Finding the sum of nearest smallest and greatest number in an array - arrays

The question is straightforward that we want to find the sum of the nearest smallest and greatest number for every index of an array. But the part which I am not able to get is how to return the resulting array with the sum values on the same index values as the numbers.
Example: [1,5,2,3,8]
The sum for each indexes is as follows:
for index 0 the element is 1 hence sum = (0 + 2) = 2
since it has no smallest number therefore taking the nearest smallest number to be 0.
similarly for index 1 sum = (3 + 8 ) = 11 {3 - nearest smallest number to 5 and 8 nearest largest number}
and so on.
What I did was sort the given array then iterate through it and in every iteration take the sum of arr[i-1] + arr[i+1] elements and storing them in the result/answer array.{ with 0th and last element being dealt with separately }
So basically
If the input array is -> [1,5,2,3,8]
the resultant array will be -> [2,4,7,11,5]
but it is required to be as -> [2,11,4,7,5]
that is the sum of each index element to be at the same index as was the initial number
(I am using C++)

You will get the desired output by running this. It is written in Go.
Copy the original input array
Sort the copied array
Create a Map Sorted Value -> Sorted Index
make an output array with same length as input
Iterate through the Input Array and check the value is largest or smallest and Do the Sum as described in the question
store the Sum in the output array in the same index as input array
package main
import (
"fmt"
"sort"
)
func main() {
indexes := []int{1, 5, 2, 3, 8}
output := findSum(indexes)
fmt.Println(output)
}
func findSum(input []int) []int {
if len(input) < 2 {
return input
}
sorted := make([]int, len(input))
copy(sorted, input)
sort.Slice(sorted, func(i, j int) bool {
return sorted[i]< sorted[j]
})
sortedMap := make(map[int]int)
for i, i2 := range sorted {
sortedMap[i2] = i
}
output := make([]int, len(input))
for j, index := range input {
i := sortedMap[index]
if i == 0 {
output[j] = sorted[i+1]
continue
}
if i == len(input) - 1 {
output[j] = sorted[i-1]
continue
}
output[j] = sorted[i - 1] + sorted[i + 1]
}
return output
}
You can run here

The trick is to create an array of indexes into the original array and sort this, rather than sorting the original array.
You don't mention what language you're using, but here's some Java code to illustrate:
Integer[] arr = {1,5,2,3,8};
System.out.println(Arrays.toString(arr));
Integer[] idx = new Integer[arr.length];
for(int i=0; i<idx.length; i++) idx[i] = i;
System.out.println(Arrays.toString(idx));
Arrays.sort(idx, (a, b) -> arr[a] - arr[b]);
System.out.println(Arrays.toString(idx));
Integer[] res = new Integer[arr.length];
for(int i=0; i<arr.length; i++)
{
res[idx[i]] = (i > 0 ? arr[idx[i-1]] : 0) + (i < arr.length - 1 ? arr[idx[i+1]] : 0);
}
System.out.println(Arrays.toString(res));
Or translated into (possibly non-idiomatic) C++ (Ideone):
int len = 5;
array<int, 5> arr{1,5,2,3,8};
for(auto i : arr) cout << i << " ";
cout << endl;
array<int, 5> idx;
for(int i=0; i<len; i++) idx[i] = i;
for(auto i : idx) cout << i << " ";
cout << endl;
sort(idx.begin(), idx.end(), [&arr](int a, int b) {return arr[a] < arr[b];});
for(auto i : idx) cout << i << " ";
cout << endl;
array<int, 5> res;
for(int i=0; i<len; i++)
res[idx[i]] = (i > 0 ? arr[idx[i-1]] : 0) + (i < len - 1 ? arr[idx[i+1]] : 0);
for(auto i : res) cout << i << " ";
cout << endl;
Output:
[1, 5, 2, 3, 8]
[0, 1, 2, 3, 4]
[0, 2, 3, 1, 4]
[2, 11, 4, 7, 5]

Related

Given an array A of size N, find all combination of four elements in the array whose sum is equal to a given value K

Given an array A of size N, find all combinations of four elements in the array whose sum is equal to a given value K. For example, if the given array is {10, 2, 3, 4, 5, 9, 7, 8} and K = 23, one of the quadruple is “3 5 7 8” (3 + 5 + 7 + 8 = 23).
The output should contain only unique quadruple For example, if the input array is {1, 1, 1, 1, 1, 1} and K = 4, then the output should be only one quadruple {1, 1, 1, 1}
My approach: I tried to solve this problem by storing all the distinct pairs formed from the given array into a hash table (std::unordered_multimap), with their sum as key. Then for each pair sum, I looked for (K - sum) key in the hash table. The problem with this approach is I am getting too many duplicated like (i, j, l, m) and (i, l, j, m) are the same, plus there are duplicates due to the same items in the array. I am not sure what is the optimal way to address that.
The code for the above-mentioned approach is:
#include <iostream>
#include <unordered_map>
#include <tuple>
#include <vector>
int main() {
size_t tc = 0;
std::cin >> tc; //number of test cases
while(tc--) {
size_t n = 0, k = 0;
std::cin >> n >> k;
std::vector<size_t> vec(n);
for (size_t i = 0; i < n; ++i)
std::cin >> vec[i];
std::unordered_multimap<size_t, std::tuple<size_t, size_t>> m;
for (size_t i = 0; i < n - 1; ++i)
for (size_t j = i + 1; j < n; ++j) {
const auto sum = vec[i] + vec[j];
m.emplace(sum, std::make_tuple(i, j));
}
for (size_t i = 0; i < n - 1; ++i)
for (size_t j = i + 1; j < n; ++j) {
const auto sum = vec[i] + vec[j];
auto r = m.equal_range(k - sum);
for (auto it = r.first; it != r.second; ++it) {
if ((i == std::get<0>(it->second))
||(i == std::get<1>(it->second))
||(j == std::get<0>(it->second))
|| (j == std::get<1>(it->second)))
continue;
std::cout << vec[i] << ' ' << vec[j] << ' '
<< vec[std::get<0>(it->second)] << ' '
<< vec[std::get<1>(it->second)] << '$';
}
r = m.equal_range(sum);
for (auto it = r.first; it != r.second; ++it) {
if ((i == std::get<0>(it->second))
&& (j == std::get<1>(it->second))) {
m.erase(it);
break;
}
}
}
std::cout << '\n';
}
return 0;
}
The above code will run as-is in the link mentioned below in the Note.
