【2020-02-28】pat甲級(jí)(1001-1021)

1001 A+B Format (20分)
Calculate a+b and output the sum in standard format -- that is, the digits must be separated into groups of three by commas (unless there are less than four digits).

Input Specification:
Each input file contains one test case. Each case contains a pair of integers a and b where ?10^?6?? ≤a,b≤10^?6?? . The numbers are separated by a space.

Output Specification:
For each test case, you should output the sum of a and b in one line. The sum must be written in the standard format.

Sample Input:
-1000000 9

Sample Output:
-999,991

nums=input()
a,b=int(nums.split(" ")[0]),int(nums.split(" ")[1])
num=a+b 
print('{:,}'.format(num)) 

1002 A+B for Polynomials (25分)
This time, you are supposed to find A+B where A and B are two polynomials.

Input Specification:
Each input file contains one test case. Each case occupies 2 lines, and each line contains the information of a polynomial:


image.png

Output Specification:
For each test case you should output the sum of A and B in one line, with the same format as the input. Notice that there must be NO extra space at the end of each line. Please be accurate to 1 decimal place.

Sample Input:
2 1 2.4 0 3.2
2 2 1.5 1 0.5

Sample Output:
3 2 1.5 1 2.9 0 3.2

# 合并兩個(gè)多項(xiàng)式
firstline={} 
secondline={}
line1=input().split(" ") #讀入第一行
for ele in range(int(line1[0])): # 非零項(xiàng)
    firstline[int(line1[1+ele*2])]=float(line1[2+ele*2])# 構(gòu)建指數(shù)和冪和對(duì)應(yīng)字典
line2=input().split(" ") #讀入第二行   
for ele in range(int(line2[0])):
    secondline[int(line2[1+ele*2])]=float(line2[2+ele*2])
a=sorted(list(firstline.keys()),key=lambda x: -x) #提取指數(shù)
b=sorted(list(secondline.keys()),key=lambda x: -x)
c=sorted(list(set(a+b)),key=lambda x: -x)
out={}
for x in c:
    if x in a and x in b:
        out[x]=firstline[x]+secondline[x] #指數(shù)一致時(shí)系數(shù)相加
    else:
        if x in a:
            out[x]=firstline[x]
        else:
            out[x]=secondline[x]
res=" "
num=0
for t in c:
    if out[t]!=0:
        num=num+1
        res=res+str(t)+" "+'{:.1f}'.format(out[t])+" "
print(str(num)+res[:-1])
      

1003 Emergency (25分)
As an emergency rescue team leader of a city, you are given a special map of your country. The map shows several scattered cities connected by some roads. Amount of rescue teams in each city and the length of each road between any pair of cities are marked on the map. When there is an emergency call to you from some other city, your job is to lead your men to the place as quickly as possible, and at the mean time, call up as many hands on the way as possible.

Input Specification:


input

Output Specification:


output

Sample Input:
5 6 0 2

1 2 1 5 3
0 1 1
0 2 2
0 3 1
1 2 1
2 4 1
3 4 1

Sample Output:
2 4

# 第一行:城市數(shù)湃鹊、道路輸曲横、目前所在城市、需急救城市镊叁、
# 第二行:每個(gè)城市的急救隊(duì)數(shù)量
# C1、C2薯酝、L 兩個(gè)城市之間的路長(zhǎng)
# 尋找最短路徑
#點(diǎn)的屬性<城市編號(hào)杀怠、救急隊(duì)數(shù)量>
# 邊的屬性<<city1,city2>,L>
# 最短路徑
# dijkstra
a=input().split(" ")
cities,rodes,currenty,savecity=int(a[0]),int(a[1]),int(a[2]),int(a[3])

b=input().split(" ")
point=[int(x) for x in b] #點(diǎn)權(quán)重

route=[[0 for x in range(cities)] for i in range(cities)] #點(diǎn)到點(diǎn)的距離,初始化為0

for x in range(rodes):
    m=input().split(" ")
    p,q,k=int(m[0]),int(m[1]),int(m[2])
    route[p][q]=k
    route[q][p]=k

