Easy to solve with linear programming

## Russian ##

## 1 Идея ##

1) Представим число A в виде 10x+m1, где x - число десятков
m1=2 (m1 не может быть равно 1, так как в этом случае искомое число A нечетное и на 2^N не разделится). Разделим число на 2, получим A=5x+1.
2) Пусть x=10y+m2, где y - число сотен. После подстановки получим A=5(10y+m2)+1=50y+5m2+1. Чтобы число A разделилось на 2, надо, чтобы m2 было нечетным. Следовательно выбираем m2=1. После деления на 2 получим: A=(50y+5*1+1)/2=25y+3.
3) Пусть y=10z+m3, где z - число тысяч. После подстановки получим A=25(10z+m3)+3=250z+25m3+3. Чтобы число A разделилось на 2, надо, чтобы m3 было нечетным. Следовательно выбираем m3=1. После деления на 2 получим: A=(250z+25*1+3)/2=125z+14.
4) Пусть z=10t+m4, где t - число десятков тысяч. После подстановки получим A=125(10t+m4)+14=1250t+125m4+14. Чтобы число A разделилось на 2, надо, чтобы m4 было четным. Следовательно выбираем m4=2. После деления на 2 получим: A=(1250t+125*2+14)/2=625t+132.

Далее процесс повторяется N раз. Последовательность mN...m4m3m2m1 образует ответ. Алгоритм требует применения длинной арифметики. Общее решение достигается за N шагов.

## 2 Алгоритм ##
Пусть m[1]=2; a_[1]=5; b_[1]=1;
Цикл i = от 2 до n
нц
  m_[i]=(если b_[i-1] нечетное, то 1, иначе 2)
  b_[i]=(если b_[i-1] нечетное, то (a_[i-1]+b_[i-1])/2, иначе (2*a_[i-1]+b_[i-1])/2)
  (так как a_[i-1] нечетное всегда по определению)
  a_[i]=a_[i-1]*5;
кц

## English (in short) ##

## 1 The Idea ##

1) Let me A = 10x+m1, where x - number of Tens
m1=2 (m1<>1, as A - odd). Division A in 2, let's receive A=5x+1.
2) Let me x=10y+m2, where y - number of Hundreds. Then A=5(10y+m2)+1=50y+5m2+1. if A%2==0, m2 is odd. Then m2=1 and A=(50y+5*1+1)/2=25y+3.
3) Let me y=10z+m3, where z - number of Thousand. Then A=25(10z+m3)+3=250z+25m3+3. if A%2==0, m3 is odd. Then m3=1 and A=(250z+25*1+3)/2=125z+14.
4) Let me z=10t+m4, где t - number of Tens thousand. Then A=125(10t+m4)+14=1250t+125m4+14. if A%2==0, m3 is even. Then m3=1 and A=(1250t+125*2+14)/2=625t+132.

Further process repeats N time. Sequence mN... m4m3m2m1 forms the answer. The algorithm demands application of long arithmetics.

## 2 The Algo ##
Let me m[1]=2; a_[1]=5; b_[1]=1;
for i = 2 to n
begin
  m_[i]=(if b_[i-1] is odd, then 1, else 2)
  b_[i]=(if b_[i-1] is odd, then (a_[i-1]+b_[i-1])/2, else (2*a_[i-1]+b_[i-1])/2)
  a_[i]=a_[i-1]*5;
end

whats in test 8 ?
cant find out :(

using System;

class Entrypiont
{
    static void Main()
    {
        string[] Input = Console.ReadLine().Split(' ');
        int a = Convert.ToInt32(Input[0]);
        int b = Convert.ToInt32(Input[1]);
        int c = Convert.ToInt32(Input[2]);
        if(((c-1)%a)==((c-1)%b) && ((c - 1) % a) == 0)
        {
            int x=1, y=1, z=1;
            while (true)
            {
                if(Math.Pow(x,a)+ Math.Pow(y, b)== Math.Pow(z, c))
                {
                    Console.Write(x);
                    Console.Write(y);
                    Console.Write(z);
                    break;
                }
                else
                {
                    if(Math.Pow(x, a) + Math.Pow(y, b) >Math.Pow(z, c))
                    {
                        z++;
                    }
                    else
                    {
                        if (x >= y)
                        {
                            y++;
                        }
                        else
                        {
                            x++;
                        }

                    }
                }
            }
        }

        Console.ReadLine();
    }
}

Can anybody help me?

