dynamic_programming_on_trees

DSA PYTHON/Dynamic Programming/Dynamic_Programming_on trees.py

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+# Python3 code to find the maximum path sum
+dp = [0]*100
+
+# Function for dfs traversal and
+# to store the maximum value in
+# dp[] for every node till the leaves
+def dfs(a, v, u, parent):
+
+    # Initially dp[u] is always a[u]
+    dp[u] = a[u - 1]
+
+    # Stores the maximum value from nodes
+    maximum = 0
+
+    # Traverse the tree
+    for child in v[u]:
+
+        # If child is parent, then we continue
+        # without recursing further
+        if child == parent:
+            continue
+
+        # Call dfs for further traversal
+        dfs(a, v, child, u)
+
+        # Store the maximum of previous visited 
+        # node and present visited node
+        maximum = max(maximum, dp[child])
+
+    # Add the maximum value
+    # returned to the parent node
+    dp[u] += maximum
+
+
+# Function that returns the maximum value
+def maximumValue(a, v):
+    dfs(a, v, 1, 0)
+    return dp[1]
+
+# Driver Code
+def main():
+
+    # Number of nodes
+    n = 14
+
+    # Adjacency list as a dictionary
+    v = {}
+    for i in range(n + 1):
+        v[i] = []
+
+    # Create undirected edges
+    # initialize the tree given in the diagram
+    v[1].append(2), v[2].append(1)
+    v[1].append(3), v[3].append(1)
+    v[1].append(4), v[4].append(1)
+    v[2].append(5), v[5].append(2)
+    v[2].append(6), v[6].append(2)
+    v[3].append(7), v[7].append(3)
+    v[4].append(8), v[8].append(4)
+    v[4].append(9), v[9].append(4)
+    v[4].append(10), v[10].append(4)
+    v[5].append(11), v[11].append(5)
+    v[5].append(12), v[12].append(5)
+    v[7].append(13), v[13].append(7)
+    v[7].append(14), v[14].append(7)
+
+    # Values of node 1, 2, 3....14
+    a = [ 3, 2, 1, 10, 1, 3, 9,
+          1, 5, 3, 4, 5, 9, 8 ]
+
+    # Function call
+    print(maximumValue(a, v))
+main()
+
+# This code is contributed by stutipathak31jan