✨ adds knapsack with quantity

algorithms/dynamic-programming/knapsack-with-quantity-(no-recover).cpp

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+ll knapsack(const vi &weight, const vll &value, const vi &qtd, int maxCost) {
+    vi costs;
+    vll values;
+    for (int i = 0; i < len(weight); i++) {
+        ll q = qtd[i];
+        for (ll x = 1; x <= q; q -= x, x <<= 1) {
+            costs.eb(x * weight[i]);
+            values.eb(x * value[i]);
+        }
+        if (q) {
+            costs.eb(q * weight[i]);
+            values.eb(q * value[i]);
+        }
+    }
+
+    vll dp(maxCost + 1);
+    for (int i = 0; i < len(values); i++) {
+        for (int j = maxCost; j > 0; j--) {
+            if (j >= costs[i]) dp[j] = max(dp[j], values[i] + dp[j - costs[i]]);
+        }
+    }
+    return dp[maxCost];
+}

algorithms/dynamic-programming/knapsack-with-quantity-(no-recover).tex

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+\subsection{Knapsack with quantity (no recover)}
+
+finds the maximum score you can achieve, given that you have $n$ items, each item has a $cost$, a $point$ and a $quantity$, you can spent at most $maxcost$ and buy each item the maximum quantity it has.
+
+time: $O(n \cdot maxcost \cdot \log{maxqtd})$
+memory: $O(maxcost)$.