AtCoder ABC146

最新推荐文章于 2025-12-09 19:50:25 发布

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文章讲述了在ACM竞赛中，如何运用递推（如A×N+B×d(N)的单调性）、深度优先搜索（DFS）和广度优先搜索（BFS）解决题目。还涉及动态规划、单调队列以及处理前缀和问题的技巧。

C题
可以证明 $A \times N + B \times d (N)$ 是单调递增，因此二分

# -*- coding: utf-8 -*-
# @time     : 2023/6/2 13:30
# @file     : atcoder.py
# @software : PyCharm

import bisect
import copy
import sys
from itertools import permutations
from sortedcontainers import SortedList
from collections import defaultdict, Counter, deque
from functools import lru_cache, cmp_to_key
import heapq
import math
sys.setrecursionlimit(100050)


def main():
    items = sys.version.split()
    if items[0] == '3.10.6':
        fp = open("in.txt")
    else:
        fp = sys.stdin
    n, m = map(int, fp.readline().split())
    s = fp.readline().strip()
    pre = {}
    qu = deque()
    qu.append((0, 0))
    for i in range(1, n + 1):
        while len(qu) > 0 and qu[0][1] < i - m:
            qu.popleft()
        if s[i] == '0':
            if len(qu) > 0:
                v = qu[0][0] + 1
                while len(qu) > 0:
                    if v < qu[-1][0]:
                        qu.pop()
                    else:
                        break
                pre[i] = qu[0][1]
                qu.append((v, i))
    ans = -1
    for item in qu:
        v, pos = item
        if pos == n:
            ans = v
    if ans == -1:
        print(-1)
        return
    cur = n
    a = []
    while cur != 0:
        a.append(cur - pre[cur])
        cur = pre[cur]
    a = a[::-1]
    print(*a)


if __name__ == "__main__":
    main()

D题
BFS不好写，还是要用DFS
题目比较简单，点出度最大的度数就是颜色的种类，从该点开始搜索

# -*- coding: utf-8 -*-
# @time     : 2023/6/2 13:30
# @file     : atcoder.py
# @software : PyCharm

import bisect
import copy
import sys
from itertools import permutations
from sortedcontainers import SortedList
from collections import defaultdict, Counter, deque
from functools import lru_cache, cmp_to_key
import heapq
import math
sys.setrecursionlimit(100050)


def main():
    items = sys.version.split()
    if items[0] == '3.10.6':
        fp = open("in.txt")
    else:
        fp = sys.stdin

    es = []
    n = int(fp.readline())
    g = [[] for _ in range(n)]
    m = {}
    for i in range(1, n):
        u, v = map(int, fp.readline().split())
        u, v = u - 1, v - 1
        if u > v:
            u, v = v, u
        es.append((u, v))
        g[u].append(v)
        g[v].append(u)

    root = -1
    mx = 0
    for u in range(n):
        if len(g[u]) > mx:
            mx, root = len(g[u]), u

    def dfs(node, fa, ec):
        idx = 0
        for chd in g[node]:
            if fa == chd:
                continue
            if idx == ec:
                idx += 1
            a, b = node, chd
            if a > b:
                a, b = b, a
            m[(a, b)] = idx
            dfs(chd, node, idx)
            idx += 1

    dfs(root, -1, -1)
    print(mx)
    for edge in es:
        u, v = edge
        print(m[(u, v)] + 1)


if __name__ == "__main__":
    main()

E题
本题需要列出公式
$\equiv r-(l-1)$
变形为
$\equiv S(l-1)-(l-1)$
那么设 $F (i) = S (i) - i$
然后遍历哈希就好。注意遍历到当前时有长度限制。

# -*- coding: utf-8 -*-
# @time     : 2023/6/2 13:30
# @file     : atcoder.py
# @software : PyCharm

import bisect
import copy
import sys
from itertools import permutations
from sortedcontainers import SortedList
from collections import defaultdict, Counter, deque
from functools import lru_cache, cmp_to_key
import heapq
import math
sys.setrecursionlimit(100050)


def main():
    items = sys.version.split()
    if items[0] == '3.10.6':
        fp = open("in.txt")
    else:
        fp = sys.stdin
    n, k = map(int, fp.readline().split())
    a = list(map(int, fp.readline().split()))
    s = [0] * (n + 1)

    for i in range(n):
        s[i + 1] = (s[i] + a[i]) % k
    for i in range(n + 1):
        s[i] = (s[i] - i) % k

    ct = Counter(s[:k])
    ans = 0
    for _, v in ct.items():
        ans += v * (v - 1) // 2

    for i in range(k, n + 1):
        ct[s[i - k]] -= 1
        v = s[i]
        ans += ct[v]
        ct[s[i]] += 1

    print(ans)


if __name__ == "__main__":
    main()

F题
经典模型。动态求前m个数的 $min⁡\min$ 。
比较暴力的方法是维护一个堆，但是不知道为什么一直RE，卡在第3个handmake点上。
于是改成了单调队列的方法。
维护一个单调递增的队列，队列头是 $min⁡\min$ ，在队列后面插入，如果当前的数据比队列后面的数据要小，那么那些排在前面的就没有必要维护了（因为前面的肯定比当前数据先出队列）

# -*- coding: utf-8 -*-
# @time     : 2023/6/2 13:30
# @file     : atcoder.py
# @software : PyCharm

import bisect
import copy
import sys
from itertools import permutations
from sortedcontainers import SortedList
from collections import defaultdict, Counter, deque
from functools import lru_cache, cmp_to_key
import heapq
import math
sys.setrecursionlimit(100050)


def main():
    items = sys.version.split()
    if items[0] == '3.10.6':
        fp = open("in.txt")
    else:
        fp = sys.stdin
    n, m = map(int, fp.readline().split())
    s = fp.readline().strip()
    pre = {}
    qu = deque()
    qu.append((0, 0))
    for i in range(1, n + 1):
        while len(qu) > 0 and qu[0][1] < i - m:
            qu.popleft()
        if s[i] == '0':
            if len(qu) > 0:
                v = qu[0][0] + 1
                while len(qu) > 0:
                    if v < qu[-1][0]:
                        qu.pop()
                    else:
                        break
                pre[i] = qu[0][1]
                qu.append((v, i))
    ans = -1
    for item in qu:
        v, pos = item
        if pos == n:
            ans = v
    if ans == -1:
        print(-1)
        return
    cur = n
    a = []
    while cur != 0:
        a.append(cur - pre[cur])
        cur = pre[cur]
    a = a[::-1]
    print(*a)


if __name__ == "__main__":
    main()