Note: This problem is taken from https://practice.geeksforgeeks.org/problems/find-all-four-sum-numbers/0
To handle duplicate values in array
Consider [2, 2, 2, 3, 3] with goal 10.
The only solution is the 4-tuple <2,2,3,3>. The main point is to avoid choosing two 2 among three 2.
Let's consider the k-class, the set of tuples in which every tuple contain only k.
e.g: in our array we have the 2-class and 3-class.
The 2-class contains:
<2>
<2,2>
<2,2,2>
while the 3-class contains:
<3>
<3,3>
An idea is to reduce the array of elem (elem being an integer value) to an array of k-class.
idem
[[<2>, <2,2>, <2,2,2>], [<3>, <3,3>]]
We can think of taking the cartesian product between the 2-class set and the 3-class set, and check which result lead to solution.
More concretely, let's take some tuple T, whose last (==rightmost) value is k. (in <2,3,4> rightmost value would be 4).
We can pick any l-class from our array (* l > k) and join the tuples from that l-class to T.
e.g
consider array [2, 9, 9, 3, 3, 4, 6] and tuple <2, 3, 3>
The rightmost value is 3.
The candidate k-class are 4-class, 6-class, 9-class
we can join:
<4>
<6>
<9>
<9,9>
so the next candidates will be:
<2, 3, 3, 4>
<2, 3, 3, 6>
<2, 3, 3, 9>
<2, 3, 3, 9, 9> //that one has too many elem, left for illustration
(* The purpose of l > k is to prevent the permutation. (if <1,2> is solution you don't want <2,1> since addition is commutative))
Algorithm
Foreach tuple, try to create new ones by rightjoining tuples from a "greater" k-class.
discard the resulting ones which have too many elements or whose sum is already too big...
At some point we won't have new candidates, so algorithm will stop
example of cuts:
given array [2,3,7,8,10,11], and tuple <2,3> and S == 13
<2,3,7> is candidate (2+3+7 = 12 < 13)
<2,3,10> is not candidate (2+3+10 = 15 > 13)
<2,3,11> even more so. not
<2,3,8> is not candidate either since the next rightjoin (to reach a 4-tuple) will overflow S
given array [2,3,4,4,4] given tuple <2,3> and candidate <4,4,4>
resulting tuple would be <2,3,4,4,4> which has too many elems, discard it!
Obviously the initialization is
some empty tuple
whose sum is 0
and whose rightmost element is less than any k from the array (you can rightjoin it anybody)
I believe it should not be too hard to translate to C++
class TupleClass {
sum = 0
rightIdx = -1
values = [] // an array of integers (hopefully summing to solution)
//idx is the position of the k-class found in array
add (val, idx) {
const t = new TupleClass()
t.values = this.values.concat(val)
t.sum = this.sum + val
t.rightIdx = idx
return t;
}
toString () {
return `<${this.values.join(',')}>`
}
addTuple (tuple, idx) {
const t = new TupleClass
t.values = this.values.concat(tuple.values)
t.sum = this.sum + tuple.sum
t.rightIdx = idx
return t;
}
get size () {
return this.values.length
}
}
function nodupes (v, S) {
v = v.reduce((acc, klass) => {
acc[klass] = (acc[klass] || {duplicity: 0, klass})
acc[klass].duplicity++
return acc
}, {})
v = Object.values(v).sort((a,b) => a.klass - b.klass).map(({ klass, duplicity }, i) => {
return Array(duplicity).fill(0).reduce((acc, _) => {
const t = acc[acc.length-1].add(klass, i)
acc.push(t)
return acc
}, [new TupleClass()]).slice(1)
})
//v is sorted by k-class asc
//each k-class is an array of tuples with increasing length
//[[<2>, <2,2>, <2,2,2>], [<3>,<3,3>]]
let tuples = [new TupleClass()]
const N = v.length
let nextTuples = []
const solutions = []
while (tuples.length) {
tuples.forEach(tuple => {
//foreach kclass after our rightmost value
for (let j = tuple.rightIdx + 1; j <= N - 1; ++j) {
//foreach tuple of that kclass
for (let tclass of v[j]) {
const nextTuple = tuple.addTuple(tclass, j)
if (nextTuple.sum > S || nextTuple.size > 4) {
break
}
//candidate to solution
if (nextTuple.size == 4) {
if (nextTuple.sum === S) {
solutions.push(nextTuple)
}
//invalid sum so adding more elem won't help, do not push
} else {
nextTuples.push(nextTuple)
}
}
}
})
tuples = nextTuples
nextTuples = []
}
return solutions;
}
const v = [1,1,1,1,1,2,2,2,3,3,3,4,0,0]
const S = 7
console.log('v:', v.join(','), 'and S:',S)
console.log(nodupes(v, 7).map(t=>t.toString()).join('\n'))

Range values in C

So I want to solve a problem in C
We have 10 numbers {1,1,8,1,1,3,4,9,5,2} in an array. We break the array into 3 pecies A, B, C.