visited=[0 for x in range(cities)]# 標(biāo)識(shí)走過(guò)的點(diǎn)
weight=[float('inf') for x in range(cities)]#邊權(quán)重甚垦,點(diǎn)到點(diǎn)的最短路徑,初始化為無(wú)窮大
power=[0 for x in range(cities)] # 累積的點(diǎn)權(quán)重

weight[currenty]=0 

power[currenty]=point[currenty]
visited[currenty]=1
x=currenty
num=[0 for x in range(cities)]
num[currenty]=1
while visited[savecity]==0:
    for i in range(cities):
        if route[x][i]!=0 and visited[i]!=1:# x->i 有路徑涣雕,且未訪問(wèn)
            if weight[i]>=weight[x]+route[x][i]: 
                if weight[i]==weight[x]+route[x][i]:
                    num[i]=num[i]+num[x]
                    if power[i]<power[x]+point[i]:
                        power[i]=power[x]+point[i]
                else:
                    if weight[i]>weight[x]+route[x][i]:
                        power[i]=power[x]+point[i]
                        num[i]=num[x]
                weight[i]=weight[x]+route[x][i]
    small=sorted([weight[x] for x in range(cities) if visited[x]!=1])[0]
    index=[x for x in range(cities) if weight[x]==small and visited[x]!=1][0]
    visited[index]=1
    x=index
print(num[savecity],power[savecity])

1004 Counting Leaves (30分)


題目
# 沒(méi)通過(guò)
# 給定一棵樹(shù)艰亮,求每一層的葉子節(jié)點(diǎn)數(shù)
# 第一行n(節(jié)點(diǎn)個(gè)數(shù)),m(無(wú)葉子節(jié)點(diǎn)的節(jié)點(diǎn)個(gè)數(shù))
# 第二行   id無(wú)葉子節(jié)點(diǎn),k葉子節(jié)點(diǎn)個(gè)數(shù)挣郭,id[1].....id[k]
tmap={} # 記錄非葉子節(jié)點(diǎn)
record=[0 for i in range(101)] #記錄數(shù)的深度
def dfs(id,level):
    if not id in tmap:
        record[level]+=1
        return
    for cid in tmap[id]:
        dfs(cid,level+1)

n,m=map(int,input().split())# n 節(jié)點(diǎn)個(gè)數(shù)迄埃,m無(wú)葉子節(jié)點(diǎn)的節(jié)點(diǎn)個(gè)數(shù)
for i in range(m):
    line=input().split() #讀取數(shù)據(jù)
    rid=int(line[0]) #
    k=int(line(1)) # 葉子節(jié)點(diǎn)個(gè)數(shù)
    
    tmap[rid]=[]
    
    for cid in line[2:]:
        cid=int(cid)
        tmap[rid].append(cid)

dfs(1,0)
cnt=record[0]
cle=n-m 
result=str(record[0])
for i in range(1,101):
    if cnt>=cle:
        break
    result+=" "+str(record[i])
    cnt+=record[i]
print(result)

1005 Spell It Right (20分)


dict={1:'one',2:'two',3:'three',4:'four',5:'five',6:'six',7:'seven',8:'eight',9:'nine',0:'zero'}
a=input()
b=[int(x) for x in str(a)]
c=sum(b)
for x in str(c):
    result=result+dict[int(x)]+" "
  
print(result[:-1])

1006 Sign In and Sign Out (25分)


題目
import time
num = int(input())
record = []
for x in range(num):
    line = input().split(" ")
    unit = [line[0]]
    for i in line[1:]:
        timeStruct = time.strptime('2020-01-01 '+i, "%Y-%m-%d %H:%M:%S")
        timeStamp = int(time.mktime(timeStruct))
        unit.append(timeStamp)
    record.append(unit)
early = min([ x[1] for x in record])
late = max([x[2] for x in record]) 
first = [x for x in range(num) if record[x][1] == early][0]
last = [x for x in range(num) if record[x][2] == late][0]
print(record[first][0], record[last][0])

