教学计划-找规律

Problem 3. Spaced Out

https://usaco.org/index.php?page=viewproblem2&cpid=1088

从小规模数据开始绘制，发现要么第一行确定后，每一行与上一行相反。要么第一列确定后，每一行与上一行相反。证明：首先考虑第一行存在连续的 11 或者 00 情况

我们用 f[j][0] 表示第一行第 j 列为 0 时，整个第 j 列的收益，f[j][1] 相反。

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n = int(input())
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f = [[0, 0] for _ in range(n)]
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v = [[0, 0] for _ in range(n)]
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for i in range(n):
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    s = list(map(int, input().split()))
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    for j, x in enumerate(s):
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        f[j][(i + 1) % 2] += x
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        v[i][(j + 1) % 2] += x
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ans1 = 0
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for x, y in f:
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    ans1 += max(x, y)
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ans2 = 0
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for x, y in v:
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    ans2 += max(x, y)
1 collapsed line
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print(max(ans1, ans2))

程序填空：

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n = int(input())
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f = [[0, 0] for _ in range(n)]
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v = [[0, 0] for _ in range(n)]
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for i in range(n):
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    s = list(map(int, input().split()))
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    for j, x in enumerate(s):
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        f[___][___] += x
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        v[___][___] += x
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ans1 = 0
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for x, y in f:
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    ans1 += __
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ans2 = 0
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for x, y in v:
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    ans2 += ___
1 collapsed line
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print(max(ans1, ans2))

Problem 3. Moo Route

大胆猜测如果能不改方向就不改。往右走如果遇到剩余次数为 0 就掉头。往左走如果左边剩余次数 <= 2 且右边还有可以走的就掉头。否则就回不来了。

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n = int(input())
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a = list(map(int, input().split())) + [0]
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s = sum(a)
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p = 0
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d = 1
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for _ in range(s):
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    if (d == 1 and a[p] == 0) or (d == -1 and a[p - 1] <= 2 and a[p] > 0):
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        d = -d
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    if d == 1:
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        print("R", end='')
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        a[p] -= 1
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    else:
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        print("L", end='')
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        a[p - 1] -= 1
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    p += d

读题 + 思考

USACO 2022 December Contest, Silver

Problem 2. Circular Barn

https://usaco.org/index.php?page=viewproblem2&cpid=1255