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47 lines
1.3 KiB
47 lines
1.3 KiB
4 months ago
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# 一个正整数有可能可以被表示为n（n≥2）个连续的正整数之和，如n=15时，
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# 15=1+2+3+4+5
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# 15=4+5+6
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# 15=7+8
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# 请编写算法，根据输入的任何一个正整数，找出符合这种要求的所有连续正整数序列。
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# 需要找到所有可能的连续正整数序列，这些序列的和等于给定的正整数 N 。
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# 考虑到一个连续的正整数序列 a, a+1, a+2, ..., a+(k-1) ，和可以表示为：
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#
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# S = a + (a + 1) + (a + 2) + ... + (a + k - 1)
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#
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# 简化为：
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#
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# S = k * a + (k*(k - 1)) / 2
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#
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# S 是给定的正整数 N，a 是序列的起始数，k 是序列中的项数。
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#
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# 所以有：
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#
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# N = k * a + (k*(k - 1)) / 2
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#
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# 即：
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#
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# 2N = k * (2a + k - 1)
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#
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# 为了找到所有满足条件的序列，从 2 开始遍历可能的 k 值，直到 k*(k-1) < 2N为止，检查是否有整数 a 使得上面的等式成立。
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def find_consecutive_sequences(N):
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result = []
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k = 2
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while k * (k - 1) < 2 * N:
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if (2 * N - k * (k - 1)) % (2 * k) == 0:
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a = (2 * N - k * (k - 1)) // (2 * k)
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sequence = [a + i for i in range(k)]
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result.append(sequence)
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k += 1
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return result
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N = 15
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sequences = find_consecutive_sequences(N)
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for seq in sequences:
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print(seq)
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