【python/アルゴリズム】競プロ頻出アルゴリズムライブラリ一覧

共通

import sys
import bisect
import itertools
import collections
import fractions
import heapq
import math
from operator import mul
from functools import reduce
from functools import lru_cache


def solve():
    input = sys.stdin.readline
    mod = 10 ** 9 + 7
    


if __name__ == '__main__':
    solve()

これ以降のライブラリはこの共通テンプレを前提のコードとなっています。

共通テンプレを使わない場合には、適宜import等を記述する必要があります。

標準入力

整数

1行

 = int(input().rstrip('\n'))

1行リスト

 = list(map(int, input().rstrip('\n').split()))

複数行

 = [int(input().rstrip('\n')) for _ in range()]

複数行リスト

 = [list(map(int, input().rstrip('\n').split())) for _ in range()]

文字列

1行

 = str(input().rstrip('\n'))

1行リスト

 = list(map(str, str(input().rstrip('\n')).split()))

複数行

 = [str(input().rstrip('\n')) for _ in range()]

複数行リスト

 = [list(map(int, input().rstrip('\n').split())) for _ in range()]

幅優先探索（BFS）

グリッド

h, w = list(map(int, input().rstrip('\n').split()))

#スタートを設定
ql = [[0, ]]
ql = collections.deque(ql)
fq = collections.defaultdict(list)
#スタートを設定
fq[]
while True:
    if len(ql) != 0:
        cost, yv, xv = ql.popleft()
        for yv, xv in [[yv + 1, xv], [yv - 1, xv], [yv, xv + 1], [yv, xv - 1]]:
            if 0 <= yv < h and 0 <= xv < w:
                if (yv, xv) not in fq:
                    ql.append([cost + 1, yv, xv])
                    fq[yv, xv]
    else:
        break

ツリー

mpl = collections.defaultdict(list)
#経路情報の数を設定
for i in range():
    mpa, mpb = list(map(int, input().rstrip('\n').split()))
    mpl[mpa-1] += [mpb-1]
    mpl[mpb-1] += [mpa-1]

#スタートを設定
ql = [[0, ]]
ql = collections.deque(ql)
fq = collections.defaultdict(list)
#スタートを設定
fq[]
while True:
    if len(ql) != 0:
        cost, tmp = ql.popleft()
        for tmn in mpl[tmp]:
            if tmn not in fq:
                ql.append([cost + 1, tmn])
                fq[tmn]
    else:
        break

Union-Find

class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

セグメントツリー

基本

class SegmentTree:
    def __init__(self, size, f=lambda x, y: x + y, default=0):
        self.size = 2 ** (size - 1).bit_length()
        self.default = default
        self.dat = [default] * (self.size * 2)
        self.f = f

    def update(self, i, x):
        i += self.size
        self.dat[i] = x
        while i > 0:
            i >>= 1
            self.dat[i] = self.f(self.dat[i * 2], self.dat[i * 2 + 1])

    def query(self, left, right):
        left += self.size
        right += self.size
        left_res, right_res = self.default, self.default
        while left < right:
            if left & 1:
                left_res = self.f(left_res, self.dat[left])
                left += 1

            if right & 1:
                right -= 1
                right_res = self.f(self.dat[right], right_res)
            left >>= 1
            right >>= 1
        res = self.f(left_res, right_res)
        return res

遅延評価　範囲変更

class AlgSegmentTreeRangeUpdate:
    def __init__(self, size, f=lambda x, y: min(x, y), default=2 ** 31 - 1):
        self.size = (size - 1).bit_length()
        self.no = 2 ** self.size
        self.default = default
        self.data = [default] * (self.no * 2)
        self.lazy = [None] * (self.no * 2)
        self.f = f

    def get_index(self, left, right):
        l_left = (left + self.no) >> 1
        r_right = (right + self.no) >> 1
        lc = 0 if left & 1 else (l_left & -l_left).bit_length()
        rc = 0 if right & 1 else (r_right & -r_right).bit_length()
        for i in range(self.size):
            if rc <= i:
                yield r_right
            if l_left < r_right and lc <= i:
                yield l_left
            l_left >>= 1
            r_right >>= 1

    def propagates(self, *ids):
        for i in reversed(ids):
            v = self.lazy[i - 1]
            if v is None:
                continue
            self.lazy[2 * i - 1] = v
            self.data[2 * i - 1] = v
            self.lazy[2 * i] = v
            self.data[2 * i] = v
            self.lazy[i - 1] = None

