タプルの中の配列の連続した合計値を算出したい

Question

タプルの中の配列の連続した合計値を算出したいです。

total_ans =[ ( sum( [ dict( zip( a, b ) )[v] for i, v in enumerate(x) if i > a.index( v ) ] ), list(x) ) for x in permutations( a ) ]
print(total_ans)

と書いて実行したら

[(0, [2, 5, 7, 3, 6]), (8, [2, 5, 7, 6, 3]), (6, [2, 5, 3, 7, 6]), (6, [2, 5, 3, 6, 7]), (14, [2, 5, 6, 7, 3]), (6, [2, 5, 6, 3, 7]), (3, [2, 7, 5, 3, 6]), (11, [2, 7, 5, 6, 3]), (3, [2, 7, 3, 5, 6]), (3, [2, 7, 3, 6, 5]), (11, [2, 7, 6, 5, 3]), (3, [2, 7, 6, 3, 5]), (9, [2, 3, 5, 7, 6]), (9, [2, 3, 5, 6, 7]), (3, [2, 3, 7, 5, 6]), (3, [2, 3, 7, 6, 5]), (9, [2, 3, 6, 5, 7]), (9, [2, 3, 6, 7, 5]), (17, [2, 6, 5, 7, 3]), (9, [2, 6, 5, 3, 7]), (11, [2, 6, 7, 5, 3]), (3, [2, 6, 7, 3, 5]), (9, [2, 6, 3, 5, 7]), (9, [2, 6, 3, 7, 5]), (1, [5, 2, 7, 3, 6]), (9, [5, 2, 7, 6, 3]), (7, [5, 2, 3, 7, 6]), (7, [5, 2, 3, 6, 7]), (15, [5, 2, 6, 7, 3]), (7, [5, 2, 6, 3, 7]), (1, [5, 7, 2, 3, 6]), (9, [5, 7, 2, 6, 3]), (1, [5, 7, 3, 2, 6]), (1, [5, 7, 3, 6, 2]), (9, [5, 7, 6, 2, 3]), (1, [5, 7, 6, 3, 2]), (7, [5, 3, 2, 7, 6]), (7, [5, 3, 2, 6, 7]), (1, [5, 3, 7, 2, 6]), (1, [5, 3, 7, 6, 2]), (7, [5, 3, 6, 2, 7]), (7, [5, 3, 6, 7, 2]), (15, [5, 6, 2, 7, 3]), (7, [5, 6, 2, 3, 7]), (9, [5, 6, 7, 2, 3]), (1, [5, 6, 7, 3, 2]), (7, [5, 6, 3, 2, 7]), (7, [5, 6, 3, 7, 2]), (4, [7, 2, 5, 3, 6]), (12, [7, 2, 5, 6, 3]), (4, [7, 2, 3, 5, 6]), (4, [7, 2, 3, 6, 5]), (12, [7, 2, 6, 5, 3]), (4, [7, 2, 6, 3, 5]), (1, [7, 5, 2, 3, 6]), (9, [7, 5, 2, 6, 3]), (1, [7, 5, 3, 2, 6]), (1, [7, 5, 3, 6, 2]), (9, [7, 5, 6, 2, 3]), (1, [7, 5, 6, 3, 2]), (4, [7, 3, 2, 5, 6]), (4, [7, 3, 2, 6, 5]), (4, [7, 3, 5, 2, 6]), (4, [7, 3, 5, 6, 2]), (4, [7, 3, 6, 2, 5]), (4, [7, 3, 6, 5, 2]), (12, [7, 6, 2, 5, 3]), (4, [7, 6, 2, 3, 5]), (12, [7, 6, 5, 2, 3]), (4, [7, 6, 5, 3, 2]), (4, [7, 6, 3, 2, 5]), (4, [7, 6, 3, 5, 2]), (10, [3, 2, 5, 7, 6]), (10, [3, 2, 5, 6, 7]), (4, [3, 2, 7, 5, 6]), (4, [3, 2, 7, 6, 5]), (10, [3, 2, 6, 5, 7]), (10, [3, 2, 6, 7, 5]), (7, [3, 5, 2, 7, 6]), (7, [3, 5, 2, 6, 7]), (1, [3, 5, 7, 2, 6]), (1, [3, 5, 7, 6, 2]), (7, [3, 5, 6, 2, 7]), (7, [3, 5, 6, 7, 2]), (4, [3, 7, 2, 5, 6]), (4, [3, 7, 2, 6, 5]), (4, [3, 7, 5, 2, 6]), (4, [3, 7, 5, 6, 2]), (4, [3, 7, 6, 2, 5]), (4, [3, 7, 6, 5, 2]), (10, [3, 6, 2, 5, 7]), (10, [3, 6, 2, 7, 5]), (10, [3, 6, 5, 2, 7]), (10, [3, 6, 5, 7, 2]), (4, [3, 6, 7, 2, 5]), (4, [3, 6, 7, 5, 2]), (18, [6, 2, 5, 7, 3]), (10, [6, 2, 5, 3, 7]), (12, [6, 2, 7, 5, 3]), (4, [6, 2, 7, 3, 5]), (10, [6, 2, 3, 5, 7]), (10, [6, 2, 3, 7, 5]), (15, [6, 5, 2, 7, 3]), (7, [6, 5, 2, 3, 7]), (9, [6, 5, 7, 2, 3]), (1, [6, 5, 7, 3, 2]), (7, [6, 5, 3, 2, 7]), (7, [6, 5, 3, 7, 2]), (12, [6, 7, 2, 5, 3]), (4, [6, 7, 2, 3, 5]), (12, [6, 7, 5, 2, 3]), (4, [6, 7, 5, 3, 2]), (4, [6, 7, 3, 2, 5]), (4, [6, 7, 3, 5, 2]), (10, [6, 3, 2, 5, 7]), (10, [6, 3, 2, 7, 5]), (10, [6, 3, 5, 2, 7]), (10, [6, 3, 5, 7, 2]), (4, [6, 3, 7, 2, 5]), (4, [6, 3, 7, 5, 2])]

