added three new code about dp

dp/0-1-knapsack-rv.cpp

@@ -0,0 +1,42 @@
+// time O(N*W)
+// space O(N+W) for dp + O(N) for recursion stack
+# include <bits/stdc++.h>
+using namespace std;
+const int N = 1e5;
+const int maxW = 1e2;
+const long long int inf = 1e15;
+
+int weight[N+5];
+long long int value[N+5];
+long long int dp[N+5][maxW+5];
+
+long long int calc(int n, int taken){
+    if(n == 0){
+        if(taken == 0) return 0;
+        else return -inf;
+    }
+    if(dp[n][taken] != -1) return dp[n][taken];
+
+    dp[n][taken] = calc(n-1, taken);     // not taking nth item
+    if(taken >= weight[n]) dp[n][taken] = max(dp[n][taken], calc(n-1, taken-weight[n]) + value[n]);
+
+    return dp[n][taken];
+}
+int main(){
+    memset(dp, -1, sizeof(dp));
+    int n, W;
+    cin>>n>>W;
+    for(int i= 1; i<=n; i++) cin>>weight[i]>>value[i];
+
+    long long int ans = -inf;
+    for(int w = 0; w <= W; w++){
+        ans = max(ans, calc(n, w));
+    }
+
+    cout<<ans<<endl;
+    return 0;
+}
+
+
+
+

dp/0-1-knapsack.cpp

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+// time O(N*W)
+// memory O(N)
+
+int knapSack(int W, int wt[], int val[], int n)
+{
+	// making and initializing dp array
+	int dp[W + 1];
+	memset(dp, 0, sizeof(dp));
+
+	for (int i = 1; i < n + 1; i++) {
+		for (int w = W; w >= 0; w--) {
+			if (wt[i - 1] <= w) // finding the maximum value
+				dp[w] = max(dp[w], dp[w - wt[i - 1]] + val[i - 1]);
+		}
+	}
+	return dp[W]; // returning the maximum value of knapsack
+}

dp/double-knapsack.txt

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+For each ‘i’, we can either: 
+1. Don’t select the item ‘i’.
+2. Fill the item ‘i’ in first knapsack.
+3. Fill the item ‘i’ in second knapsack.