The answer might be obvious to the trained eye, but I've been hitting the books for a few hours now, my eyes are straining, and I can't seem to see the bug.
Below are two implementations of selection sort I wrote, and neither is sorting the input correctly. You can play with this code on an online interpreter.
def selection_sort_enum(array)
n = array.length - 1
0.upto(n - 1) do |i|
smallest = i
(i + 1).upto(n) do |j|
smallest = j if array[j] < array[i]
end
array[i], array[smallest] = array[smallest], array[i] if i != smallest
end
end
def selection_sort_loop(array)
n = array.length - 1
i = 0
while i <= n - 1
smallest = i
j = i + 1
while j <= n
smallest = j if array[j] < array[i]
j += 1
end
array[i], array[smallest] = array[smallest], array[i] if i != smallest
i += 1
end
end
Here's the test of the first implementation, selection_sort_enum:
puts "Using enum:"
a1 = [*1..10].shuffle
puts "Before sort: #{a1.inspect}"
selection_sort_enum(a1)
puts "After sort: #{a1.inspect}"
Here's the test of the second implementation, selection_sort_loop:
puts "Using while:"
a2 = [*1..10].shuffle
puts "Before sort: #{a2.inspect}"
selection_sort_enum(a2)
puts "After sort: #{a2.inspect}"
Here's the output of the first implementation, selection_sort_enum:
Using enum:
Before sort: [7, 5, 2, 10, 6, 1, 3, 4, 8, 9]
After sort: [4, 3, 1, 9, 5, 2, 6, 7, 8, 10]
Here's the output of the second implementation, selection_sort_loop:
Using while:
Before sort: [1, 10, 5, 3, 7, 4, 8, 9, 6, 2]
After sort: [1, 2, 4, 3, 6, 5, 7, 8, 9, 10]
In both the code snippets you are comparing with index i instead of index smallest.
This should work :
def selection_sort_enum(array)
n = array.length - 1
0.upto(n - 1) do |i|
smallest = i
(i + 1).upto(n) do |j|
smallest = j if array[j] < array[smallest]
end
array[i], array[smallest] = array[smallest], array[i] if i != smallest
end
end
def selection_sort_loop(array)
n = array.length - 1
i = 0
while i <= n - 1
smallest = i
j = i + 1
while j <= n
smallest = j if array[j] < array[smallest]
j += 1
end
array[i], array[smallest] = array[smallest], array[i] if i != smallest
i += 1
end
end
Output :
Using enum:
Before sort: [5, 6, 7, 9, 2, 4, 8, 1, 10, 3]
After sort: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Using while:
Before sort: [6, 5, 9, 2, 1, 3, 10, 4, 7, 8]
After sort: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Link to solution : http://ideone.com/pKLriY
def selection_sort_enum(array)
n = array.length - 1
0.upto(n) do |i| # n instead of (n - 1)
smallest_index = i
(i + 1).upto(n) do |j|
smallest_index = j if array[j] < array[i]
end
puts "#{array}", smallest_index
array[i], array[smallest_index] = array[smallest_index], array[i] if i != smallest_index
end
end
You might be interested in this:
def selection_sort_enum(array)
n = array.length - 1
0.upto(n - 1) do |i|
smallest = i
(i + 1).upto(n) do |j|
smallest = j if array[j] < array[i]
end
array[i], array[smallest] = array[smallest], array[i] if i != smallest
end
array # <-- added to return the modified array
end
def selection_sort_loop(array)
n = array.length - 1
i = 0
while i <= n - 1
smallest = i
j = i + 1
while j <= n
smallest = j if array[j] < array[i]
j += 1
end
array[i], array[smallest] = array[smallest], array[i] if i != smallest
i += 1
end
array # <-- added to return the modified array
end
require 'fruity'
ARY = (1 .. 100).to_a.shuffle
compare do
_enum { selection_sort_enum(ARY.dup) }
_loop { selection_sort_loop(ARY.dup) }
end
Which results in:
# >> Running each test once. Test will take about 1 second.
# >> _enum is faster than _loop by 3x ± 1.0
Related
I'm new to programming. I start to learn Ruby freshly and I can't understand how to implement an algorithm for permuting negative(or positive) elements of an array without using an additional array.
