Please help me to understand the following code and what will be the possiable output.
What will be the output of the following pseudo code for input 7?
1.Input n
2.Set m = 1, T = 0
3.if (m > n)
Go to step 9
5.else
T = T + m
m = m + 1
8.Go to step 3
9.Print T
0
n is less than n so go to step 9 which is print T which is equal to 0 as set in step 2.
T should be 28. It will loop till m>7 (since n=7) and in each iteration T adds m to itself, since T is 0 initially it is only summing up m after incrementing it by 1 in each iteration.So if you add 1+2+3.....+7 you get 28 and that is when the loop breaks since m is now equal to 8.
for m = 1 2 3 4 5 6 7 and for 8 m>n will be true and it will go to step 9
T=(T+M)= 1 3 6 10 15 21 28 basically T is a series where next is added as 2,3,4,5,6,7 to prev number 2 3 4 5 6 7 if one look from other angle
Related
I am trying to solve Euler 18 in Dyalog APL, and I am not able to understand why my solution does not work.
The problem is as follow:
By starting at the top of the triangle below and moving to adjacent
numbers on the row below, the maximum total from top to bottom is 23.
3
7 4
2 4 6
8 5 9 3
That is, 3 + 7 + 4 + 9 = 23.
Taking the example that I represent this way:
d ← (3 0 0 0) (7 4 0 0) (2 4 6 0) (8 5 9 3)
I am trying to solve it this way:
{⍵+((2⌈/⍺)),0}/⌽d
Which gives me this array: 22 19 15 0, where the bigger number is 22, which is not the right answer for the problem, which would be 23.
I am getting this behavior (left to right for ease of reading):
(2⌈/(8 5 9 3),0)+(2⌈/(2 4 6 0),0)+(2⌈/(7 4 0 0),0)+(2⌈/(3 0 0 0),0)
Which gives me the same result as the function.
What I would expect is this behavior (where each statement is substituted directly in the next line):
(2⌈/(8 5 9 3)),0
(2 4 6 0)+8 9 9 0
(2⌈/(10 13 15 0)),0
(7 4 0 0)+13 15 15 0
(2⌈/(20 19 15 0)),0
(3 0 0 0) + 20 19 15 0
23 19 15 0
Am I wondering where I am misunderstanding something in the APL process that leads to a different result than the one I am expecting.
Thank you!
/ works in the reverse way to what you expected - it evaluates through the array right-to-left.
F/a b c d is ⊂a F b F c F d, or, with parentheses, ⊂(a F (b F (c F d))).
After removing the ⌽ and swapping ⍺ and ⍵, you get {⍺+(2⌈/⍵),0}/d, which gives the result you want.
I think the best way to show the problem is with an example. Column A is what i have now, and column B is what I would want.
A
B
1
1
1
1
2
2
2
2
5
3
5
3
5
3
8
4
8
4
9
5
9
5
14
6
14
6
17
7
17
7
17
7
Update: Based on your comment, use this formula
=ArrayFormula(IF(ISNUMBER(A1:A), VLOOKUP(A1:A, {UNIQUE(A1:A), ArrayFormula(RANK(UNIQUE(A1:A), UNIQUE(A1:A), 1))}, 2, 0), ""))
Previous answer: Have you already used the SORT formula?
Try =SORT(A1:A, 1, 1) in cell B1
Assuming your data starts at row 2 through row 10 column A. In B2 :
=arrayformula(1/COUNTIF($A$2:$A$10,$A$2:$A$10))
in C2
=sumproduct(($B$1:$B1)*($A$1:$A1<A2))+1
Problem originally is in this link. I wrote a Python code but I got 64 points (total points is 100) and this indicates that my code has some missing points. I passed 11 of 16 test cases but 5 test cases have problematic for me. Could you say where my code has some missing points and how can I fix it?
import math
m = int(raw_input())
liste = []
y_liste = []
md = 0
ad = 0
sum = 0
sum2 = 0
for k in range(m):
temp = str(raw_input())
liste.append(temp)
liste[k] = liste[k].split(" ")
liste[k] = [int(i) for i in liste[k]]
for k in range(m):
md += liste[k][k]
ad += liste[k][m-k-1]
if md == ad:
print 0
else:
for k in range(m):
for l in range(m):
sum2 += liste[l][k]
sum += liste[k][l]
if sum2 != md and -(k+1) is not y_liste:
y_liste.append(-(k+1))
if sum != md and (k+1) is not y_liste:
y_liste.append(k+1)
sum2 = 0
sum = 0
if md != ad:
y_liste.append(0)
print len(y_liste)
y_liste.sort()
for i in y_liste:
print i
Problem Statement
Magic Square
Johnny designed a magic square (square of numbers with the same sum for all rows, columns and diagonals i.e. both the main diagonal - meaning the diagonal that leads from the top-left corner towards bottom-right corner - and the antidiagonal - meaning the diagonal that leads from top-right corner towards bottom-left corner). Write a program to test it.
Task
Write a program that will check if the given square is magic (i.e. has the same sum for all rows, columns and diagonals).
Input
First line: N , the size of the square (1 <= N <= 600).
Next N lines: The square, N space separated integers pre line, representing the entries per each row of the square.
Output
First line: M , the number of lines that do not sum up to the sum of the main diagonal (i.e. the one that contains the first element of the square). If the Square is magic, the program should output 0.
Next M lines: A sorted (in incremental order ) list of the lines that do not sum up to the sum of the main diagonal. The rows are numbered 1,2,…,N; the columns are numbered -1,-2,…,-N; and the antidiagonal is numbered zero.