1007 Maximum Subsequence Sum (25分)


題目
a=int(input())
number=input().split()
seq=[int(x) for x in number]
flag=True
if len([x for x in seq if x>=0])==0:
    flag=False
    print(0,seq[0],seq[-1])
res= -1
tmp,tmpleft,index,right,left=0,0,0,0,0
if flag==True:
    while(index!=len(seq)):
        tmp=tmp+seq[index]
        index+=1
        if tmp<0:
            tmp=0
            tmpleft=index
        elif tmp>res:
            res=tmp
            left=tmpleft
            right=index-1
    print(res,seq[left],seq[right])

1008、Elevator (20分)


題目
# 升一層需6s 降一層需4s 每一層停留5s
a=input()
a=a.split()
floor=[0]
for i in range(1,len(a)):
    floor.append(int(a[i]))
res=0
for i in range(1,len(floor)):
    if  floor[i-1]-floor[i]<0: 
        res=res+5+abs(floor[i-1]-floor[i])*6
    else:
        res=res+5+abs(floor[i-1]-floor[i])*4
print(res)

1009兑障、Product of Polynomials (25分)


題目
line1=input().split()
line2=input().split()
dic1={}
dic2={}

for i in range(int(line1[0])):
    dic1[int(line1[1+i*2])]=float(line1[2+i*2])
for i in range(int(line2[0])):
    dic2[int(line2[1+i*2])]=float(line2[2+i*2])
dic1 = {key:value for key,value in dic1.items() if value!=0}
dic2 = {key:value for key,value in dic2.items() if value!=0}
result = [[x,0] for x in range(2001)]
for x in dic1 :
    for y in dic2:
        result[x+y][1]+=dic1[x]*dic2[y]
output=str(len([x for x in result if x[1]!=0]))+" "
for x in result[::-1]:
    if x[1]!=0:
        output = output + str(x[0])+" "+ "{:.1f}" .format(x[1])+" "
print(output[:-1])

1010侄非、Radix (25分)


題目

題目
# N1 N2 tag(標(biāo)記第幾位的進(jìn)制) radix(標(biāo)記第幾位的進(jìn)制)
def convert(s,radix):
    t=0
    point=0
    for x in range(len(s)):
        t+=int(s[-x-1],36)*(radix**point)
        point+=1
    return t
def find(target,n):
    low=max([int(x,36) for x in n])+1
    high=max([low,target])
    while(low<=high):
        rad=round((low+high)/2)
        t=convert(n,rad)
        if t==target:
            return rad
        else:
            if t>target:
                high=rad-1
            else:
                low=rad+1
    return 'Impossible'

a=input().split()
n1=a[0]
n2=a[1]
tag=int(a[2])
radix=int(a[3])
if tag==1:
    t=convert(n1,radix)
    print(find(t,n2))
else:
    t=convert(n2,radix)
    print(find(t,n1))

1011、World Cup Betting (20分)


題目

題目
profit = 1
wtl = ['W','T','L']
out =[]
for i in range(3):
    l = list(map(float,input().split()))
    out.extend(wtl[l.index(max(l))])
    profit *= max(l)
    
profit = (profit*0.65-1)*2
print(' '.join(out),round(profit,2))

1012流译、The Best Rank (25分)


題目

題目
# C  M  E  A
class student:
    def __init__(self, C, M, E, ID):
        self.grade = [round((C+M+E)/3),C,M,E]
        self.id = ID
        self.rank = [-1, -1, -1, -1]
def main():
    line = input().split(" ")
    n = int(line[0])
    m = int(line[1])
    students = {}
    for x in range(n):
        line = input().split(" ")
        ID = line[0]
        C = int(line[1])
        M = int(line[2])
        E = int(line[3])
        s = student(C, M, E, ID)
        students[ID]=s
    for x in range(4):
        p = sorted(students.values(), key=lambda i : -i.grade[x])
        p[0].rank[x] = 1
        for i in range(1, n):
            p[i].rank[x] = i + 1
            if p[i].grade[x] == p[i-1].grade[x] :
                p[i].rank[x] = p[i-1].rank[x]
    for x in range(m):
        line = input()
        try:
            unit = students[line]
            temp = zip(unit.rank, ['0A','1C','2M','3E'])
            temp = sorted(temp)
            print(str(min(unit.rank)), temp[0][1][-1])
        except:
            print('N/A')
if __name__ == "__main__":
    main()