For example:
Like this: [-10, 3, -1, 0, -9 ] -> [-10, 3, -9, 0, -1 ] (sort only negatives)
Either that: [-5, 5, -8, 2, 1] -> [-5, 1, -8, 2, 5] (sort only positives)
def sort_positives(arr)
(arr.size-1).times do |i|
next if arr[i] <= 0
smallest = i
(i+1..arr.size-1).each do |j|
smallest = j if arr[j] > 0 && arr[j] < arr[smallest]
end
if smallest > i
tmp = arr[i]
arr[i] = arr[smallest]
arr[smallest] = tmp
end
end
arr
end
arr = [-2, 5, 3, -4, 6, 1, -3]
sort_positives arr
#=> [-2, 1, 3, -4, 5, 6, -3]
arr
#=> [-2, 1, 3, -4, 5, 6, -3]
sort_negatives is a straightforward modification to sort_positives.
def swap(arr, i, j)
arr[i] = arr[i] ^ arr[j]
arr[j] = arr[j] ^ arr[i]
arr[i] = arr[j] ^ arr[i]
end
def sort_negative(arr)
size = arr.size
i = 0
while i < size - 1
next if arr[i] > 0 # first index of negative number
next_neg = 0
min_neg = i
(i + 1).upto(size - 1) do |j|
if arr[i] < 0 && arr[j] < 0
next_neg = j if next_neg == 0
min_neg = j if arr[min_neg] > arr[j]
end
end
swap(arr, i, min_neg) if min_neg > i
if next_neg > 0
i = next_neg # jump to next negative number
else
break
end
end
end
arr = [-10, 0, 2, 6, 10, -1, 7, 20, 1, 0, -9, 13, 6, 88, -11, -156]
sort_negative(arr)
puts arr.inspect # [-156, 0, 2, 6, 10, -11, 7, 20, 1, 0, -10, 13, 6, 88, -9, -1]
I am given a string S (of integers) and a number N. I want to insert arbitrary number of '+' in S so that the sum becomes equal to N.
Ex:<br>
S = 15112 and N = 28<br>
Ans is : 15+11+2<br>
S = 120012 and N = 33<br>
Ans is : 1+20+012<br>
S = 123 and N = 123<br>
Ans is : 123
given : |S| <= 120 and N <= 10^6
It is guarenteed that S and N are given such that it is always possible to form valid expression. Is there any algorithm which can solve this? I tried to think on it but couldn't come up with solution.
There may be more efficient ways to do this, but since you have nothing so far…
You can simply find all combinations of a boolean array that indicates whether a plus should exist between the numbers or not.
For example: with an input of 112134, 1 + 12 + 13 + 4 can be represented with the boolean array [true, false, true, false, true] indicating that there is a plus after the 1st, 3rd, and 5th numbers. The problem then reduces to finding which combinations add to your number. There are lot of ways to find combinations. Recursive backtracking is a classic.
In javascript/node this might look like this:
function splitOnIndexes(arr, a) {
// split the array into numbers based on the booleans
let current = "" + arr[0]
let output = []
for (let i = 0; i < a.length; i++) {
if (!a[i]) {
current += arr[i + 1]
} else {
output.push(current)
current = "" + arr[i + 1]
}
}
output.push(current)
return output
}
function findSum(input, total) {
function backtrack(n, k = 0, a = []) {
const sum = (arr) => arr.reduce((a, c) => a + parseInt(c), 0)
if (k === n) {
let ans = splitOnIndexes(input, a)
if (sum(ans) === total) {
console.log(ans.join(' + '))
}
} else {
k = k + 1
let c = [true, false]
for (let i = 0; i < 2; i++) {
a[k - 1] = c[i]
backtrack(n, k, a)
}
}
}
backtrack(input.length - 1)
}
findSum('15112', 28)
findSum('120012', 33)
findSum('123', 123)
As you can see, more than one answer is possible. Your first example is solved with both 15+1+12 and 15+11+2. If you only need one, you can of course stop early.