Note: There is a newline character at the end of the last line of the output.
Sample Input 1
3
8 1 6
3 5 7
4 9 2
Sample Output 1
0
Sample Input 2
4
16 3 2 13
5 10 11 8
6 9 7 12
4 15 14 1
Sample Output 2
3
-2
-1
0
Explanation of Sample Output 2
The input square looks as follows: http://i.stack.imgur.com/JyMgc.png
(Sorry for link but I cannot add image due to reputation)
The square has 4 rows (labeled from 1 to 4 in orange) and 4 columns (labeled from -1 to -4 in green) as depicted in the image above. The main diagonal and antidiagonal of the square are highlighted in red and blue respectively.
The main diagonal has sum = 16 + 10 + 7 +1 = 34.
The antidiagonal has sum = 13 + 11 + 9 + 4 = 37. This is different to the sum of the main diagonal so value 0 corresponding to the antidiagonal should be reported.
Row 1 has sum = 16 + 3 + 2 + 13 = 34.
Row 2 has sum = 5 + 10 + 11 + 8 = 34.
Row 3 has sum = 6 + 9 + 7 + 12 = 34.
Row 4 has sum = 4 + 15 + 14 + 1 = 34.
Column -1 has sum = 16 + 5 + 6 + 4 = 31. This is different to the sum of the main diagonal so value -1 should be reported.
Column -2 has sum = 3 + 10 + 9 + 15 = 37. This is different to the sum of the main diagonal so value -2 should be reported.
Column -3 has sum = 2 + 11 + 7 + 14 = 34.
Column -4 has sum = 13 + 8 + 12 + 1 = 34.
Based on the above, there are 3 lines that do not sum up to the sum of the elements of the main diagonal. Since they should be sorted in incremental order, the output should be:
3
-2
-1
0
Your explanation doesn't discuss this clause which is a potential source of error:
if md == ad:
print 0
else:
It says that if the main diagonal and antidiagonal add up to the same value, print just a 0 (no bad lines) indicating the magic square is valid (distinct from reporting a 0 in the list of bad lines). Consider this valid magic square:
9 6 3 16
4 15 10 5
14 1 8 11
7 12 13 2
If I swap 13 and 11, the diagonals still equal each other but the square is invalid. So the above code doesn't appear to be correct. In the else clause for the above if statement, you test:
if md != ad:
y_liste.append(0)
a fact you already know to be true from the previous/outer test so your code seems to be out of agreement with itself.
I need help finding the formula of the sequence for the next problem.
What I think and have for now is Sn=n(10^n-1)/9 but it just works in some cases...
Here is the description of the problem:
Description
Sn is based upon the sequence positive integers numbers. The value n can be found n times, so the first 25 terms of this sequence are as follows:
1 2 2 3 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7...
For this problem, you have to write a program that calculates the i-th term in the sequence. That is, determine Sn(i).
Input specification
Input may contain several test cases (but no more than 10^5). Each test case is given in a line of its own, and contains an integer i (1 <= i <= 2 * 10^9). Input ends with a test case in which i is 0, and this case must not be processed.
Output specification
For each test case in the input, you must print the value of Sn(i) in a single line.
Sample input
1
25
100
0
Sample output
1
7
14
Thanks solopilot! I made the code but the online judge show me Time Limit Exceeded, what could be my error?
#include <iostream> #include <math.h> using namespace std; int main() {int i;
int NTS;
cin>>i;
while (i>=1){
NTS=ceil((sqrt(8*i+1)-1)/2);
cout<<" "<<NTS<<endl;
cin>>i;
}
return 0;}
F(n) = ceiling((sqrt(8*n+1)-1)/2)
Say F(n) = a.
Then n ~= a * (a+1) / 2.
Rearranging: a^2 + a - 2n ~= 0.
Solving: a = F(n) = (-1 + sqrt(1+8n)) / 2.
Ignore the negative answer.
The pattern looks like a pyramid.
Level : 1 3 6 10 15 21 28...
No : 1 2 3 4 5 6 7...
Level = n(n+1)/2 => elements
3 = 3*4/2 => 6
6 = 6*7/2 => 21
In Stata I want to have a variable calculated by a formula, which includes multiplying by the previous value, within blocks defined by a variable ID. I tried using a lag but that did not work for me.
In the formula below the Y-1 is intended to signify the value above (the lag).
gen Y = 0
replace Y = 1 if count == 1
sort ID
by ID: replace Y = (1+X)*Y-1 if count != 1
X Y count ID
. 1 1 1
2 3 2 1
1 6 3 1
3 24 4 1
2 72 5 1
. 1 1 2
1 2 2 2
7 16 3 2
Your code can be made a little more concise. Here's how:
input X count ID
. 1 1
2 2 1
1 3 1
3 4 1
2 5 1
. 1 2
1 2 2
7 3 2
end
gen Y = count == 1
bysort ID (count) : replace Y = (1 + X) * Y[_n-1] if count > 1
The creation of a dummy (indicator) variable can exploit the fact that true or false expressions are evaluated as 1 or 0.
Sorting before by and the subsequent by command can be condensed into one. Note that I spelled out that within blocks of ID, count should remain sorted.
This is really a comment, not another answer, but it would be less clear if presented as such.
Y-1, the lag in the formula would be translated as seen in the below.
gen Y = 0
replace Y = 1 if count == 1
sort ID
by ID: replace Y = (1+X)*Y[_n-1] if count != 1