One way to unlock an Android phone is through a pattern of swipes across a 1-9 keypad.
For a pattern to be valid, it must satisfy the following:
All of its keys must be distinct.
It must not connect two keys by jumping over a third key, unless that key has already been used.
For example, 4 - 2 - 1 - 7 is a valid pattern, whereas 2 - 1 - 7 is not.
Find the total number of valid unlock patterns of length N, where 1 <= N <= 9.
Invalid move: 4 - 1 - 3 - 6
Line 1 - 3 passes through key 2 which had not been selected in the pattern.
Invalid move: 4 - 1 - 9 - 2
Line 1 - 9 passes through key 5 which had not been selected in the pattern.
Valid move: 2 - 4 - 1 - 3 - 6
Line 1 - 3 is valid because it passes through key 2, which had been selected in the pattern
Valid move: 6 - 5 - 4 - 1 - 9 - 2
Line 1 - 9 is valid because it passes through key 5, which had been selected in the pattern.
| 1 | 2 | 3 |
| 4 | 5 | 6 |
| 7 | 8 | 9 |
I am able to solve the problem using DFS. But we have to also consider skip / jump. For solving it, i have seen people saving/using only the following combinations of valid jump.
for e.g
int skip[][] = new int[10][10];
skip[1][3] = skip[3][1] = 2;
skip[1][7] = skip[7][1] = 4;
skip[3][9] = skip[9][3] = 6;
skip[7][9] = skip[9][7] = 8;
skip[1][9] = skip[9][1] = skip[2][8] = skip[8][2] = skip[3][7] = skip[7][3] = skip[4][6] = skip[6][4] = 5;
Can someone help explain why the following combination is not included in skip/jump?
skip[1][6] = skip[6][1] = 2;
skip[1][6] = skip[6][1] = 5;
Example
https://medium.com/#rebeccahezhang/leetcode-351-android-unlock-patterns-d9bae4a8a958
Related
I am using the finite element method and separating a unit isosceles triangle into triangles with six nodes. While calculating coordinates of the nodes I noticed that the variables in the for loop get messed up for some reason and I cannot figure out why. Here is my code:
PROGRAM triangle
IMPLICIT NONE
INTEGER, PARAMETER :: stepSize = 4
INTEGER, PARAMETER :: numberOfNodes = ((2*stepSize - 1) * (2*stepSize)) / 2
INTEGER :: i, j, counter
REAL, DIMENSION(2, numberOfNodes) :: nodeCoordinates
counter = 0
DO j = 1, 2*stepSize - 1
DO i = 1, 2*stepSize - 1 - counter
nodeCoordinates(1, i + (j-1)*(2*stepSize - 1)) = ((REAL(i-1)) / REAL(2*stepSize - 2))
nodeCoordinates(2, i + (j-1)*(2*stepSize - 1)) = ((REAL(j-1)) / REAL(2*stepSize - 2))
END DO
counter = counter + 1
END DO
END PROGRAM triangle
When I print the variable j in the inner for loop, the following is shown:
1
1
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
3
4
4
4
4
0
0
0
1
1
2
I'm confused how to write the code on LINGO for this model (the model is on pic). I want the "Periode" (period on English) to be consecutive. I tried this code, it's feasible but it's not in consecutive periods. Can someone help me with this problem?
(here's the code that i tried)
SETS:
HARI/I1..I3/;
PERIODE/J1..J4/;
PERIOD/P1..P3/;
SKS/T1..T2/;
KM/K1..K4/:A;
DOSEN/L1..L4/:G;
MK/M1..M8/:H, B;
RUANGAN/N1..N3/;
JADWAL(HARI, PERIODE, KM, DOSEN, MK, RUANGAN):X;
PREFERENSI(HARI, PERIODE, DOSEN):Y;
ULANG(HARI, PERIODE, KM):Z;
CONSECUTIVE(HARI, PERIOD, KM, SKS, MK, RUANGAN):W;
ENDSETS
DATA:
H = 2 2 2 2 2 2 2 2;
B = 1 1 1 1 1 1 1 1;
G = 4 4 4 4;
A = 4 4 4 4;
ENDDATA
#FOR(HARI(I): #FOR(KM(K): #FOR(DOSEN(L): #FOR(MK(M): #FOR(RUANGAN(N): #FOR(SKS(T)|T#EQ#2: X(I,1,K,L,M,N) - X(I,T,K,L,M,N)<=0))))));
#FOR(HARI(I): #FOR(KM(K): #FOR(DOSEN(L): #FOR(MK(M): #FOR(RUANGAN(N): #FOR(PERIOD(P)|P#EQ#1#AND#P#EQ#2#AND#P#EQ#3: #FOR(SKS(T)|T#EQ#2:T+P<=4)))))));
#FOR(HARI(I): #FOR(KM(K): #FOR(DOSEN(L): #FOR(MK(M): #FOR(RUANGAN(N): #FOR(PERIOD(P)|P#EQ#1#AND#P#EQ#2#AND#P#EQ#3: #FOR(SKS(T)|T#EQ#2:-X(I,J,K,L,M,N)+X(I,P+1,K,L,M,N)-X(I,P+T,K,L,M,N)<=0)))))));
#FOR(HARI(I): #FOR(KM(K): #FOR(DOSEN(L): #FOR(MK(M): #FOR(RUANGAN(N): #FOR(SKS(T)|T#EQ#2: X(I,4,K,L,M,N) - X(I,4-T,K,L,M,N)<=0))))));