And wemake the bellow procedure (I prefered to create a small diagram so you can undertand me better). Diagram here
As you see this isn't all the procedure just the start of it.
I created a code but I getting false results. What have I missed?
#define N 10
int sum_array(int* array, int first, int last) {
int res = 0;
for (int i = first ; i <= last ; i++) {
res += array[i];
}
return res;
}
int main(){
int array[N] = {1,1,8,1,1,3,4,9,5,2};
int Min = 0;
for (int A = 1; A < N - 2; A++) {
int ProfitA = sum_array(array, 0 , A-1);
int ProfitB = array[A];
int ProfitC = sum_array(array,A+1,N-1);
for (int B = 1; B < N - 1; B++) {
//here the values are "current" - valid
int temp = (ProfitA < ProfitB) ? ProfitA : ProfitB;
Min = (ProfitC < temp) ? ProfitC : temp;
//Min = std::min(std::min(ProfitA,ProfitB),ProfitC);
if (Min > INT_MAX){
Min = INT_MAX;
}
//and here they are being prepared for the next iteration
ProfitB = ProfitB + array[A+B-1];
ProfitC = ProfitC - array[A+B];
}
}
printf("%d", Min);
return 0;
}
Complexity of program is Ο(n (n+n))=O(n^2 )
To find the number of permutations here is the function : 1+0.5*N*(N-3) where N is the number of elements in the array.*
Here is the first though of the program in pseudocode. Complexity O(n^3)
//initialization, fills salary array
n:= length of salary array
best_min_maximum:=infinity
current_min_maximum:=infinity
best_bound_pos1 :=0
best_bound_pos2 :=0
for i = 0 .. (n-2):
>> for j = (i+1) .. (n-1)
>>>> current_min_maximum = max_bros_profit(salary, i, j)
>>>> if current_min_maximum < best_min_maximum:
>>>>>> best_min_maximum:=current_min_maximum
>>>>>> best_bound_pos1 :=i
>>>>>> best_bound_pos2 :=j
max_bros_profit(profit_array, position_of_bound_1, position_of_bound_2)
so max_bros_profit([8 5 7 9 6 2 1 5], 1(==1st space between days, counted from 0) , 3) is interpreted as:
8 . 5 | 7 . 9 | 6 .2 . 1 . 5 - which returns max sum of [8 5] [7 9] [6 2 1 5] => 14
> ^ - ^ - ^ - ^ - ^ - ^ - ^
> 0 , 1 , 2 , 3 , 4 , 5 , 6
This is my take. It is a greedy algorithm that starts with a maximal B range and then starts chopping off values one after another until the result cannot be improved. It hast complexity O(n).
#include <iostream>
#include <utility>
#include <array>
#include <algorithm>
#include <cassert>
// Splits an array `arr` into three sections A,B,C.
// Returns the indices to the first element of B and C.
// (the first element of A obviously has index 0)
template <typename T, ::std::size_t len>
::std::pair<::std::size_t,::std::size_t> split(T const (& arr)[len]) {
assert(len > 2);
// initialise the starting indices of section A, B, and C
// such that A: {0}, B: {1,...,len-2}, C: {len-1}
::std::array<::std::size_t,3> idx = {0,1,len-1};
// initialise the preliminary sum of all sections
::std::array<T,3> sum = {arr[0],arr[1],arr[len-1]};
for (::std::size_t i = 2; i < len-1; ++i)
sum[1] += arr[i];
// the preliminary maximum
T max = ::std::max({ sum[0], sum[1], sum[2] });
// now we iterate until section B is not empty
while ((idx[1]+1) < idx[2]) {
// in our effort to shrink B, we must decide whether to cut of the
// left-most element to A or the right-most element to C.
// So we figure out what the new sum of A and C would be if we
// did so.
T const left = (sum[0] + arr[idx[1]]);
T const right = (sum[2] + arr[idx[2]-1]);
// We always fill the smaller section first, so if A would be
// smaller than C, we slice an element off to A.
if (left <= right && left <= max) {
// We only have to update the sums to the newly computed value.
// Also we have to move the starting index of B one
// element to the right
sum[0] = left;
sum[1] -= arr[idx[1]++];
// update the maximum section sum
max = ::std::max(sum[1],sum[2]); // left cannot be greater
} else if (right < left && right <= max) {
// Similar to the other case, but here we move the starting
// index of C one to the left, effectively shrinking B.
sum[2] = right;
sum[1] -= arr[--idx[2]];
// update the maximum section sum
max = ::std::max(sum[1],sum[0]); // right cannot be greater
} else break;
}
// Finally, once we're done, we return the first index to
// B and to C, so the caller knows how our partitioning looks like.
return ::std::make_pair(idx[1],idx[2]);
}
It returns the index to the start of the B range and the index to the start of the C range.
This is your pseudocode in C (just for reference because you tagged your problem with C++ yet want a C only solution). Still, the greedy solution that bitmask provided above is a better O(N) solution; you should try to implement that algorithm instead.
