Add all_construct dynamic programming implementation (#5626)

* Add all_construct dynamic programming implementation

* all_construct: remove the main function

* all_construct: Add type hints

* all_construct: changed map to list comprehension,fix mutable default arguments

* all_construct: fixed type hints

* all_construct: cleaner code for initializing word_bank argument

* all_construct: added an import for annotations

* all_construct: added None in the argument with word_bank

* all_construct: fixed a type hint

* all_construct: Fixed some more type hints

dynamic_programming/all_construct.py

@@ -0,0 +1,58 @@
+"""
+Program to list all the ways a target string can be
+constructed from the given list of substrings
+"""
+from __future__ import annotations
+
+
+def all_construct(target: str, word_bank: list[str] | None = None) -> list[list[str]]:
+    """
+        returns the list containing all the possible
+        combinations a string(target) can be constructed from
+        the given list of substrings(word_bank)
+    >>> all_construct("hello", ["he", "l", "o"])
+    [['he', 'l', 'l', 'o']]
+    >>> all_construct("purple",["purp","p","ur","le","purpl"])
+    [['purp', 'le'], ['p', 'ur', 'p', 'le']]
+    """
+
+    word_bank = word_bank or []
+    # create a table
+    table_size: int = len(target) + 1
+
+    table: list[list[list[str]]] = []
+    for i in range(table_size):
+        table.append([])
+    # seed value
+    table[0] = [[]]  # because empty string has empty combination
+
+    # iterate through the indices
+    for i in range(table_size):
+        # condition
+        if table[i] != []:
+            for word in word_bank:
+                # slice condition
+                if target[i : i + len(word)] == word:
+                    new_combinations: list[list[str]] = [
+                        [word] + way for way in table[i]
+                    ]
+                    # adds the word to every combination the current position holds
+                    # now,push that combination to the table[i+len(word)]
+                    table[i + len(word)] += new_combinations
+
+    # combinations are in reverse order so reverse for better output
+    for combination in table[len(target)]:
+        combination.reverse()
+
+    return table[len(target)]
+
+
+if __name__ == "__main__":
+    print(all_construct("jwajalapa", ["jwa", "j", "w", "a", "la", "lapa"]))
+    print(all_construct("rajamati", ["s", "raj", "amat", "raja", "ma", "i", "t"]))
+    print(
+        all_construct(
+            "hexagonosaurus",
+            ["h", "ex", "hex", "ag", "ago", "ru", "auru", "rus", "go", "no", "o", "s"],
+        )
+    )