As my school Project, I need to build a solver for Countdown Numbers & Letters rounds. I wanted to develop a structure which I can use to build both solvers, and I first developed a Numbers solver. However, before using this solution for Letters, I need to improve my current algorithm. I think I'm wrong somewhere, because I don't get the same results with other tools I am using to compare my program. Here is program for my solver;
/// numbers_game_solver.dart
import 'dart:collection';
import 'package:trotter/trotter.dart';
/* Import statements was package-based, I turned them into relative paths for question. */
import 'number_generator.dart';
import 'operation.dart';
import 'solution.dart';
import 'solutions.dart';
/* Will try to combine numbers with operations, as shown below;
* List<List<Operation>> operations = <Operations>[a, ,b, ,c, ,d, ,e, ,f
* + - + * / ]
* Then if last operations result is equal to target, will result it.
* If not will show closest result.
*/
const List<String> kOperators = const <String>[kOpAdd, kOpDiv, kOpMul, kOpSub];
class NumbersGameSolver {
NumbersGameSolver()
: this.solutions = Solutions(_expectedResult);
/* TODO: Do tests with smaller numbers and targets. */
final List<int> _numbers = const <int>[1, 2, 3, 4]; // NumberGenerator.numbers;
static final int _expectedResult = 15; //NumberGenerator.expectedResult;
final Solutions solutions;
void solve() {
/* All permutations of operators with replacement, which will be inserted between numbers. */
final Set<List<String>> amalgamsOperators = Amalgams<String>(_numbers.length - 1, kOperators)().toSet();
/* There may duplicates occur in numbers list, because of this, numbers will be mapped
using permutations of indices. */
final List<int> indices = List<int>.generate(_numbers.length, (int index) => index);
final Iterable<List<int>> permutationsIndices = Permutations<int>(indices.length, indices)();
final Set<List<int>>
permutationsNumbers = permutationsIndices.map(
(List<int> listPerm) => listPerm.map(
(int index) => _numbers[index]
).toList()
).toSet();
for (final List<int> numbers in permutationsNumbers) {
for (final List<String> operators in amalgamsOperators) {
Queue<int> stackNums = Queue<int>.from(numbers);
Queue<String> stackOprts = Queue<String>.from(operators);
Solution tempSolution = Solution(_expectedResult);
do {
int left = stackNums.removeFirst(), right = stackNums.removeFirst();
Operation tempOperation = Operation(stackOprts.removeFirst(), left, right);
/* Record solutions current state. */
SolutionState solutionState = tempSolution.addOperation(tempOperation);
if (solutionState == SolutionState.currentlyValid) {
/* If valid, add result to the current numbers stack. */
stackNums.addFirst(tempOperation.result);
} else if (solutionState == SolutionState.lastOperationRedundant) {
/* If operation is redundant, dispose it and continue. */
continue;
} else if (solutionState == SolutionState.lastResultInvalid) {
/* If results is invalid at any stage, dispose whole solution. */
break;
}
if (solutions.addSolution(tempSolution) == true) break;
} while (stackNums.length > 1);
}
}
/* Will show only accurate solutions.
* If there is no accurate solutions, will show solutions which results
* are closest to the expected result.
*/
solutions.showSolutions();
}
}
There are 5 classes, to shorten the question I added them in this Gist.
My algorithm is as follows;
Rules for this Project are; program must randomly generate 5 single digit number and 1 two digit number where twoDigitNumber % 10 == 0 and a three digit number as target.
I get permutations of 4 operators and numbers that will be used in operations (Using trotter package.)
For each permutation of numbers, I apply each permutation of operators; using Operation class and add them into a Solution instance for each permutation.
I pass some redundant operations in each iteration, and if there is an invalid result at any stage, I dispose that solution and continue. (I'm taking this DataGenetics blog about this topic as a reference.)
To test my algorithm I used numbers 1, 2, 3, 4 and set target as 15. The results from dcode.fr Solver are as is;
15 (2 op.)
4 + 1 = 5
5 x 3 = 15
15 (3 op.)
4 + 3 = 7
7 x 2 = 14
14 + 1 = 15
15 (3 op.)
