Backtracking: Dynamic solution first working version

Backtracking/cs412_rockets_dynamic.py

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+"""
+name: Nicholas Tamassia
+
+Honor Code and Acknowledgments:
+
+        This work complies with the JMU Honor Code.
+
+       Comments here on your code and submission.
+"""
+
+
+def construct(sections: list[int], target: int) -> list[tuple[int, int]]:
+    s: list[int] = sorted(sections, reverse=True)
+    n: int = len(s)
+
+    IMPOSSIBLE: int = target + 1
+
+    memo: list[list[int]] = [([IMPOSSIBLE] * (target + 1)) for _ in range(0, n + 1)]
+
+    for i in range(n + 1):
+        memo[i][0] = 0
+
+    for i in range(n - 1, -1, -1):
+        for t in range(1, target + 1):
+            skip: int = memo[i + 1][t]
+
+            t_new: int = t - s[i]
+            use: int = memo[i][t_new] + 1 if t_new >= 0 else IMPOSSIBLE
+
+            memo[i][t] = min(skip, use)
+
+    total_sections: list[int] = [0] * n
+
+    i, t = 0, target
+
+    while i < n or t > 0:
+        skipped: int = memo[i + 1][t]
+
+        t_new2: int = t - s[i]
+        used: int = memo[i][t_new2] + 1 if t_new2 >= 0 else IMPOSSIBLE
+
+        if used <= skipped:
+            total_sections[i] += 1
+            t -= s[i]
+        else:
+            i += 1
+
+    return list(zip(s, total_sections))
+
+
+# All modules for CS 412 must include a main method that allows it
+# to imported and invoked from other python scripts
+def main():
+    sections: list[int] = list(map(int, input().split()))
+    target: int = int(input())
+
+    best_sections: list[tuple[int, int]] = construct(sections, target)
+    total: int = 0
+
+    for i, n in sorted(best_sections):
+        total += n
+        print(f"{n} of length {i}")
+
+    print(f"{total} rocket sections minimum")
+
+
+if __name__ == "__main__":
+    main()