    def update(self, left, right, x):
        *ids, = self.get_index(left, right)
        self.propagates(*ids)
        l_left = self.no + left
        r_right = self.no + right
        while l_left < r_right:
            if r_right & 1:
                r_right -= 1
                self.lazy[r_right - 1] = x
                self.data[r_right - 1] = x
            if l_left & 1:
                self.lazy[l_left - 1] = x
                self.data[l_left - 1] = x
                l_left += 1
            l_left >>= 1
            r_right >>= 1
        for i in ids:
            self.data[i - 1] = self.f(self.data[2 * i - 1], self.data[2 * i])

    def query(self, left, right):
        self.propagates(*self.get_index(left, right))
        l_left = self.no + left
        r_right = self.no + r

        res = self.default
        while l_left < r_right:
            if r_right & 1:
                r_right -= 1
                res = self.f(res, self.data[r_right - 1])
            if l_left & 1:
                res = self.f(res, self.data[l_left - 1])
                l_left += 1
            l_left >>= 1
            r_right >>= 1
        return res

遅延評価　範囲加算

class SegmentTreeRangeAdd:
    def __init__(self, size, f=lambda x, y: min(x, y), default=2 ** 31 - 1):
        self.size = (size - 1).bit_length()
        self.no = 2 ** self.size
        self.default = default
        self.data = [default] * (self.no * 2)
        self.lazy = [None] * (self.no * 2)
        self.f = f

    def get_index(self, left, right):
        l_left = (left + self.no) >> 1
        r_right = (right + self.no) >> 1
        lc = 0 if left & 1 else (l_left & -l_left).bit_length()
        rc = 0 if right & 1 else (r_right & -r_right).bit_length()
        for i in range(self.size):
            if rc <= i:
                yield r_right
            if l_left < r_right and lc <= i:
                yield l_left
            l_left >>= 1
            r_right >>= 1

    def propagates(self, *ids):
        for i in reversed(ids):
            v = self.lazy[i - 1]
            if v is None:
                continue
            self.lazy[2 * i - 1] += v
            self.data[2 * i - 1] += v
            self.lazy[2 * i] += v
            self.data[2 * i] += v
            self.lazy[i - 1] = 0

    def update(self, left, right, x):
        *ids, = self.get_index(left, right)
        self.propagates(*ids)
        l_left = self.no + left
        r_right = self.no + right
        while l_left < r_right:
            if r_right & 1:
                r_right -= 1
                self.lazy[r_right - 1] += x
                self.data[r_right - 1] += x
            if l_left & 1:
                self.lazy[l_left - 1] += x
                self.data[l_left - 1] += x
                l_left += 1
            l_left >>= 1
            r_right >>= 1
        for i in ids:
            self.data[i - 1] = self.f(self.data[2 * i - 1], self.data[2 * i])

    def query(self, left, right):
        self.propagates(*self.get_index(left, right))
        l_left = self.no + left
        r_right = self.no + right

        res = self.default
        while l_left < r_right:
            if r_right & 1:
                r_right -= 1
                res = self.f(res, self.data[r_right - 1])
            if l_left & 1:
                res = self.f(res, self.data[l_left - 1])
                l_left += 1
            l_left >>= 1
            r_right >>= 1
        return res

二分探索

cor_v = 10 ** 20
inc_v = -1
while cor_v - inc_v > 1:
    bin_v = (cor_v + inc_v) // 2
    cost = 0
    #条件を満たすcostを全検索

    #costが制約を満たすか
    if cost <= bin_v:
        cor_v = bin_v
    else:
        inc_v = bin_v
print(cor_v)

最小共通祖（LCA）

class Lca(object):
    def __init__(self, graph, root=0):
        self.graph = graph
        self.root = root
        self.n = len(graph)
        self.bit_len = (self.n - 1).bit_length()
        self.depth = [-1 if i != root else 0 for i in range(self.n)]
        self.parent = [[-1] * self.n for _ in range(self.bit_len)]
        self.bfs()
        self.doubling()

    def bfs(self):
        ql = [[0, self.root]]
        ql = collections.deque(ql)
        fq = collections.defaultdict(list)
        fq[self.root] = 0
        while True:
            if len(ql) != 0:
                cost, tmp = ql.popleft()
                for tmv in self.graph[tmp]:
                    if tmv not in fq:
                        ql.append([cost + 1, tmv])
                        fq[tmv] = cost + 1
            else:
                break