1013 Battle Over Cities (25分)


題目
class city:
    def __init__(self, name):
        self.name = name
        self.conn = []
def main():
    line = input().split(" ")
    n = int(line[0])
    m = int(line[1])
    k = int(line[2])
    cities = {}
    for x in range(n):
        c = city(x+1)
        cities[x+1] = c
    for x in range(m):
        line = input().split(" ")
        come = int(line[0])
        to = int(line[1])
        cities[come].conn.append(to)
        cities[to].conn.append(come)
    line = input().split(" ")
    conc = [int(x) for x in line]
    for x in conc:
        a = [0 for x in range(n)]
        a[x-1] = 1
        repair = -1
        while(sum(a) <n):
            start = a.index(0)
            step = [start+1]
            new = [start+1]
            temp = []
            while(len(new) > 0):
                for i in new:
                    for j in cities[i].conn:
                        if j not in step and j !=x:
                            temp.append(j)
                step += temp
                new = temp
                temp = []
            repair += 1
            for i in step:
                a[i-1] = 1
        print(repair)
if __name__ == "__main__":
    main()

1014 Waiting in Line (30分)


題目

題目
n,m,k,q=[int(x) for x in input().split()]
# n個(gè)窗口逞怨,每個(gè)窗口可容納m個(gè)顧客,一共k個(gè)顧客福澡,q個(gè)顧客在排
people_time_list=[int(x) for x in input().split()]
line_time_list=[0 for x in range(n)]
dict1={}
list_wait=[]

for j in range(m): 
    list_kaishi=[]
    for i in range(n):
        if j*n+i>=k:
            pass
        else:
            line_time_list[i]=line_time_list[i]+people_time_list[j*n+i]
            dict1[j*n+i+1]=line_time_list[i]
            list_kaishi.append(line_time_list[i])
    list_wait.append(list_kaishi)
for i in range(n*m,k):
    index=list_wait[0].index(min(list_wait[0]))
    for l in range(m-1):
        list_wait[l][index]=list_wait[l+1][index]
    line_time_list[index] = line_time_list[index] + people_time_list[i]
    list_wait[m-1][index]=line_time_list[index]
    dict1[i+1] = line_time_list[index]
list1=[int(x) for x in input().split()]
for i in list1:
    hour=dict1[i]//60+8
    minute=dict1[i]%60
    time_now=dict1[i]-people_time_list[i-1]
    if time_now>=540:
        print("Sorry")
    elif dict1[i]>=600:
        print("Sorry")
    elif hour<10 and minute<10:
        print("0"+str(hour)+":"+"0"+str(minute))
    elif hour<10:
        print("0" + str(hour) + ":" + str(minute))
    elif minute<10:
        print(str(hour) + ":" + "0" + str(minute))
    else:
        print(str(hour) + ":"+ str(minute))

1015 Reversible Primes (20分)


題目
"""
輸入整數(shù)和進(jìn)制
如果整數(shù)是素?cái)?shù)叠赦,轉(zhuǎn)換為指定的進(jìn)制后反轉(zhuǎn),再轉(zhuǎn)為10進(jìn)制后是否是素?cái)?shù)
"""
import math
def is_prime(num):
    if num<=1:
        return 0
    flag=1
    for x in range(2,round(math.sqrt(num))+1):
        if num%x==0:
            flag=0
            return flag
    return flag
def reverse(num,radix):
    result=''
    while (num!=0):
        temp=num%radix
        result=str(temp)+result
        num=num//radix
    return result

while (True):
    line=input().split()
    if len(line)<2:
        break
    num=int(line[0])
    radix=int(line[1])
    if is_prime(num)==1:
        rever=reverse(num,radix)
        rever=rever[::-1]
        rever=int(rever,radix)
        if is_prime(rever)==1:
            print("Yes")
        else:
            print("No")
    else:
        print("No")