The idea is to use dynamic programming, you only care about sums between 0 and 10^6 and only have 120 possible indexes. if dp[i][j] = x, it means that from index x of the string, we went to index i (so we added a + before i) and we got a sum of j. This leads to a O(|S| * N) solution:
#include <iostream>
#include <string>
#include <vector>
using namespace std;
string s;
long n;
long dp[123][1000001];
void solve (int index, long sum) {//index = what index of s still remains to scan. sum = the sum we have accumulated till now
if (sum >= n or index >= s.length()) return;
if (dp[index][sum] != -1) return;
if (index == n and sum == n) return;
long num = 0;
for (int i = 0; i < 7 && index + i < s.length(); i++) { //N has 6 digits at most
num = stoi(s.substr(index, i + 1));
solve(index + i + 1, sum + num);
if (sum + num <= n) {
dp[index + i + 1][sum + num] = index;
}
}
}
int main () {
cin >> s;
cin >> n;
for (int i = 0; i < 121; i++) {
for (int j = 0; j < 1000001; j++) {
dp[i][j] = -1;
}
}
solve(0, 0);
int sum = n;
int idx = s.length();
vector<string> nums;
//reconstruct solution
while (idx != 0) {
nums.push_back(s.substr(dp[idx][sum], idx - dp[idx][sum]));
idx = dp[idx][sum];
sum -= stoi(nums[nums.size() - 1]);
}
for (int i = nums.size() -1; i >= 0; i--) {
cout << nums[i];
if (i != 0) cout << "+";
}
}
This is a Ruby version with step by step explanation of the algorithm, so you can easily code in C++ (or I'll try later).
# Let's consider that we extracted the values from text, so we already have the string of int and the result as integer:
string_of_int = "15112"
result = 28
# The basic idea is to find a map (array) that tells how to group digits, for example
sum_map = [2, 1, 2]
# This means that string_of_int is mapped into the following numbers
# 15, 1, 12
# then sum the numbers, in this case 15+1+12 = 28
# For finding a the solution we need to map
# all the possible combinations of addition given the n digits of the string_of_int then check if the sum is equal to the result
# We call k the number of digits of string_of_int
# in ruby we can build an array called sum_maps
# containing all the possible permutations like this:
k = string_of_int.length # => 5
sum_maps = []
k.times do |length|
(1..k).to_a.repeated_permutation(length).each {|e| sum_maps << e if e.inject(:+) == k}
end
sum_maps
# => [[1, 5], [2, 4], [3, 3], [4, 2], [5, 1], [1, 1, 4], [1, 2, 3], [1, 3, 2], [1, 4, 1], [2, 1, 3], [2, 2, 2], [2, 3, 1], [3, 1, 2], [3, 2, 1], [4, 1, 1]]
# Now must check which of of the sum_map is giving us the required result.
#
# First, to keep the code short and DRY,
# better to define a couple of useful methods for the String class to use then:
class String
def group_digits_by(sum_map)
string_of_int_splitted = self.split("")
grouped_digits = []
sum_map.each { |n| grouped_digits << string_of_int_splitted.shift(n).join.to_i}
grouped_digits.reject { |element| element == 0 }
end
def sum_grouped_of_digits_by(sum_map)
group_digits_by(sum_map).inject(:+)
end
end
# So we can call the methods directly on the string
# for example, in ruby:
string_of_int.group_digits_by sum_map #=> [15, 1, 12]
string_of_int.sum_grouped_of_digits_by sum_map #=> 28
# Now that we have this metods, we just iterate through the sum_maps array
# and apply it for printing out the sm_map if the sum of grouped digits is equal to the result
# coded in ruby it is:
combinations = []
sum_maps.each { |sum_map| combinations << string_of_int.group_digits_by(sum_map) if string_of_int.sum_grouped_of_digits_by(sum_map) == result }
p combinations.uniq
# => [[15, 1, 12], [15, 11, 2]]
In short, written as a Ruby module it becomes:
module GuessAddition
class ::String
def group_digits_by(sum_map)
string_of_int_splitted = self.split("")
grouped_digits = []
sum_map.each { |n| grouped_digits << string_of_int_splitted.shift(n).join.to_i}
grouped_digits.reject { |element| element == 0 }
end
def sum_grouped_of_digits_by(sum_map)
group_digits_by(sum_map).inject(:+)
end
end
def self.guess_this(string_of_int, result)
k = string_of_int.length
sum_maps = []
k.times { |length| (1..k).to_a.repeated_permutation(length).each {|e| sum_maps << e if e.inject(:+) == k} }
combinations = []
sum_maps.each { |sum_map| combinations << string_of_int.group_digits_by(sum_map) if string_of_int.sum_grouped_of_digits_by(sum_map) == result }
combinations.uniq
end
end
p GuessAddition::guess_this("15112", 28) # => [[15, 1, 12], [15, 11, 2]]
I have implemented this quicksort but I seem to have bug that I can not fix, would someone mind taking a quick look at it?