    def doubling(self):
        for i in range(1, self.bit_len):
            for v in range(self.n):
                if self.parent[i - 1][v] != -1:
                    self.parent[i][v] = self.parent[i - 1][self.parent[i - 1][v]]

    def get(self, u, v):
        if self.depth[v] < self.depth[u]:
            u, v = v, u
        du = self.depth[u]
        dv = self.depth[v]

        for i in range(self.bit_len):
            if (dv - du) >> i & 1:
                v = self.parent[i][v]
        if u == v:
            return u

        for i in range(self.bit_len - 1, -1, -1):
            pu, pv = self.parent[i][u], self.parent[i][v]
            if pu != pv:
                u, v = pu, pv
        return self.parent[0][u]

メモ化再帰

@lru_cache(maxsize=None)
def memo_func():

ワーシャルフロイド

wn = list(map(int, input().rstrip('\n').split()))
inf = 10 ** 13
wl = [[inf] * wn for _ in range(wn)]
for i in range(wn):
    wl[i][i] = 0

for i in range(wn):
    wa, wb, wc = list(map(int, input().rstrip('\n').split()))
    wl[wa - 1][wb - 1] = wc
    wl[wb - 1][wa - 1] = wc

for i in range(wn):
    for j in range(wn):
        for k in range(wn):
            wl[j][k] = min(wl[j][k], wl[j][i] + wl[i][k])

Zアルゴリズム

#対象文字列を指定
st = 
st_len = len(st)
z_algorithm = [0] * st_len
z_i = 1
z_j = 0
while z_i < st_len:
    while z_i + z_j < st_len and st[z_j] == st[z_i + z_j]:
        z_j += 1
    z_algorithm[z_i] = z_j
    if z_j == 0:
        z_i += 1
        continue
    z_k = 1
    while z_i + z_k < st_len and z_k + z_algorithm[z_k] < z_j:
        z_algorithm[z_i + z_k] = z_algorithm[z_k]
        z_k += 1
    z_i += z_k
    z_j -= z_k

組合せ

基本

def combination(n, r):
    r = min(n - r, r)
    if r == 0:
        return 1
    else:
        denominator = 1
        for i in range(n, n - r, -1):
            denominator = (denominator * i)
        molecule = 1
        for i in range(1, r + 1):
            molecule = (molecule * i)
        return denominator // molecule

MOD

def combination_mod(n, r, mod):
    r = min(n - r, r)
    if r == 0:
        return 1
    else:
        denominator = 1
        for i in range(n, n - r, -1):
            denominator = (denominator * i) % mod
        molecule = 1
        for i in range(1, r + 1):
            molecule = (molecule * i) % mod
        return denominator * pow(molecule, mod - 2, mod) % mod

重複組合せ

基本

def duplicate_combination(n, r):
    n = n + r - 1
    r = min(n - r, r)
    if r == 0:
        return 1
    else:
        denominator = 1
        for i in range(n, n - r, -1):
            denominator = (denominator * i)
        molecule = 1
        for i in range(1, r + 1):
            molecule = (molecule * i)
        return denominator // molecule

MOD

def duplicate_combination_mod(n, r, mod):
    n = n + r - 1
    r = min(n - r, r)
    if r == 0:
        return 1
    else:
        denominator = 1
        for i in range(n, n - r, -1):
            denominator = (denominator * i) % mod
        molecule = 1
        for i in range(1, r + 1):
            molecule = (molecule * i) % mod
        return denominator * pow(molecule, mod - 2, mod) % mod

順列

基本

def permutation(n, r):
    if r == 0:
        return 1
    else:
        denominator = 1
        for i in range(n, n - r, -1):
            denominator = (denominator * i)
        return denominator // 1

MOD

def permutation_mod(n, r, mod):
    if r == 0:
        return 1
    else:
        denominator = 1
        for i in range(n, n - r, -1):
            denominator = (denominator * i) % mod
        return denominator // 1

階乗

基本

def factorial(denominator_no):
    return math.factorial(denominator_no)

MOD

def factorial_mod(denominator_no, molecule_list, mod):
    denominator = 1
    for i in range(1, denominator_no + 1):
        denominator = (denominator * i) % mod
    molecule = 1
    for molecule_no in molecule_list:
        for i in range(1, molecule_no + 1):
            molecule = (molecule * i) % mod
    return denominator * pow(molecule, mod - 2, mod) % mod