#include <stdio.h>
#include <stdint.h>
#include <limits.h>
#define N 10
int sum_array(int* array, int cnt)
{
int res = 0;
int i;
for ( i = 0; i < cnt ; ++i)
res += array[i];
return res;
}
int main()
{
int array[N] = {1,1,8,1,1,3,4,9,5,2};
int Min = 0;
int bestA = 0, bestB = 0, bestMin = INT_MAX;
int A, B;
int i;
for ( A = 0; A < N - 2; ++A)
{
for ( B = A + 1; B < N - 1; ++B)
{
int ProfitA = sum_array(array, A + 1);
int ProfitB = sum_array(array + A + 1, B - A );
int ProfitC = sum_array(array + B + 1, N - 1 - B );
//here the values are "current" - valid
Min = (ProfitA > ProfitB) ? ProfitA : ProfitB;
Min = (ProfitC > Min) ? ProfitC : Min;
if( Min < bestMin )
bestA = A, bestB = B, bestMin = Min;
#if 0
printf( "%2d,%2d or (%3d,%3d,%3d) ", A, B, ProfitA, ProfitB, ProfitC );
for( i = 0; i < N; ++i )
printf( "%d%c", array[i], ( ( i == A ) || ( i == B ) ) ? '|' : ' ' );
printf( " ==> %d\n", Min);
#endif
}
}
printf("%d # %d, %d\n", bestMin, bestA, bestB);
return 0;
}
I made this solution before you removed the [C++] tag so I thought I'd go ahead and post it.
It runs in O(n*n):
const vector<int> foo{ 1, 1, 8, 1, 1, 3, 4, 9, 5, 2 }; // Assumed to be of at least size 3 For pretty printing each element is assumed to be less than 10
map<vector<int>::const_iterator, pair<int, string>> bar; // A map with key: the beginning of the C partition and value: the sum and string of that partition of C
auto mapSum = accumulate(next(foo.cbegin(), 2), foo.cend(), 0); // Find the largest possible C partition sum
auto mapString = accumulate(next(foo.cbegin(), 2), foo.cend(), string(), [](const string& init, int i){return init + to_string(i) + ' ';}); // Find the largest possible C partiont string
for (auto i = next(foo.cbegin(), 2); i < foo.cend(); mapSum -= *i++, mapString.erase(0, 2)){ // Fill the map with all possible C partitions
bar[i] = make_pair(mapSum, mapString);
}
mapSum = foo.front(); // mapSum will be reused for the current A partition sum
mapString = to_string(mapSum); // mapString will be reused for the current A partition string
cout << left;
for (auto aEnd = next(foo.cbegin()); aEnd < foo.cend(); ++aEnd){ // Iterate through all B partition beginings
auto internalSum = *aEnd; // The B partition sum
auto internalString = to_string(internalSum); // The B partition string
for (auto bEnd = next(aEnd); bEnd < foo.cend(); ++bEnd){ // Iterate through all B partition endings.
// print current partitioning
cout << "A: " << setw(foo.size() * 2 - 5) << mapString << " B: " << setw(foo.size() * 2 - 5) << internalString << " C: " << setw(foo.size() * 2 - 4) << bar[bEnd].second << "Max Sum: " << max({ mapSum, internalSum, bar[bEnd].first }) << endl;
internalSum += *bEnd; // Update B partition sum
internalString += ' ' + to_string(*bEnd); // Update B partition string
}
mapSum += *aEnd; // Update A partition sum
mapString += ' ' + to_string(*aEnd); // Update A partition string
}

Pseudocode - Arrays - Maxrun

I'm trying to solve a problem but I have difficulties with algorithms.
I have to write pseudocode for an iterative algorithm maxRun(A) that takes an array A of integer as input and return the maximal length of a run in A.
The subarray A[k...l] is a run if A[j] <= A[j + 1] for all j where k <= j < l. So it is a non decreasing segment of A.
Ex. A = [1,5,2,3,4,1], the max length would be 3 [2,3,4].
Thanks.
Simple Java implementation:
public class FindRun {
public static int maxRun(int[] a) {
int max = 0;
int index = 0;
int previous = a[0] + 1;
int run = 0;
while (index < a.length) {
if (a[index] >= previous) {
run++;
} else {
max = Math.max(max, run);
run = 1;
}
previous = a[index];
index++;
}
return Math.max(max, run);
}
public static void main(String[] args) {
System.out.println(maxRun(new int[] { 1, 5, 2, 3, 4, 1 }));
}
}
Here's a solution similar to #Michael's, in Ruby:
a = [1,5,2,3,4,1]
r = [1]
(1...a.size).each { |i| r << ((a[i] == a[i-1] + 1) ? r[i-1] + 1 : 1) }
r.max #=> 3
r.index(r.max) #=> 4
indicating the the maximum run is of length 3 and ends at a offset 4; that is, the run 2,3,4. I will now explain the algorithm I used. For those who don't know Ruby, this will also give you a taste of the language:
r = [1] creates an array with one element, whose value is 1. This is read, "The longest run ending at a offset 0 is of length 1.
(1...a.size) is the sequence 1, 2, 3, 4, 5. Three dots between 1 and a.size means the sequence ends with a.size - 1, which is 5.
each causes the following block, enclosed by {} to be executed once for each element of the sequence. The block variable i (in |i|) represents the sequence element.
r << x means add x to the end of the array r.
the expression to the right of r << says, "if the element of a at index i is one greater than element of a at index i-1, then the length of the run ending at index i is one greater than the length of the run ending at index i-1; else, a new run begins, whose length at offset i is 1.
After each is finished:
# r => [1, 1, 1, 2, 3, 1]
All that is required now is to find the element of r whose value is greatest:
r.max #=> 3
and the associated index:
r.index(r.max) #=> 4
Actually, the code above would more typically be written like this:
(1...a.size).each_with_object([1]) {|i,r| r << a[i] == a[i-1]+1 ? r[i-1]+1 : 1}
start, length = r.index(r.max) + 1 - r.max, r.max #=> 2, 3
Alternatively, we could have made r a hash (call it h) rather than an array, and written:
(1...a.size).each_with_object({0 => 1}) {|i,h|
h[i] = a[i] == a[i-1]+1 ? h[i-1]+1 : 1}.max_by {|_,v| v} #=> [4, 3]

Find the 2nd largest element in an array with minimum number of comparisons

For an array of size N, what is the number of comparisons required?