と出力されました。
この

(0, [2, 5, 7, 3, 6]), (8, [2, 5, 7, 6, 3]), (6, [2, 5, 3, 7, 6]), (6, [2, 5, 3, 6, 7]), (14, [2, 5, 6, 7, 3])・・・

と続くタプル（配列？）の[2, 5, 7, 3, 6]、[2, 5, 7, 6, 3]、[2, 5, 3, 7, 6]、[2, 5, 3, 6, 7]、[2, 5, 6, 7, 3]の連続した合計値を算出したいです。
ただし、”合計値”と書いていますがただの合計値ではなく
例えばa=[2, 5, 7, 3, 6] とすると
a[0]+(a[0]+a[1])+(a[0]+a[1]+a[2])+(a[0]+a[1]+a[2]+a[3])+(a[0]+a[1]+a[2]+a[3]+a[4])=63 のような配列の要素の連続の合計値を算出したいです。

なので理想のアウトプットは

(0, [63]),・・・

のような形です。

total_ans =[ ( sum( [ dict( zip( a, b ) )[v] for i, v in enumerate(x) if i > a.index( v ) ] ), list(x) ) for x in permutations( a ) ]
x2= sorted(total_ans.items(), key=lambda x: x[1])
print(x2)

までコードを実装したのですが
連続した合計値を算出する方法の実装がわかりません。
どのように書けますか？

Answer 1

いま欲しいのは [2, 5, 7, 3, 6] → 63 をする方法です。

In [1]: x = [2, 5, 7, 3, 6]

In [2]: list(range(1, len(x) + 1))
Out[2]: [1, 2, 3, 4, 5]

In [3]: [x[:i] for i in range(1, len(x) + 1)]
Out[3]: [[2], [2, 5], [2, 5, 7], [2, 5, 7, 3], [2, 5, 7, 3, 6]]

In [4]: [sum(x[:i]) for i in range(1, len(x) + 1)]
Out[4]: [2, 7, 14, 17, 23]

In [5]: sum(sum(x[:i]) for i in range(1, len(x) + 1))
Out[5]: 63

という具合に欲しいものに向かって変形していって、欲しい式を得ます。

def sum_of_sum_of_sub_sequence(x):
    return sum(sum(x[:i]) for i in range(1, len(x) + 1))