The output for the example I give is close to the answer but some indices are misplaced.
def partition(array, pivot, start, end):
# move pivot to the end
temp = array[pivot]
array[pivot] = array[end]
array[end] = temp
i = start
j = end - 1
while(i < j):
# check from left for element bigger than pivot
while(i < j and array[end] > array[i]):
i = i + 1
# check from right for element smaller than pivot
while(i < j and array[end] < array[j]):
j = j - 1
# if we find a pair of misplaced elements swap them
if(i < j):
temp = array[i]
array[i] = array[j]
array[j] = temp
# move pivot element to its position
temp = array[i]
array[i] = array[end]
array[end] = temp
# return pivot position
return i
def quicksort_helper(array, start, end):
if(start < end):
pivot = (start + end) / 2
r = partition(array, pivot, start, end)
quicksort_helper(array, start, r - 1)
quicksort_helper(array, r + 1, end)
def quicksort(array):
quicksort_helper(array, 0, len(array) - 1)
array = [6, 0, 5, 1, 3, 4, -1, 10, 2, 7, 8, 9]
quicksort(array)
print array
I have a feeling the answer will be obvious but I can not find it.
Desired output:
[-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Actual output:
[-1, 0, 2, 3, 1, 4, 5, 6, 7, 8, 9, 10]
The critical repair is in the inner while loops, where you march i and j toward each other. If all you're worried about is swapping the correct non-pivot elements, the logic you posted is fine. However, that first loop needs to be
while(i <= j and array[end] > array[i]):
i = i + 1
to ensure that i has the correct value for swapping the pivot element into the middle. Otherwise, you can swap it one element to the left of its proper position, which is why your sort fails.
You can also use Python's multiple assignment for a cleaner swap:
while(i < j):
# check from left for element bigger than pivot
while(i <= j and array[end] > array[i]):
i = i + 1
# check from right for element smaller than pivot
while(i < j and array[end] < array[j]):
j = j - 1
# if we find a pair of misplaced elements swap them
if(i < j):
array[i], array[j] = array[j], array[i]
I'm trying to generate decent partition of given integer number N numbered K in lexicographical order, e.g. for N = 5, K = 3 we got:
5 = 1 + 1 + 1 + 1 + 1
5 = 1 + 1 + 1 + 2
5 = 1 + 1 + 3
5 = 1 + 2 + 2
5 = 1 + 4
5 = 2 + 3
5 = 5
And the third one is 1 + 1 + 3.
How can I generate this without generating every partition(in C language, but most of all I need algorithm)?
Going to find maximal number in partition(assuming we can find number of partitions d[i][j], where i is number and j is maximal integer in its partition), then decrease the original number and number we are looking for. So yes, I'm trying to use dynamic programming. Still working on code.