The optimal algorithm uses n+log n-2 comparisons. Think of elements as competitors, and a tournament is going to rank them.
First, compare the elements, as in the tree
|
/ \
| |
/ \ / \
x x x x
this takes n-1 comparisons and each element is involved in comparison at most log n times. You will find the largest element as the winner.
The second largest element must have lost a match to the winner (he can't lose a match to a different element), so he's one of the log n elements the winner has played against. You can find which of them using log n - 1 comparisons.
The optimality is proved via adversary argument. See https://math.stackexchange.com/questions/1601 or http://compgeom.cs.uiuc.edu/~jeffe/teaching/497/02-selection.pdf or http://www.imada.sdu.dk/~jbj/DM19/lb06.pdf or https://www.utdallas.edu/~chandra/documents/6363/lbd.pdf
You can find the second largest value with at most 2·(N-1) comparisons and two variables that hold the largest and second largest value:
largest := numbers[0];
secondLargest := null
for i=1 to numbers.length-1 do
number := numbers[i];
if number > largest then
secondLargest := largest;
largest := number;
else
if number > secondLargest then
secondLargest := number;
end;
end;
end;
Use Bubble sort or Selection sort algorithm which sorts the array in descending order. Don't sort the array completely. Just two passes. First pass gives the largest element and second pass will give you the second largest element.
No. of comparisons for first pass: n-1
No. of comparisons for second pass: n-2
Total no. of comparison for finding second largest: 2n-3
May be you can generalize this algorithm. If you need the 3rd largest then you make 3 passes.
By above strategy you don't need any temporary variables as Bubble sort and Selection sort are in place sorting algorithms.
Here is some code that might not be optimal but at least actually finds the 2nd largest element:
if( val[ 0 ] > val[ 1 ] )
{
largest = val[ 0 ]
secondLargest = val[ 1 ];
}
else
{
largest = val[ 1 ]
secondLargest = val[ 0 ];
}
for( i = 2; i < N; ++i )
{
if( val[ i ] > secondLargest )
{
if( val[ i ] > largest )
{
secondLargest = largest;
largest = val[ i ];
}
else
{
secondLargest = val[ i ];
}
}
}
It needs at least N-1 comparisons if the largest 2 elements are at the beginning of the array and at most 2N-3 in the worst case (one of the first 2 elements is the smallest in the array).
case 1-->9 8 7 6 5 4 3 2 1
case 2--> 50 10 8 25 ........
case 3--> 50 50 10 8 25.........
case 4--> 50 50 10 8 50 25.......
public void second element()
{
int a[10],i,max1,max2;
max1=a[0],max2=a[1];
for(i=1;i<a.length();i++)
{
if(a[i]>max1)
{
max2=max1;
max1=a[i];
}
else if(a[i]>max2 &&a[i]!=max1)
max2=a[i];
else if(max1==max2)
max2=a[i];
}
}
Sorry, JS code...
Tested with the two inputs:
a = [55,11,66,77,72];
a = [ 0, 12, 13, 4, 5, 32, 8 ];
var first = Number.MIN_VALUE;
var second = Number.MIN_VALUE;
for (var i = -1, len = a.length; ++i < len;) {
var dist = a[i];
// get the largest 2
if (dist > first) {
second = first;
first = dist;
} else if (dist > second) { // && dist < first) { // this is actually not needed, I believe
second = dist;
}
}
console.log('largest, second largest',first,second);
largest, second largest 32 13
This should have a maximum of a.length*2 comparisons and only goes through the list once.
I know this is an old question, but here is my attempt at solving it, making use of the Tournament Algorithm. It is similar to the solution used by #sdcvvc , but I am using two-dimensional array to store elements.
To make things work, there are two assumptions:
1) number of elements in the array is the power of 2
2) there are no duplicates in the array
The whole process consists of two steps:
1. building a 2D array by comparing two by two elements. First row in the 2D array is gonna be the entire input array. Next row contains results of the comparisons of the previous row. We continue comparisons on the newly built array and keep building the 2D array until an array of only one element (the largest one) is reached.
2. we have a 2D-array where last row contains only one element: the largest one. We continue going from the bottom to the top, in each array finding the element that was "beaten" by the largest and comparing it to the current "second largest" value. To find the element beaten by the largest, and to avoid O(n) comparisons, we must store the index of the largest element in the previous row. That way we can easily check the adjacent elements. At any level (above root level),the adjacent elements are obtained as:
leftAdjacent = rootIndex*2
rightAdjacent = rootIndex*2+1,
where rootIndex is index of the largest(root) element at the previous level.