1016 Phone Bills (25分)


題目

題目
# 假設(shè)開(kāi)始時(shí)間為A 結(jié)束時(shí)間為B
# 從00:00:00 到A 的話費(fèi)T1革砸,從00:00:00 到B 的話費(fèi)T2
# 話費(fèi)  T2-T1

line = input().split(" ")
rate = [int(x) for x in line]
oneday = sum([x for x in rate])*60
num = int(input())
record = {}
for x in range(num):
    line = input().split(" ")
    if line[0] in record:
        record[line[0]] .append(line[1:])
    else:
        record[line[0]] = [line[1:]]
name = sorted(record.keys())
for x in name:
    unit = sorted(record[x])
    bill = []
    stack = []
    for i in unit:
        if len(stack) == 0:
            if i[1] =='on-line':
                stack.append(i)
        else:
            if i[1] == stack[0][1]:
                stack[0] = i
            else:
                bill.append([stack[0],i])
                stack = []
    if len(bill) >0 :
        count = 0
        result = '{} {}\n'.format(x, bill[0][0][0][:2])
        for i in bill:
            start = i[0][0]
            end = i[1][0]
            result = result + start[3:] + ' '+ end[3:] + ' '
            m1, m2=0, 0
            day1, day2= int(start[3:5]), int(end[3:5])
            hour1, hour2 = int(start[6:8]), int(end[6:8])
            minute1, minute2 = int(start[9:11]), int(end[9:11])
            m1 = oneday * day1 + sum(rate[:hour1])*60 + rate[hour1]*int(minute1)
            m2 = oneday * day2 + sum(rate[:hour2])*60 + rate[hour2]*int(minute2)
            time = (day2 - day1)*24*60 + (hour2-hour1)*60 + minute2 - minute1
            result = result + str(time)+' '
            m = m2 - m1
            result = result+'$'+'{:.2f}'.format(m/100)+'\n'
            count += m
        result = result+'Total amount: ${:.2f}'.format(count/100)
        print(result)

1017 Queueing at Bank (25分)


題目
# 優(yōu)先隊(duì)列
N,K=[int(i) for i in input().split()]
cus = {}                                      #用來(lái)存放顧客的到達(dá)時(shí)間除秀,和需要處理的時(shí)間
window = [3600 * 8] * K                           #將所有窗口的開(kāi)放時(shí)間都設(shè)為8點(diǎn)
for _ in range(N):
    A=input().split()
    hh,mm,ss=[int(i) for i in A[0].split(":")]
    wait=int(A[1])
    if hh*3600+mm*60+ss<17*3600+1:                #過(guò)濾掉晚上5點(diǎn)以后的顧客
        cus[hh*3600+mm*60+ss]=wait*60
cus=dict(sorted(cus.items(),key=lambda x:x[0]))   #按照到達(dá)時(shí)間把顧客排好隊(duì)
total=0
for j in cus:
    window=sorted(window)                        #不斷的更新窗口的等待時(shí)間糯累,將短的等待時(shí)間放在前面
    if window[0]>j:                              #判斷窗口是否空閑
        total+=window[0]-j                         #將顧客等待時(shí)間存放入
        window[0]+=cus[j]                          #更新窗口下次開(kāi)放的時(shí)間
    else:
        window[0]=cus[j]+j
count=len(cus)
if count>0:
    print("{:.1f}".format(total/60/count))
else:
    print("0.0")

1018 Public Bike Management (30分)

題目

題目
cmax,n,sp,m = [int(x) for x in input().split() ]
 
C = [0] + [ int(x) for x in input().split() ]
 
Neib = [ {} for i in range(n+1) ]
 
for i in range(m):
    si,sj,t = [ int(x) for x in input().split() ]
    Neib[si][sj] = t
    Neib[sj][si] = t
 
minpath = []
minrequire = cmax+1
minextra = cmax+1
mindis = -1
vis = [0] * (n+1)
def dfs (Neib,path,dis,require,extra,st):
    global minrequire
    global minextra
    global mindis
    global minpath
 