4 x 3 = 12
12 + 2 = 14
14 + 1 = 15
15 (3 op.)
4 x 3 = 12
2 + 1 = 3
12 + 3 = 15
15 (3 op.)
3 + 2 = 5
4 - 1 = 3
5 x 3 = 15
15 (3 op.)
4 x 3 = 12
12 + 1 = 13
13 + 2 = 15
15 (3 op.)
4 - 1 = 3
3 + 2 = 5
5 x 3 = 15
15 (3 op.)
4 + 2 = 6
6 - 1 = 5
5 x 3 = 15
15 (3 op.)
2 + 1 = 3
4 x 3 = 12
12 + 3 = 15
15 (3 op.)
2 - 1 = 1
4 + 1 = 5
5 x 3 = 15
(A total of 10 solutions.)
and the solutions my program found are as is;
> SOLUTION 1 ~
4 - 1 = 3
3 + 2 = 5
5 x 3 = 15
> SOLUTION 2 ~
4 + 1 = 5
5 x 3 = 15
(A total of 2 solutions.)
Can you tell me what am I thinking wrongly; Why can't I find all solutions? What are alternative approaches I can take to solve this problem? Is there anything I'm missing?
TY for taking time.
I'm trying to figure out this algorithm that accepts an input of an int and should return an output of the sum of each element in the int.
# Input -> 4321
# output -> 10 (4+3+2+1)
def sum_func(n):
# Base case
if len(str(n)) == 1:
return n
# Recursion
else:
return n%10 + sum_func(n/10)
When Trying to break apart this algorithm this is what I come up with
1st loop -> 1 + 432 = 433
2nd loop -> 2 + 43 = 45
3rd loop -> 3 + 4 = 7
4th loop -> 4 + 4 = 8
How was it able to come up with the result of 10?
Unwinding, it would look like this:
sum_func(4321)
= 1 + sum_func(432)
= 1 + 2 + sum_func(43)
= 1 + 2 + 3 + sum_func(4)
= 1 + 2 + 3 + 4
When trying to understand recursion you'll have to clearly understand what is returned.
In this case function sum_func(n) returns the sum of the digits in it's argument n.
For concrete n task is divided into last_digit_of_n + sum_func(n_without_last_digit).
For example,
sum_func(4321) =
sum_func(432) + 1 =
sum_func(43) + 2 + 1 =
sum_func(4) + 3 + 2 + 1 =
4 + 3 + 2 + 1
Hope this helps.
(As a side note, checking if n has more than one digit using str is a bad idea. Better just to check if n <= 9)
You must reach the base case before the summation occurs:
Iteration 1: 1 + sum_func(432)
Iteration 2: 1 + 2 + sum_func(43)
Iteration 3: 1 + 2 + 3 + sum_func(4) = 1 + 2 + 3 + 4 = 10
There is a table and now add a new column -- sort_num int default 0
id level sort_num
1 1 0
2 1 0
3 2 0
4 2 0
5 2 0
6 3 0
7 3 0
8 3 0
9 3 0
Now I want to set sort_num values like below
id level sort_num
1 1 1
2 1 2
3 2 1
4 2 2
5 2 3
6 3 1
7 3 2
8 3 3
9 3 4
The Java code implement above requirement is
int sortNum = 0;
int currentLevel = fooList.get(0).getLevel();
for (RuleConf foo : fooList) {
if(currentLevel != foo.getLevel()){
sortNum = 0;
currentLevel = foo.getLevel();
}
foo.setSortNum(++sortNum);
}
I want to know if Java8 could simplify above code？
PS. Use mysql to implement this requirement
set #index:=0; update t set sort_num = (#index:=#index+1) where level = 1 order by id;
set #index:=0; update t set sort_num = (#index:=#index+1) where level = 2 order by id;
set #index:=0; update t set sort_num = (#index:=#index+1) where level = 3 order by id;
The best approach is to stick to your plain enhanced for loop. I don't think it is possible to come up with a single Stream solution, since you need to have intermediate values. Like:
Map<Integer, List<RuleConf>> levels = fooList.stream()
.collect(Collectors.groupingBy(RuleConf::getLevel));
levels.values().forEach(v ->
IntStream.range(0, v.size()).forEach(i -> v.get(i).setSortNum(i + 1))
);
If you keep track of the next order numbers yourself, you may do it with one stream. This solution is thread safe as well, hence should work with parallel streams:
Map<Integer, AtomicInteger> orders = new ConcurrentHashMap<>();
fooList.stream().forEachOrdered(foo -> {
orders.putIfAbsent(foo.getLevel(), new AtomicInteger());
foo.setOrder(orders.get(foo.getLevel()).incrementAndGet());
});
It should outperform the other stream-solutions, because it requires to iterate over the list only ones.