I know the question asks for C++, but here is my attempt at solving it in Java. (I've used lists instead of arrays, to avoid messy changing of the array size and/or unnecessary array size calculations)
public static Integer findSecondLargest(List<Integer> list) {
if (list == null) {
return null;
}
if (list.size() == 1) {
return list.get(0);
}
List<List<Integer>> structure = buildUpStructure(list);
System.out.println(structure);
return secondLargest(structure);
}
public static List<List<Integer>> buildUpStructure(List<Integer> list) {
List<List<Integer>> newList = new ArrayList<List<Integer>>();
List<Integer> tmpList = new ArrayList<Integer>(list);
newList.add(tmpList);
int n = list.size();
while (n>1) {
tmpList = new ArrayList<Integer>();
for (int i = 0; i<n; i=i+2) {
Integer i1 = list.get(i);
Integer i2 = list.get(i+1);
tmpList.add(Math.max(i1, i2));
}
n/= 2;
newList.add(tmpList);
list = tmpList;
}
return newList;
}
public static Integer secondLargest(List<List<Integer>> structure) {
int n = structure.size();
int rootIndex = 0;
Integer largest = structure.get(n-1).get(rootIndex);
List<Integer> tmpList = structure.get(n-2);
Integer secondLargest = Integer.MIN_VALUE;
Integer leftAdjacent = -1;
Integer rightAdjacent = -1;
for (int i = n-2; i>=0; i--) {
rootIndex*=2;
tmpList = structure.get(i);
leftAdjacent = tmpList.get(rootIndex);
rightAdjacent = tmpList.get(rootIndex+1);
if (leftAdjacent.equals(largest)) {
if (rightAdjacent > secondLargest) {
secondLargest = rightAdjacent;
}
}
if (rightAdjacent.equals(largest)) {
if (leftAdjacent > secondLargest) {
secondLargest = leftAdjacent;
}
rootIndex=rootIndex+1;
}
}
return secondLargest;
}
Suppose provided array is inPutArray = [1,2,5,8,7,3] expected O/P -> 7 (second largest)
take temp array
temp = [0,0], int dummmy=0;
for (no in inPutArray) {
if(temp[1]<no)
temp[1] = no
if(temp[0]<temp[1]){
dummmy = temp[0]
temp[0] = temp[1]
temp[1] = temp
}
}
print("Second largest no is %d",temp[1])
PHP version of the Gumbo algorithm: http://sandbox.onlinephpfunctions.com/code/51e1b05dac2e648fd13e0b60f44a2abe1e4a8689
$numbers = [10, 9, 2, 3, 4, 5, 6, 7];
$largest = $numbers[0];
$secondLargest = null;
for ($i=1; $i < count($numbers); $i++) {
$number = $numbers[$i];
if ($number > $largest) {
$secondLargest = $largest;
$largest = $number;
} else if ($number > $secondLargest) {
$secondLargest = $number;
}
}
echo "largest=$largest, secondLargest=$secondLargest";
Assuming space is irrelevant, this is the smallest I could get it. It requires 2*n comparisons in worst case, and n comparisons in best case:
arr = [ 0, 12, 13, 4, 5, 32, 8 ]
max = [ -1, -1 ]
for i in range(len(arr)):
if( arr[i] > max[0] ):
max.insert(0,arr[i])
elif( arr[i] > max[1] ):
max.insert(1,arr[i])
print max[1]
try this.
max1 = a[0].
max2.
for i = 0, until length:
if a[i] > max:
max2 = max1.
max1 = a[i].
#end IF
#end FOR
return min2.
it should work like a charm. low in complexity.
here is a java code.
int secondlLargestValue(int[] secondMax){
int max1 = secondMax[0]; // assign the first element of the array, no matter what, sorted or not.
int max2 = 0; // anything really work, but zero is just fundamental.
for(int n = 0; n < secondMax.length; n++){ // start at zero, end when larger than length, grow by 1.
if(secondMax[n] > max1){ // nth element of the array is larger than max1, if so.
max2 = max1; // largest in now second largest,
max1 = secondMax[n]; // and this nth element is now max.
}//end IF
}//end FOR
return max2;
}//end secondLargestValue()
Use counting sort and then find the second largest element, starting from index 0 towards the end. There should be at least 1 comparison, at most n-1 (when there's only one element!).
#include<stdio.h>
main()
{
int a[5] = {55,11,66,77,72};
int max,min,i;
int smax,smin;
max = min = a[0];
smax = smin = a[0];
for(i=0;i<=4;i++)
{
if(a[i]>max)
{
smax = max;
max = a[i];
}
if(max>a[i]&&smax<a[i])
{
smax = a[i];
}
}
printf("the first max element z %d\n",max);
printf("the second max element z %d\n",smax);
}
The accepted solution by sdcvvc in C++11.
#include <algorithm>
#include <iostream>
#include <vector>
#include <cassert>
#include <climits>
using std::vector;
using std::cout;
using std::endl;
using std::random_shuffle;
using std::min;
using std::max;
vector<int> create_tournament(const vector<int>& input) {
// make sure we have at least two elements, so the problem is interesting
if (input.size() <= 1) {
return input;
}
vector<int> result(2 * input.size() - 1, -1);
int i = 0;
for (const auto& el : input) {
result[input.size() - 1 + i] = el;
++i;
}
for (uint j = input.size() / 2; j > 0; j >>= 1) {
for (uint k = 0; k < 2 * j; k += 2) {
result[j - 1 + k / 2] = min(result[2 * j - 1 + k], result[2 * j + k]);
}
}
return result;
}
int second_smaller(const vector<int>& tournament) {
const auto& minimum = tournament[0];
int second = INT_MAX;
for (uint j = 0; j < tournament.size() / 2; ) {
if (tournament[2 * j + 1] == minimum) {
second = min(second, tournament[2 * j + 2]);
j = 2 * j + 1;
}
else {
second = min(second, tournament[2 * j + 1]);
j = 2 * j + 2;
}
}
return second;
}
void print_vector(const vector<int>& v) {
for (const auto& el : v) {
cout << el << " ";
}
cout << endl;
}
int main() {
vector<int> a;
for (int i = 1; i <= 2048; ++i)
a.push_back(i);
for (int i = 0; i < 1000; i++) {
random_shuffle(a.begin(), a.end());
const auto& v = create_tournament(a);
assert (second_smaller(v) == 2);
}
return 0;
}
I have gone through all the posts above but I am convinced that the implementation of the Tournament algorithm is the best approach. Let us consider the following algorithm posted by #Gumbo
largest := numbers[0];
secondLargest := null
for i=1 to numbers.length-1 do
number := numbers[i];
if number > largest then
secondLargest := largest;
largest := number;
else
if number > secondLargest then
secondLargest := number;
end;
end;
end;
It is very good in case we are going to find the second largest number in an array. It has (2n-1) number of comparisons. But what if you want to calculate the third largest number or some kth largest number. The above algorithm doesn't work. You got to another procedure.
