solved on 17/01/24

Author: Priyanshu-Ganatra

CS_49_01KnapsackProblem.cpp

@@ -0,0 +1,156 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+// printing dp table
+void print(vector<vector<int>> &dp)
+{
+    for (auto row : dp)
+    {
+        for (auto col : row)
+        {
+            cout << col << " ";
+        }
+        cout << endl;
+    }
+}
+
+// tc: O(2^n) sc: O(n)
+// int solvesingRecursion(int capacity, vector<int> &wt, vector<int> &profit, int i, int &n){
+//     // base case
+//     if(i >= n){
+//         return 0;
+//     }
+
+//     // inc/exc
+//     int inc = 0;
+//     if(wt[i] <= capacity){
+//         inc = profit[i] + solvesingRecursion(capacity-wt[i], wt, profit, i+1, n);
+//     }
+//     int exc = 0 + solvesingRecursion(capacity, wt, profit, i+1, n);
+//     return max(inc, exc);
+// }
+
+// tc: O(n*capacity) sc: O(n*capacity)
+// int solvesingMemo(int capacity, vector<int> &wt, vector<int> &profit, int i, int &n, vector<vector<int>> &dp)
+// {
+//     // base case
+//     if (i >= n)
+//     {
+//         return 0;
+//     }
+
+//     // check if already calculated
+//     if (dp[capacity][i] != -1)
+//     {
+//         return dp[capacity][i];
+//     }
+
+//     // inc/exc
+//     int inc = 0;
+//     if (wt[i] <= capacity)
+//     {
+//         inc = profit[i] + solvesingMemo(capacity - wt[i], wt, profit, i + 1, n, dp);
+//     }
+//     int exc = 0 + solvesingMemo(capacity, wt, profit, i + 1, n, dp);
+//     dp[capacity][i] = max(inc, exc);
+//     return dp[capacity][i];
+// }
+
+// tc: O(n*capacity) sc: O(n*capacity)
+// int solveUsingTabu(int capacity, vector<int> &wt, vector<int> &profit, vector<vector<int>> &dp, int &n)
+// {
+//     for (int row = 0; row <= capacity; row++)
+//     {
+//         dp[row][n] = 0;
+//     }
+
+//     for (int i = 0; i <= capacity; i++)
+//     {
+//         for (int j = n-1; j >= 0; j--)
+//         {
+//             // inc/exc
+//             int inc = 0;
+//             if (wt[j] <= i)
+//             {
+//                 inc = profit[j] + dp[i - wt[j]][j + 1];
+//             }
+//             int exc = 0 + dp[i][j + 1];
+//             dp[i][j] = max(inc, exc);
+//         }
+//     }
+//     return dp[capacity][0];
+// }
+
+// tc: O(n*capacity) sc: O(capacity)
+// int solveUsingTabuSpaceOpti(int capacity, vector<int> &wt, vector<int> &profit, int &n)
+// {
+//     vector<int> nextCol(capacity + 1, 0);
+//     vector<int> currCol(capacity + 1, -1);
+
+//     for (int j = n - 1; j >= 0; j--)
+//     {
+//         for (int i = 0; i <= capacity; i++)
+//         {
+//             // inc/exc
+//             int inc = 0;
+//             if (wt[j] <= i)
+//             {
+//                 inc = profit[j] + nextCol[i - wt[j]];
+//             }
+//             int exc = 0 + nextCol[i];
+//             currCol[i] = max(inc, exc);
+//         }
+//         nextCol = currCol;
+//     }
+//     return currCol[capacity];
+// }
+
+// tc: O(n*capacity) sc: O(capacity)
+int solveUsingTabuSpaceOpti2(int capacity, vector<int> &wt, vector<int> &profit, int &n)
+{
+    vector<int> nextCol(capacity + 1, 0);
+    // vector<int> currCol(capacity + 1, -1);
+
+    for (int j = n - 1; j >= 0; j--)
+    {
+        for (int i = capacity; i >= 0; i--)
+        {
+            // inc/exc
+            int inc = 0;
+            if (wt[j] <= i)
+            {
+                inc = profit[j] + nextCol[i - wt[j]];
+            }
+            int exc = 0 + nextCol[i];
+            nextCol[i] = max(inc, exc);
+        }
+        
+    }
+    return nextCol[capacity];
+}
+
+int knapsack(vector<int> weight, vector<int> profit, int n, int capacity)
+{
+    int i = 0;
+    // return solvesingRecursion(capacity, weight, profit, i, n);
+    vector<vector<int>> dp(capacity + 1, vector<int>(n + 1, -1));
+    // return solveUsingMemo(capacity, weight, profit, i, n, dp);
+    // int ans = solveUsingTabu(capacity, weight, profit, dp, n);
+    // int ans = solveUsingTabuSpaceOpti(capacity, weight, profit, n);
+    int ans = solveUsingTabuSpaceOpti2(capacity, weight, profit, n);
+    cout << "DP table:" << endl;
+    print(dp);
+    cout << endl;
+    cout << "Max profit:" << endl;
+    return ans;
+}
+
+int main()
+{
+    vector<int> weight = {1, 2, 3};
+    vector<int> profit = {10, 15, 40};
+    int n = weight.size();
+    int capacity = 6;
+    cout << knapsack(weight, profit, n, capacity) << endl;
+    return 0;
+}