    #print(path,dis,require,extra,st)
 
    vis[st] = 1
    if st == sp:
        if mindis == -1 or dis < mindis \
           or (dis == mindis and (require < minrequire or \
            require == minrequire and extra < minextra )):
            
                    minextra = extra
                    minrequire = require
                    mindis = dis
                    minpath = path
        vis[st] = 0
        return
 
    for i,t in Neib[st].items():
        if not vis[i]:
            #deal with need and take
            need,take = require,extra
            # get i's Current state
            diff = C[i] - cmax // 2
            # if i's state less than perfection
            if diff < 0 :
            # if take can feed i's need , decrease take
                if take >= (-diff) :
                    take += diff
            # if can't , let take be 0, increase need
                else:
                    
                    need += (-diff) - take
                    take = 0
            # if i's state more than perfection , just increase take
            # need can't be feed by i's state
            # the bike needed is used in adjusting the state before approching i's state
            # so we can just take more, can't need less
            # 2 test cases here.
            elif diff > 0:
                take += diff
 
 
            #dfs i
            dfs(Neib,path+[i],dis + t,need,take,i)
    vis[st] = 0
 
 
dfs(Neib,[0],0,0,0,0)
#print(minpath,minrequire,minextra,mindis)
strpath = '->'.join([str(x) for x in minpath])
print(minrequire,strpath,minextra)

1019 General Palindromic Number (20分)


題目

題目
def transform(a,b):
    # a 整數(shù) b 進(jìn)制
    if a==0:
        return '0'
    result = []
    while(a != 0):
        result.insert(0, str(a % b))
        a = a//b
    return result

a,b=map(int, input().split())
num = transform(a,b)
result = ''
if len(num) == 1:
    result = "Yes" +"\n" + num[0]
else:
    for x in range(len(num)//2):
        if num[x] != num[len(num) - 1-x]:
            result = "No"+"\n"+" ".join(num)
            break
    if result == '':
        result = "Yes" + "\n" +" ".join(num)
print(result)

1020 Tree Traversals (25分)


題目
def trav(poster, inorder):
    global result, temp
    root = poster[-1]
    result.append(root)
    index = inorder.index(root)
    inleft,inright = inorder[:index], inorder[index+1:]
    posleft, posright = poster[:len(inleft)], poster[len(inleft):len(inleft)+len(inright)]
    if len(inleft) >0:
        temp.append([posleft,inleft])
    if len(inright) >0:
        temp.append([posright,inright])
if __name__ =="__main__":
    num = int(input())
    line = input().split(" ")
    poster = [int(x) for x in line]
    line = input().split(" ")
    inorder = [int(x) for x in line]
    result = []
    temp = []
    part = [[poster,inorder]]
    while(True):
        for x in part:
            trav(x[0], x[1])
        if len(temp)==0:
            break
        else:
            part = temp
            temp = []
    result = [str(x) for x in result]
    print(' '.join(result))

1021 Deepest Root (25分)


題目

題目
def bfs(graph,start):
    global n
    count = 0
    visted = [0 for x in range(n)]
    for x in range(n):
        if x+1 not in graph:
            visted[x] = 1
            count += 1
    step = [start]
    while(count == 0):
        temp = []
        for x in step:
            visted[x-1] = 1
            for j in graph[x]:
                if visted[j-1] == 0:
                    temp.append(j)
        if len(temp) == 0:
            if 0 not in visted:
                return True, step
            else:
                break
        step = temp
    while(0 in visted):
        count += 1
        start = [x for x in graph if visted[x-1] ==0][0]
        step = [start]
        while(len(step)>0):
            temp = []
            for x in step:
                visted[x-1] = 1
                for j in graph[x]:
                    if visted[j-1] == 0:
                        temp.append(j)
            if len(temp)==0:
                if 0 not in visted:
                    return False, count
            step = temp
if __name__ == "__main__":
    n = int(input())
    if n==1:
        print(1)
    else:
        graph = {}
        for x in range(n-1):
            line = input().split(" ")
            start, to = int(line[0]), int(line[1])
            try:
                graph[start].append(to)
            except:
                graph[start] = [to]
            try:
                graph[to].append(start)
            except:
                graph[to] = [start]
        back = bfs(graph, start)
        if back[0]:
            another = bfs(graph, back[1][0])
            result = sorted(set(back[1] + another[1]))
            for x in result:
                print(x)
        else:
            print('Error: {} components'.format(back[1]))
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