This doesn't work at all:
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
FILE *F1, *F2;
main()
{
long long i, j, p, n, k, l, m[102][102];
short c[102];
F1 = fopen("num2part.in", "r");
F2 = fopen ("num2part.out", "w");
n = 0;
fscanf (F1, "%lld %lld", &n, &k);
p = 0;
m[0][0] = 1;
for ( i = 0; i <= n; i++)
{
for (j = 1; j <= i; j++)
{
m[i][j] = m[i - j][j] + m[i][j - 1];
}
for (j = i + 1; j <= n; j++)
{
m[i][j] = m[i][i];
}
}
l = n;
p = n;
j = n;
while (k > 0)
{
while ( k < m[l][j])
{
if (j == 0)
{
while (l > 0)
{
c[p] = 1;
p--;
l--;
}
break;
}
j--;
}
k -=m[l][j];
c[p] = j + 1;
p--;
l -= c[p + 1];
}
//printing answer here, answer is contained in array from c[p] to c[n]
}
Here is some example Python code that generates the partitions:
cache = {}
def p3(n,val=1):
"""Returns number of ascending partitions of n if all values are >= val"""
if n==0:
return 1 # No choice in partitioning
key = n,val
if key in cache:
return cache[key]
# Choose next value x
r = sum(p3(n-x,x) for x in xrange(val,n+1))
cache[key]=r
return r
def ascending_partition(n,k):
"""Generate the k lexicographically ordered partition of n into integer parts"""
P = []
val = 1 # All values must be greater than this
while n:
# Choose the next number
for x in xrange(val,n+1):
count = p3(n-x,x)
if k >= count:
# Keep trying to find the correct digit
k -= count
elif count: # Check that there are some valid positions with this digit
# This must be the correct digit for this location
P.append(x)
n -= x
val = x
break
return P
n=5
for k in range(p3(n)):
print k,ascending_partition(n,k)
It prints:
0 [1, 1, 1, 1, 1]
1 [1, 1, 1, 2]
2 [1, 1, 3]
3 [1, 2, 2]
4 [1, 4]
5 [2, 3]
6 [5]
This can be used to generate an arbitrary partition without generating all the intermediate ones. For example, there are 9253082936723602 partitions of 300.
print ascending_partition(300,10**15)
prints
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 7, 8, 8, 11, 12, 13, 14, 14, 17, 17, 48, 52]
def _yieldParts(num,lt):
''' It generate a comination set'''
if not num:
yield ()
for i in range(min(num,lt),0,-1):
for parts in _yieldParts(num-i,i):
yield (i,)+parts
def patition(number,kSum,maxIntInTupple):
''' It generates a comination set with sum of kSum is equal to number
maxIntInTupple is for maximum integer can be in tupple'''
for p in _yieldParts(number,maxIntInTupple):
if(len(p) <=kSum):
if(len(p)<kSum):
while len(p) < kSum:
p+=(0,)
print p
patition(40,8,40)
Output:
-------
(40,0,0,0,0,0,0,0)
(39,1,0,0,0,0,0,0)
.
.
.
.
I need to create one array of numbers inside one range, like:
[1..5] in 10 times = [1,1,2,2,3,3,4,4,5,5]
[1..5] in 5 times = [1,2,3,4,5]
[1..5] in 3 times = [1,3,5]
def distribute(start_value, end_value, times, is_integer)
array = Array.new(times-1)
min_value = [end_value,start_value].min
max_value = [end_value,start_value].max
if max_value-min_value<times
factor = (max_value-min_value).abs/(array.size).to_f
else
factor = (max_value-min_value).abs/(array.size-1).to_f
end
for i in 0..array.size
v = [ [max_value, factor*(i+1)].min, min_value].max
is_integer ? array[i] = v.round : array[i] = v
end
start_value < end_value ? array : array.reverse
end
distribute(1, 5, 10, true)
=> [1, 1, 1, 2, 2, 3, 3, 4, 4, 4] #WRONG should be [1,1,2,2,3,3,4,4,5,5]
distribute(5, 1, 5, true)
=> [5, 4, 3, 2, 1] #OK
distribute(1, 5, 3, true)
=> [4, 5, 5] #WRONG should be [1, 3, 5]
How 'bout this:
def distribute(min,max,items)
min,max = [min,max].sort
(0...items).map {|i| (min + i * (max - min) / (items-1.0)).round}
end
Or if you really need the int/float flag:
def distribute(min,max,items,ints)
min,max = [min,max].sort
a = (0...items).map {|i| min + i * (max - min) / (items-1.0)}
ints ? a.map {|i| i.round} : a
end
And if you really need this to go in reverse if the parameters are given to you backwards:
def distribute(min,max,items,ints)
usemin,usemax = [min,max].sort
diff = usemax - usemin
a = (0...items).map {|i| usemin + i * diff / (items-1.0)}
a.map! {|i| i.round} if ints
min != usemin ? a.reverse : a
end
just a little correction... when the array_size is 0
def distribute(start_value, end_value, array_size, want_ints)
diff = 1.0 * (end_value - start_value)
n = [array_size-1, 1].max
(0..(array_size-1)).map { |i|
v = start_value + i * diff / n
want_ints ? v.round : v
}
end