From a9f906208016817c05f9daf660f7bd4823951c0d Mon Sep 17 00:00:00 2001
From: bharath-123 <vedabharath12345@gmail.com>
Date: Mon, 23 Jul 2018 00:36:53 +0530
Subject: [PATCH 1/2] Added code for memory function implementation

Added a function which implements knapsack using memory functions. Also I updated the test cases to include test cases for the memory function implementation.
---
 dynamic_programming/knapsack.py | 28 ++++++++++++++++++++++++++++
 1 file changed, 28 insertions(+)

diff --git a/dynamic_programming/knapsack.py b/dynamic_programming/knapsack.py
index a1e4f0d80..a0b006a58 100644
--- a/dynamic_programming/knapsack.py
+++ b/dynamic_programming/knapsack.py
@@ -1,6 +1,21 @@
 """
 Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack.
 """
+def MF_knapsack(i,wt,val,j):
+    '''
+    This code involves the concept of memory functions. Here we solve the subproblems which are needed
+    unlike the below example
+    F is a 2D array with -1s filled up
+    '''
+    global F  # a global dp table for knapsack
+    if F[i][j] < 0:
+        if j < wt[i - 1]:
+            val = MF_knapsack(i - 1,wt,val,j)
+        else:
+            val = max(MF_knapsack(i - 1,wt,val,j),MF_knapsack(i - 1,wt,val,j - wt[i - 1]) + val[i - 1])
+        F[i][j] = val
+    return F[i][j]
+
 def knapsack(W, wt, val, n):
     dp = [[0 for i in range(W+1)]for j in range(n+1)]
 
@@ -12,3 +27,16 @@ def knapsack(W, wt, val, n):
                 dp[i][w] = dp[i-1][w]
 
     return dp[n][w]
+
+if name == '__main__':
+    '''
+    Adding test case for knapsack
+    '''
+    val = [3,2,4,4]
+    wt = [4,3,2,3]
+    n = 4
+    w = 6
+    F = [[0]*(w + 1)] + [[0] + [-1 for i in range(w + 1)] for j in range(n + 1)]
+    print(knapsack(w,wt,val,n))
+    print(MF_knapsack(n,wt,val,w))  # switched the n and w 
+    

From bd7054ace9404dec5116cd858b72eb3d1cad2b16 Mon Sep 17 00:00:00 2001
From: bharath-123 <vedabharath12345@gmail.com>
Date: Mon, 23 Jul 2018 13:01:02 +0530
Subject: [PATCH 2/2] updated testcase

Changed name to __name__. Sorry for the typo!
---
 dynamic_programming/knapsack.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/dynamic_programming/knapsack.py b/dynamic_programming/knapsack.py
index a0b006a58..27d1cfed7 100644
--- a/dynamic_programming/knapsack.py
+++ b/dynamic_programming/knapsack.py
@@ -28,7 +28,7 @@ def knapsack(W, wt, val, n):
 
     return dp[n][w]
 
-if name == '__main__':
+if __name__ == '__main__':
     '''
     Adding test case for knapsack
     '''