Test: ABBCC
Answer: BB

#include <iostream>
#include <cmath>
#include <vector>
#include <algorithm>
#include <string>
#include <iomanip>
#include <set>
using namespace std;
int main()
{
    int x1, x2, y1, y2, x3, y3, l;
    cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3 >> l;
    // h = 2/s3 в€љp(p-s3)(p-s1)(p-s2),
    int a = y1 - y2, b = x2 - x1, c = x1 * y2 - x2 * y1;
    double s1 = sqrt((x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3)),
        s2 = sqrt((x2 - x3) * (x2 - x3) + (y2 - y3) * (y2 - y3)),
        s3 = sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
    double p = s1 + s2 + s3; p /= 2;
    double ans = (2 / s3 * sqrt(p * (p - s3) * (p - s1) * (p - s2)));
    if (max(s1, s2) * max(s1, s2) > min(s1, s2) * min(s1, s2) + s3 * s3) {
        ans = min(sqrt((x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3)), sqrt((x2 - x3) * (x2 - x3) + (y2 - y3) * (y2 - y3)));
    }
    if (s3 == 0.0) {
        ans = sqrt((x1 - x3) * (x1 - x3) + (y1 - y3) *(y1 - y3));
    }
    printf("%0.2f\n", max(0.0, ans - l));
    printf("%0.2f\n", max(0.0, max(sqrt((x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3)), sqrt((x2 - x3) * (x2 - x3) + (y2 - y3) * (y2 - y3))) - l));
}

k=2 => k-1 = 1. But everything is divisible by 1, what's wrong?

#include<iostream>
#include<cmath>
#include<iomanip>
#define pi 3.1415926
using namespace std;

int main(){
    float side,len;
    cin>>side>>len;
    if(len>(side/2)*sqrt(2)){
        cout<<fixed<<setprecision(3)<<side*side;
        return 0;
    }
    if((side/2)>=len){
        cout<<fixed<<setprecision(3)<<len*len*pi;
        return 0;
    }
    float cosx=(side/2)/len;
    float sinx=sqrt(1-cosx*cosx);
    float cosA=2*sinx*cosx;
    float theta=acos(cosA);
    cout<<fixed<<setprecision(3)<<len*len*0.5*theta*4+sqrt(len*len-(side/2)*(side/2))*(side/2)*4;

return 0;
}

qalesan

GOOD peoples Please help me! I have got WA#5! I used DSU!! My program gives right answer for all my tests! But again WA#5 and I can not found my mistake! I shall wait advices or tests! Thank you advance!!!

just consider this condiction:
2
A\A
B\A
the correct output is
A
 A
B
 A
but if you are mistaken, you will output
A
 A

Please help me. TLE #39

I think that most people trying to solve this problem will try to deal with two problems, they are:
1. How to calculate a[n] fast?
2. How to find those n that a[n] is the maximum in [1...n]?
Here is my method.

1. Calculating a[n] (without calculating a[1...n-1]).
Directly calculation will lead to a long time.
But, after some observation, I found that:
a[4n] = a[n]
a[4n + 1] = a[2n] + a[2n + 1] = 2a[n] + a[n + 1]
a[4n + 2] = a[n] + a[n + 1]
a[4n + 3] = a[n] + 2a[n + 1]
So, a[4n] to a[4n + 3] could be presented as the linear form of a[n] and a[n + 1].
We will soon realise that, a[2^k n] to a[2^k n + (2^k - 1)]  could also be presented as linear form of a[n] and a[n + 1].
So, pre-calculation is done to calculate all the linear forms of a[65536n] to a[65536n + 65535]. This will take about O(65536 * 2) time.
After this pre-calc, calculation for any number K will go very fast.

