[], int w[], int W, int& maxProfit)
+{
+  priority_queue<node> Q;
+  node u, v;
+  Q.empty();
+
+  v.level = 0;
+  v.profit = 0;
+  v.weight = 0;
+
+  maxProfit = 0;
+
+  v.bound = bound(v, n, W, p, w);
+  Q.push(v);
+
+  while (Q.size() > 0)
+  {
+    Q.pop();
+    if (v.bound > maxProfit)
+    {
+      u.level = v.level + 1;
+      u.weight = v.weight + w[u.level];
+      u.profit = v.profit + p[u.level];
+      if (u.weight <= W && u.profit > maxProfit)
+      {
+        maxProfit = u.profit;
+      }
+      u.bound = bound(u, n, W, p, w);
+      if (u.bound > maxProfit)
+      {
+        Q.push(u);
+      }
+      u.weight = v.weight;
+      u.profit = v.profit;
+      u.bound = bound(u, n, W, p, w);
+      if (u.bound > maxProfit)
+      {
+        Q.push(u);
+      }
+    }
+  }
+}
+
+
+int main()
+{
+  int maxProfit;
+  int n = 4;
+  int W = 7;
+  int p[4] = {2, 5, 3, 4};
+  int w[4] = {2, 40, 18, 28};
+
+  knapsack(n, p, w, W, maxProfit);
+
+  cout << maxProfit << endl;
+}