[mypy] Fix type annotations for Dynamic Programming algorithms

dynamic_programming/fractional_knapsack_2.py

@@ -7,7 +7,7 @@
 
 def fractional_knapsack(
     value: list[int], weight: list[int], capacity: int
-) -> tuple[int, list[int]]:
+) -> tuple[int, list[float]]:
     """
     >>> value = [1, 3, 5, 7, 9]
     >>> weight = [0.9, 0.7, 0.5, 0.3, 0.1]
@@ -20,7 +20,7 @@ def fractional_knapsack(
     >>> fractional_knapsack(value, weight, 26)
     (25, [1, 1, 1, 1, 1])
     >>> fractional_knapsack(value, weight, -1)
-    (-90.0, [0, 0, 0, 0, -10.0])
+    (-90, [0.0, 0.0, 0.0, 0.0, -10.0])
     >>> fractional_knapsack([1, 3, 5, 7], weight, 30)
     (16, [1, 1, 1, 1])
     >>> fractional_knapsack(value, [0.9, 0.7, 0.5, 0.3, 0.1], 30)
@@ -33,26 +33,34 @@ def fractional_knapsack(
     index.sort(key=lambda i: ratio[i], reverse=True)
 
     max_value = 0
-    fractions = [0] * len(value)
+    fractions = [0.0] * len(value)
     for i in index:
         if weight[i] <= capacity:
             fractions[i] = 1
             max_value += value[i]
             capacity -= weight[i]
         else:
-            fractions[i] = capacity / weight[i]
-            max_value += value[i] * capacity / weight[i]
+            fractions[i] = round(capacity / weight[i], 2)
+            max_value += round(value[i] * capacity / weight[i])
             break
 
     return max_value, fractions
 
 
 if __name__ == "__main__":
     n = int(input("Enter number of items: "))
-    value = input(f"Enter the values of the {n} item(s) in order: ").split()
-    value = [int(v) for v in value]
-    weight = input(f"Enter the positive weights of the {n} item(s) in order: ".split())
-    weight = [int(w) for w in weight]
+    value = [
+        int(v)
+        for v in input(f"Enter the values of the {n} item(s) in order: ")
+        .strip()
+        .split()
+    ]
+    weight = [
+        int(w)
+        for w in input(f"Enter the positive weights of the {n} item(s) in order: ")
+        .strip()
+        .split()
+    ]
     capacity = int(input("Enter maximum weight: "))
 
     max_value, fractions = fractional_knapsack(value, weight, capacity)

dynamic_programming/knapsack.py

@@ -91,7 +91,7 @@ def knapsack_with_example_solution(W: int, wt: list, val: list):
             )
 
     optimal_val, dp_table = knapsack(W, wt, val, num_items)
-    example_optional_set = set()
+    example_optional_set: set[int] = set()
     _construct_solution(dp_table, wt, num_items, W, example_optional_set)
 
     return optimal_val, example_optional_set

dynamic_programming/longest_increasing_subsequence.py

@@ -36,7 +36,7 @@ def longest_subsequence(array: list[int]) -> list[int]:  # This function is recu
     pivot = array[0]
     isFound = False
     i = 1
-    longest_subseq = []
+    longest_subseq: list[int] = []
     while not isFound and i < array_length:
         if array[i] < pivot:
             isFound = True