2. Finding the maximum.
After listing some of the 'maximum index', we found that:
1
3
5
9
11
19
21
35
37
43
......
Maybe my math is not so good, so I could not find so useful properties in the array, but I noticed one thing:
------------------------------------------------------------------------------------------
Every 'maximunm index' could be presented as its max 2-power and some former 'maximum index'.
------------------------------------------------------------------------------------------
Sorry for my poor English, let's take a look at the examples:
1
3 = 2 + 1
5 = 4 + 1
9 = 8 + 1
11 = 8 + 3
19 = 16 + 3
21 = 16 + 5
35 = 32 + 3
37 = 32 + 5
43 = 32 + 11
......
So, we just need to use every 2^k number to ITERATE the list of 'maximum index'. As the list is of size O(Log N), the algo runs quite fast.

With above methods, I got AC in 0.046 sec.

Well, if my algo is too stupid for you, don't hesitate to post your algo here.

Have fun and good luck.

 #include <iostream>
using namespace std;

char paper[4][4], pass[4][4],rPass[16],TempPaper[4][4];
int v, i, j;

void check(char paper[4][4], char pass[4][4])
{
    for (int j = 0; j < 4; j++)// X/.
    {
        for (int i = 0; i < 4; i++)
        {
            if (paper[j][i] == 'X')
            {
                rPass[v] = pass[j][i];
                v++;
            }

        }
    }
}

int main()
{
    for (int j = 0; j < 4; j++) //paper cin
    {
        for (int i = 0; i < 4; i++)
        {
            cin >> paper[j][i];
        }
    }

    for (int j = 0; j < 4; j++)//зашифрованый пароль
    {
        for (int i = 0; i < 4; i++)
        {
            cin >> pass[j][i];
        }
    }
    for (int j = 0; j < 4; j++)//temp
    {
        for (int i = 0; i < 4; i++)
        {
            TempPaper[j][i] = paper[j][i];
        }
    }
    check(paper, pass);
    for (i = 0; i < 4; i++)
    {
        for (j = 0; j < 4; j++)
        {
            int t=0, y;
            if (j == 0)
            {
                int u = 3;
                for (y = 0; y < 4; y++)
                {
                    paper[t][u] = TempPaper[0][y];
                    t++;
                }
            }
            if (j == 1)
            {
                int u = 2;
                for (y = 0; y < 4; y++)
                {
                    paper[t][u] = TempPaper[1][y];
                    t++;
                }
            }
            if (j == 2)
            {
                int u = 1;
                for (y = 0; y < 4; y++)
                {
                    paper[t][u] = TempPaper[2][y];
                    t++;
                }
            }
            if (j == 3)
            {
                int u = 0;
                for (y = 0; y < 4; y++)
                {
                    paper[t][u] = TempPaper[3][y];
                    t++;
                }
            }
        }
        check(paper, pass);
        for (int j = 0; j < 4; j++)
        {
            for (int i = 0; i < 4; i++)
            {
                TempPaper[j][i] = paper[j][i];
            }
        }
        }
    return 0;
}

It contains more than 20 zeroes.

Totally discouraged with it. Please give some test.

I used a simple algo... I am just checking 3 consecutive numbers... If any 3 consecutive numbers from the given numbers are like this, n1>n3>n2 (mid one is the smallest, first one is the largest and the last one lies in between these two values) , then the sequence is invalid (Cheater) ... else , I print "Not a proof" ...

Is my algo ok? If so, then please help me with some test cases...
I have tried all the test cases found in the discussions and my program passed all of them...

#include<bits/stdc++.h>

using namespace std;

int main(void)   {

    int t_h,s_h,pb;


    while(cin>>pb)   {
     s_h=0,t_h=0;

    if(pb>=1 && pb<=11)    {

    s_h=12-pb;
    t_h=s_h*45;

   if(t_h<=240)                    cout<<"Yes"<<endl;
   else                            cout<<"No"<<endl;

    }

 }



return 0;

}

#include <stdio.h>
int main() {
unsigned long long int a;
scanf("%llu", &a);
if (a/7!=0)
printf("%llu\n", a%7);
else if (a < 7)
printf("%d\n", a); }