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HW2_KnapSack/.idea/.gitignore

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+# Default ignored files
+/workspace.xml

HW2_KnapSack/.idea/HW2_KnapSack.iml

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+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="inheritedJdk" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+  <component name="TestRunnerService">
+    <option name="PROJECT_TEST_RUNNER" value="Unittests" />
+  </component>
+</module>

HW2_KnapSack/.idea/inspectionProfiles/profiles_settings.xml

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+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="PROJECT_PROFILE" />
+  </settings>
+</component>

HW2_KnapSack/.idea/misc.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="JavaScriptSettings">
+    <option name="languageLevel" value="ES6" />
+  </component>
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.7" project-jdk-type="Python SDK" />
+</project>

HW2_KnapSack/.idea/modules.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/HW2_KnapSack.iml" filepath="$PROJECT_DIR$/.idea/HW2_KnapSack.iml" />
+    </modules>
+  </component>
+</project>

HW2_KnapSack/.idea/vcs.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="$PROJECT_DIR$/.." vcs="Git" />
+    <mapping directory="$PROJECT_DIR$/metapensiero.pj" vcs="Git" />
+  </component>
+</project>

HW2_KnapSack/simpleKnapsack.py

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+import time
+import matplotlib.pyplot as plt
+from random import random, randint
+import numpy as np
+
+
+def knapsackBool(i, size):
+    # knapsack is full
+    if(size == 0):
+        return True;
+    #over full
+    if(size < 0):
+        return False;
+    # no more objects
+    if(i == 0):
+        return knapsackBool(i-1, size) or knapsackBool(i-1, size -S[i])
+
+
+def modifiedKnapsack(i, k1, k2):
+    if(i == 0):
+        return 0
+    if((k2-S[i]<0) and (k1-S[i]<0)) :
+        return modifiedKnapsack(i-1, k1, k2)
+    if(i == 1):
+        return V[i]
+    if(k1 -S[i]>=0):
+        return max(modifiedKnapsack(i-1,k1,k2), modifiedKnapsack(i-1, k1-S[i],k2) + V[i])
+    return max(modifiedKnapsack(i-1,k1,k2), modifiedKnapsack(i-1, k1,k2-S[i]) + V[i])
+
+
+def memoKnap(i, k1, k2):
+    if(C[i][k1][k2] != None):
+        return C[i][k1][k2]
+    if(i == 0):
+        rv = 0
+    elif(i==1):
+        rv = 0
+    elif(S[i] > k2 and S[i]> k1):
+        rv = memoKnap(i-1, k1, k2)
+    elif (k1 - S[i] >= 0):
+        rv = max(memoKnap(i - 1, k1, k2), memoKnap(i - 1, k1 - S[i], k2) + V[i])
+
+    elif((k2-S[i] < 0) and (k1-S[i]<0)):
+        rv = memoKnap(i-1, k1, k2)
+    else:
+        rv = max(memoKnap(i-1, k1, k2), memoKnap(i-1,k1,k2-S[i])+V[i])
+    C[i][k1][k2] = rv
+    return rv
+
+
+def dpKnap(i, k1, k2):
+    if k1 < 0 or k2 < 0:
+        return float("-inf")
+    if array[i][k1][k2] is not None:
+        return array[i][k1][k2]
+    if i == 0:
+        array[i][k1][k2] = 0
+        return 0
+    array[i][k1][k2] = max(dpKnap(i - 1, k1, k2),dpKnap(i - 1, k1 - S[i], k2) + V[i], dpKnap(i - 1, k1, k2 - S[i]) + V[i])
+
+    return array[i][k1][k2]
+
+
+def probGen(N, aSize):
+    V = [random() for x in range(0, N+1)]
+    S = [randint(1, 2 * aSize) for x in range(0, N+1)]
+    return S, V
+
+
+K1 = 100
+K2 = 100
+N = 50
+
+_memoTime = []
+_size = []
+_dpTime = []
+
+for _ in range(0, 10):
+    C = [[[None for k in range(0, 100 + 1)] for t in range(0, 100 + 1)] for b in range(0, N+1)]
+    aSize = randint(1,2*N)
+    S, V = probGen(N, aSize)
+    memoTime = 0
+    dpTime = 0
+
+    for _ in range(1, 20):
+
+        startMemo = time.time()
+        memo = memoKnap(N, K1, K2)
+        endMemo = time.time()
+        memoTime += endMemo - startMemo
+
+        array = np.full((N + 1, K1 + 1, K2 + 1), None)
+
+        startDp = time.time()
+        dp = dpKnap(N, K1, K2)
+        endDp = time.time()
+        dpTime += endDp - startDp
+
+    _memoTime.append(memoTime)
+    _dpTime.append(dpTime)
+    _size.append(aSize)
+
+plt.plot(_size, _memoTime, color='blue', label = "Memo Knapsack")
+plt.plot(_size, _dpTime, color='red', label = "DP Knapsack")
+plt.xlabel('Average Size')
+plt.ylabel('Run Time (seconds)')
+plt.title("Memoized vs Dynamic Knapsack Run Times")
+plt.legend()
+plt.show()
+plt.savefig("test.png")
+