と関数化します。

total_ans = [(0, [2, 5, 7, 3, 6]), (8, [2, 5, 7, 6, 3]), (6, [2, 5, 3, 7, 6]), (6, [2, 5, 3, 6, 7]), (14, [2, 5, 6, 7, 3]), (6, [2, 5, 6, 3, 7]), (3, [2, 7, 5, 3, 6]), (11, [2, 7, 5, 6, 3]), (3, [2, 7, 3, 5, 6]), (3, [2, 7, 3, 6, 5]), (11, [2, 7, 6, 5, 3]), (3, [2, 7, 6, 3, 5]), (9, [2, 3, 5, 7, 6]), (9, [2, 3, 5, 6, 7]), (3, [2, 3, 7, 5, 6]), (3, [2, 3, 7, 6, 5]), (9, [2, 3, 6, 5, 7]), (9, [2, 3, 6, 7, 5]), (17, [2, 6, 5, 7, 3]), (9, [2, 6, 5, 3, 7]), (11, [2, 6, 7, 5, 3]), (3, [2, 6, 7, 3, 5]), (9, [2, 6, 3, 5, 7]), (9, [2, 6, 3, 7, 5]), (1, [5, 2, 7, 3, 6]), (9, [5, 2, 7, 6, 3]), (7, [5, 2, 3, 7, 6]), (7, [5, 2, 3, 6, 7]), (15, [5, 2, 6, 7, 3]), (7, [5, 2, 6, 3, 7]), (1, [5, 7, 2, 3, 6]), (9, [5, 7, 2, 6, 3]), (1, [5, 7, 3, 2, 6]), (1, [5, 7, 3, 6, 2]), (9, [5, 7, 6, 2, 3]), (1, [5, 7, 6, 3, 2]), (7, [5, 3, 2, 7, 6]), (7, [5, 3, 2, 6, 7]), (1, [5, 3, 7, 2, 6]), (1, [5, 3, 7, 6, 2]), (7, [5, 3, 6, 2, 7]), (7, [5, 3, 6, 7, 2]), (15, [5, 6, 2, 7, 3]), (7, [5, 6, 2, 3, 7]), (9, [5, 6, 7, 2, 3]), (1, [5, 6, 7, 3, 2]), (7, [5, 6, 3, 2, 7]), (7, [5, 6, 3, 7, 2]), (4, [7, 2, 5, 3, 6]), (12, [7, 2, 5, 6, 3]), (4, [7, 2, 3, 5, 6]), (4, [7, 2, 3, 6, 5]), (12, [7, 2, 6, 5, 3]), (4, [7, 2, 6, 3, 5]), (1, [7, 5, 2, 3, 6]), (9, [7, 5, 2, 6, 3]), (1, [7, 5, 3, 2, 6]), (1, [7, 5, 3, 6, 2]), (9, [7, 5, 6, 2, 3]), (1, [7, 5, 6, 3, 2]), (4, [7, 3, 2, 5, 6]), (4, [7, 3, 2, 6, 5]), (4, [7, 3, 5, 2, 6]), (4, [7, 3, 5, 6, 2]), (4, [7, 3, 6, 2, 5]), (4, [7, 3, 6, 5, 2]), (12, [7, 6, 2, 5, 3]), (4, [7, 6, 2, 3, 5]), (12, [7, 6, 5, 2, 3]), (4, [7, 6, 5, 3, 2]), (4, [7, 6, 3, 2, 5]), (4, [7, 6, 3, 5, 2]), (10, [3, 2, 5, 7, 6]), (10, [3, 2, 5, 6, 7]), (4, [3, 2, 7, 5, 6]), (4, [3, 2, 7, 6, 5]), (10, [3, 2, 6, 5, 7]), (10, [3, 2, 6, 7, 5]), (7, [3, 5, 2, 7, 6]), (7, [3, 5, 2, 6, 7]), (1, [3, 5, 7, 2, 6]), (1, [3, 5, 7, 6, 2]), (7, [3, 5, 6, 2, 7]), (7, [3, 5, 6, 7, 2]), (4, [3, 7, 2, 5, 6]), (4, [3, 7, 2, 6, 5]), (4, [3, 7, 5, 2, 6]), (4, [3, 7, 5, 6, 2]), (4, [3, 7, 6, 2, 5]), (4, [3, 7, 6, 5, 2]), (10, [3, 6, 2, 5, 7]), (10, [3, 6, 2, 7, 5]), (10, [3, 6, 5, 2, 7]), (10, [3, 6, 5, 7, 2]), (4, [3, 6, 7, 2, 5]), (4, [3, 6, 7, 5, 2]), (18, [6, 2, 5, 7, 3]), (10, [6, 2, 5, 3, 7]), (12, [6, 2, 7, 5, 3]), (4, [6, 2, 7, 3, 5]), (10, [6, 2, 3, 5, 7]), (10, [6, 2, 3, 7, 5]), (15, [6, 5, 2, 7, 3]), (7, [6, 5, 2, 3, 7]), (9, [6, 5, 7, 2, 3]), (1, [6, 5, 7, 3, 2]), (7, [6, 5, 3, 2, 7]), (7, [6, 5, 3, 7, 2]), (12, [6, 7, 2, 5, 3]), (4, [6, 7, 2, 3, 5]), (12, [6, 7, 5, 2, 3]), (4, [6, 7, 5, 3, 2]), (4, [6, 7, 3, 2, 5]), (4, [6, 7, 3, 5, 2]), (10, [6, 3, 2, 5, 7]), (10, [6, 3, 2, 7, 5]), (10, [6, 3, 5, 2, 7]), (10, [6, 3, 5, 7, 2]), (4, [6, 3, 7, 2, 5]), (4, [6, 3, 7, 5, 2])]
[(i, [sum_of_sum_of_sub_sequence(x)]) for i, x in total_ans]

と適用します。

In [8]: [(i, [sum_of_sum_of_sub_sequence(x)]) for i, x in total_ans]
Out[8]:
[(0, [63]),
 (8, [66]),
 (6, [59]),
 (6, [58]),
 (14, [65]),
 (6, [61]),
 (3, [65]),
 (11, [68]),
【略】

を得ます。