So, I believe tournament algorithm approach is the best and here is the link for that.
The following solution would take 2(N-1) comparisons:
arr #array with 'n' elements
first=arr[0]
second=-999999 #large negative no
i=1
while i is less than length(arr):
if arr[i] greater than first:
second=first
first=arr[i]
else:
if arr[i] is greater than second and arr[i] less than first:
second=arr[i]
i=i+1
print second
It can be done in n + ceil(log n) - 2 comparison.
Solution:
it takes n-1 comparisons to get minimum.
But to get minimum we will build a tournament in which each element will be grouped in pairs. like a tennis tournament and winner of any round will go forward.
Height of this tree will be log n since we half at each round.
Idea to get second minimum is that it will be beaten by minimum candidate in one of previous round. So, we need to find minimum in potential candidates (beaten by minimum).
Potential candidates will be log n = height of tree
So, no. of comparison to find minimum using tournament tree is n-1
and for second minimum is log n -1
sums up = n + ceil(log n) - 2
Here is C++ code
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <vector>
using namespace std;
typedef pair<int,int> ii;
bool isPowerOfTwo (int x)
{
/* First x in the below expression is for the case when x is 0 */
return x && (!(x&(x-1)));
}
// modified
int log_2(unsigned int n) {
int bits = 0;
if (!isPowerOfTwo(n))
bits++;
if (n > 32767) {
n >>= 16;
bits += 16;
}
if (n > 127) {
n >>= 8;
bits += 8;
}
if (n > 7) {
n >>= 4;
bits += 4;
}
if (n > 1) {
n >>= 2;
bits += 2;
}
if (n > 0) {
bits++;
}
return bits;
}
int second_minima(int a[], unsigned int n) {
// build a tree of size of log2n in the form of 2d array
// 1st row represents all elements which fights for min
// candidate pairwise. winner of each pair moves to 2nd
// row and so on
int log_2n = log_2(n);
long comparison_count = 0;
// pair of ints : first element stores value and second
// stores index of its first row
ii **p = new ii*[log_2n];
int i, j, k;
for (i = 0, j = n; i < log_2n; i++) {
p[i] = new ii[j];
j = j&1 ? j/2+1 : j/2;
}
for (i = 0; i < n; i++)
p[0][i] = make_pair(a[i], i);
// find minima using pair wise fighting
for (i = 1, j = n; i < log_2n; i++) {
// for each pair
for (k = 0; k+1 < j; k += 2) {
// find its winner
if (++comparison_count && p[i-1][k].first < p[i-1][k+1].first) {
p[i][k/2].first = p[i-1][k].first;
p[i][k/2].second = p[i-1][k].second;
}
else {
p[i][k/2].first = p[i-1][k+1].first;
p[i][k/2].second = p[i-1][k+1].second;
}
}
// if no. of elements in row is odd the last element
// directly moves to next round (row)
if (j&1) {
p[i][j/2].first = p[i-1][j-1].first;
p[i][j/2].second = p[i-1][j-1].second;
}
j = j&1 ? j/2+1 : j/2;
}
int minima, second_minima;
int index;
minima = p[log_2n-1][0].first;
// initialize second minima by its final (last 2nd row)
// potential candidate with which its final took place
second_minima = minima == p[log_2n-2][0].first ? p[log_2n-2][1].first : p[log_2n-2][0].first;
// minima original index
index = p[log_2n-1][0].second;
for (i = 0, j = n; i <= log_2n - 3; i++) {
// if its last candidate in any round then there is
// no potential candidate
if (j&1 && index == j-1) {
index /= 2;
j = j/2+1;
continue;
}
// if minima index is odd, then it fighted with its index - 1
// else its index + 1
// this is a potential candidate for second minima, so check it
if (index&1) {
if (++comparison_count && second_minima > p[i][index-1].first)
second_minima = p[i][index-1].first;
}
else {
if (++comparison_count && second_minima > p[i][index+1].first)
second_minima = p[i][index+1].first;
}
index/=2;
j = j&1 ? j/2+1 : j/2;
}
printf("-------------------------------------------------------------------------------\n");
printf("Minimum : %d\n", minima);
printf("Second Minimum : %d\n", second_minima);
printf("comparison count : %ld\n", comparison_count);
printf("Least No. Of Comparisons (");
printf("n+ceil(log2_n)-2) : %d\n", (int)(n+ceil(log(n)/log(2))-2));
return 0;
}
int main()
{
unsigned int n;
scanf("%u", &n);
int a[n];
int i;
for (i = 0; i < n; i++)
scanf("%d", &a[i]);
second_minima(a,n);
return 0;
}
function findSecondLargeNumber(arr){
var fLargeNum = 0;
var sLargeNum = 0;
for(var i=0; i<arr.length; i++){
if(fLargeNum < arr[i]){
sLargeNum = fLargeNum;
fLargeNum = arr[i];
}else if(sLargeNum < arr[i]){
sLargeNum = arr[i];
}
}
return sLargeNum;
}
var myArray = [799, -85, 8, -1, 6, 4, 3, -2, -15, 0, 207, 75, 785, 122, 17];
Ref: http://www.ajaybadgujar.com/finding-second-largest-number-from-array-in-javascript/
A good way with O(1) time complexity would be to use a max-heap. Call the heapify twice and you have the answer.
int[] int_array = {4, 6, 2, 9, 1, 7, 4, 2, 9, 0, 3, 6, 1, 6, 8};
int largst=int_array[0];
int second=int_array[0];
for (int i=0; i<int_array.length; i++){
if(int_array[i]>largst) {
second=largst;
largst=int_array[i];
}
else if(int_array[i]>second && int_array[i]<largst) {
second=int_array[i];
}
}
I suppose, follow the "optimal algorithm uses n+log n-2 comparisons" from above, the code that I came up with that doesn't use binary tree to store the value would be the following:
During each recursive call, the array size is cut in half.
