ARC115 B - Plus Matrix

備忘録

問題

atcoder.jp

回答

import sys
import os
import math
import bisect
import itertools
import collections
import heapq
import queue
import array
import time
import datetime

# 時々使う
# import numpy as np
# from decimal import Decimal, ROUND_HALF_UP
# from scipy.sparse.csgraph import csgraph_from_dense, floyd_warshall

# 再帰の制限設定
sys.setrecursionlimit(10000000)


def ii(): return int(sys.stdin.buffer.readline().rstrip())
def il(): return list(map(int, sys.stdin.buffer.readline().split()))
def it(): return tuple(map(int, sys.stdin.buffer.readline().split()))
def fl(): return list(map(float, sys.stdin.buffer.readline().split()))
def iln(n): return [int(sys.stdin.buffer.readline().rstrip())
                    for _ in range(n)]


def iss(): return sys.stdin.buffer.readline().decode().rstrip()
def sl(): return list(map(str, sys.stdin.buffer.readline().decode().split()))
def isn(n): return [sys.stdin.buffer.readline().decode().rstrip()
                    for _ in range(n)]


def lcm(x, y): return (x * y) // math.gcd(x, y)


# MOD = 10 ** 9 + 7
MOD = 998244353
INF = float('inf')


def main():
    if os.getenv("LOCAL"):
        sys.stdin = open("input.txt", "r")

    N = ii()
    C = [il() for _ in range(N)]

    A = [-1] * N
    B = [-1] * N

    m, idx = INF, -1
    for i in range(N):
        if m > C[i][0]:
            m = C[i][0]
            idx = i
    A[idx] = 0

    for i in range(N):
        B[i] = C[idx][i]
    for i in range(N):
        A[i] = C[i][i] - B[i]

    for i in range(N):
        for j in range(N):
            if A[i] < 0 or B[i] < 0:
                print('No')
                exit()
            if C[i][j] == A[i] + B[j]:
                continue
            else:
                print('No')
                exit()
    else:
        print('Yes')
        print(*A)
        print(*B)


if __name__ == '__main__':
    main()

考え方

公式の解説動画をみて、ふんわり理解