Atcoder ABC179
这期的题都可以用py写
C - A x B + C
因为N非常大，暴力是不可取的
遍历C，将N-C分解求每个数的因子个数
可以用欧拉筛的方法，我这里采用了积性函数的性质
# -*- 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(100010)
def main():
items = sys.version.split()
fp = open("in.txt") if items[0] == "3.10.6" else sys.stdin
n = int(fp.readline())
f = [0] * (n + 1)
f[1] = 1
for i in range(2, n + 1):
t = i
for j in range(2, n):
c = 0
while t % j == 0:
c += 1
t //= j
if c > 0:
f[i] = f[t] * (c + 1)
break
if j * j > i:
break
if i == t:
f[i] = 2
ans = sum(f[1: n])
print(ans)
if __name__ == "__main__":
main()
D - Leaping Tak
f ( n ) = f ( n − l ) + f ( n − l + 1 ) + . . . . f ( n − r ) f(n)=f(n-l)+f(n -l+1)+....f(n-r) f(n)=f(n−l)+f(n−l+1)+....f(n−r)
前缀数组加速
# -*- 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(100010)
def main():
items = sys.version.split()
fp = open("in.txt") if items[0] == "3.10.6" else sys.stdin
n, m = map(int, fp.readline().split())
a = []
for _ in range(m):
a.append(list(map(int, fp.readline().split())))
f = [0] * n
s = [0] * (n + 1)
f[0] = 1
s[0] = 0
s[1] = 1
mod = 998244353
for i in range(1, n):
for l, r in a:
sl, sr = i - r, i - l
sl = max(0, sl)
if sr >= 0:
f[i] += s[sr + 1] - s[sl]
f[i] %= mod
s[i + 1] = (s[i] + f[i]) % mod
print(f[n - 1])
if __name__ == "__main__":
main()
E - Sequence Sum
找循环节啦。。四年级数奥题
# -*- 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(100010)
def main():
items = sys.version.split()
fp = open("in.txt") if items[0] == "3.10.6" else sys.stdin
n, x, m = map(int, fp.readline().split())
h = {x: 0}
seq = [x]
rep = -1
while True:
x = x * x % m
if x in h:
rep = h[x]
break
h[x] = len(seq)
seq.append(x)
l = len(seq)
if n <= l:
print(sum(seq[:n]))
return
loop = l - rep
ans = sum(seq[:rep])
t, r = (n - rep) // loop, (n - rep) % loop
ans += sum(seq[rep:]) * t + sum(seq[rep: rep + r])
print(ans)
if __name__ == "__main__":
main()
F - Simplified Reversi
动手画一画就知道，线段树的入门题
区间更新，单点查询最小值
# -*- 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(100010)
row, col = [], []
mark_r, mark_c = [], []
def push_down(op, idx):
if op == 1:
a, mark_a = row, mark_r
else:
a, mark_a = col, mark_c
if mark_a[idx] == 1e9:
return
a[idx * 2] = min(a[idx * 2], mark_a[idx])
a[idx * 2 + 1] = min(a[idx * 2 + 1], mark_a[idx])
mark_a[idx * 2] = min(mark_a[idx * 2], mark_a[idx])
mark_a[idx * 2 + 1] = min(mark_a[idx * 2 + 1], mark_a[idx])
mark_a[idx] = 1e9
def update(op, L, R, l, r, idx, val):
if op == 1:
a, mark_a = row, mark_r
else:
a, mark_a = col, mark_c
if L <= l and r <= R:
a[idx] = min(a[idx], val)
mark_a[idx] = min(a[idx], val)
return
push_down(op, idx)
m = (l + r) >> 1
if L <= m:
update(op, L, R, l, m, idx * 2, val)
if m < R:
update(op, L, R, m + 1, r, idx * 2 + 1, val)
def query(op, l, r, x, idx):
if op == 1:
a, mark_a = row, mark_r
else:
a, mark_a = col, mark_c
if l == r:
return a[idx]
push_down(op, idx)
m = (l + r) >> 1
if x <= m:
return query(op, l, m, x, idx * 2)
else:
return query(op, m + 1, r, x, idx * 2 + 1)
def main():
items = sys.version.split()
fp = open("in.txt") if items[0] == "3.10.6" else sys.stdin
n, q = map(int, fp.readline().split())
global row, col, mark_r, mark_c
row = [n] * (n << 2)
col = [n] * (n << 2)
mark_r = [1e9] * (n << 2)
mark_c = [1e9] * (n << 2)
tot_w = (n - 2) * (n - 2)
for _ in range(q):
op, b = map(int, fp.readline().split())
op -= 1
pos = query(1 - op, 1, n, b, 1)
tot_w -= pos - 2
update(op, 1, pos, 1, n, 1, b)
print(tot_w)
if __name__ == "__main__":
main()