So the number of comparison is:
1st iteration: n/2 comparisons
2nd iteration: n/4 comparisons
3rd iteration: n/8 comparisons
...
Up to log n iterations?
Hence, total => n - 1 comparisons?
function findSecondLargestInArray(array) {
let winner = [];
if (array.length === 2) {
if (array[0] < array[1]) {
return array[0];
} else {
return array[1];
}
}
for (let i = 1; i <= Math.floor(array.length / 2); i++) {
if (array[2 * i - 1] > array[2 * i - 2]) {
winner.push(array[2 * i - 1]);
} else {
winner.push(array[2 * i - 2]);
}
}
return findSecondLargestInArray(winner);
}
Assuming array contain 2^n number of numbers.
If there are 6 numbers, then 3 numbers will move to the next level, which is not right.
Need like 8 numbers => 4 number => 2 number => 1 number => 2^n number of number
package com.array.orderstatistics;
import java.util.Arrays;
import java.util.Collections;
public class SecondLargestElement {
/**
* Total Time Complexity will be n log n + O(1)
* #param str
*/
public static void main(String str[]) {
Integer[] integerArr = new Integer[] { 5, 1, 2, 6, 4 };
// Step1 : Time Complexity will be n log(n)
Arrays.sort(integerArr, Collections.reverseOrder());
// Step2 : Array.get Second largestElement
int secondLargestElement = integerArr[1];
System.out.println(secondLargestElement);
}
}
Sort the array into ascending order then assign a variable to the (n-1)th term.

Algorithm to find added/removed elements in an array

I am looking for the most efficent way of solving the following
Problem:
given an array Before = { 8, 7, 2, 1} and an array After ={1, 3, 8, 8}
find the added and the removed elements
the solution is:
added = 3, 8
removed = 7, 2
My idea so far is:
for i = 0 .. B.Lenghtt-1
{
for j= 0 .. A.Lenght-1
{
if A[j] == B[i]
A[j] = 0;
B[i] = 0;
break;
}
}
// B elemnts different from 0 are the Removed elements
// A elemnts different from 0 are the Added elemnts
Does anyone know a better solution perhaps more efficent and that doesn't overwrite the original arrays
Sorting is your friend.
Sort the two arrays (a and b), and then walk them (using x and y as counters). Move down both 1 at a time. You can derive all your tests from there:
if a[x] < b[y], then a[x] was removed (and only increment x)
if a[x] > b[y], then b[y] was added (and only increment y)
(I may have missed an edge case, but you get the general idea.)
(edit: the primary edge case that isn't covered here is handling when you reach the end of one of the arrays before the other, but it's not hard to figure out. :)
You could also use a Dictionary<int, int> and a algorithm similar to this:
foreach i in source_list: dictionary[i]++;
foreach i in dest_list: dictionary[i]--;
The final dictionary tells you which elements were inserted/removed (and how often). This solution should be quite fast even for bigger lists - faster than sorting.
if your language as multiset available (set with count of elements) your question is a standard operation.
B = multiset(Before)
A = multiset(After)
result is A.symdiff(B) (symdiff is union minus intersection and that is exactly what you are looking for to have removed and added).
Obviously you can also get removed only or added only using classical difference between sets.
It can trivially be implemented using hashes and it's O(n) (using sort is slightly less efficient as it is O(n.log(n)) because of the sort itself).
In some sort of C++ pseudo code:
Before.sort();
After.sort();
int i = 0;
int j = 0;
for (; i < Before.size() && j < After.size(); ) {
if (Before[i] < After[j]) {
Removed.add(Before[i]);
++i;
continue;
}
if (Before[i] > After[j]) {
Added.add(After[j]);
++j;
continue;
}
++i;
++j;
}
for (; i < Before.size(); ++i) {
Removed.add(Before[i]);
}
for (; j < After.size(); ++j) {
Added.add(After[j]);
}
This can be solved in linear time.
Create a map for calculating the number of repetitions of each element.
Go through the before array and fill the map.
Go through the after array and decrease the value in the map for each element.
At the end, go through the map and if you find a negative value, that element was added - if positive, that element was removed.
Here is some Java code for this (not tested, just written right now):
Map<Integer, Integer> repetitionMap = new HashMap<Integer, Integer>();
for (int i = 0; i < before.length; i++) {
Integer number = repetitionMap.get(before[i]);
if (number == null) {
repetitionMap.put(before[i], 1);
} else {
repetitionMap.put(before[i], number + 1);
}
}
for (int i = 0; i < after.length; i++) {
Integer number = repetitionMap.get(after[i]);
if (number == null) {
repetitionMap.put(after[i], -1);
} else {
repetitionMap.put(after[i], number - 1);
}
}
Set<Integer> keySet = repetitionMap.keySet();
for (Integer i : keySet) {
Integer number = repetitionMap.get(i);
if (number > 0) {
System.out.println("removed " + number + "times value " + i);
}
if (number < 0) {
System.out.println("added " + number + "times value " + i);
}
}
perl:
#a = ( 8, 7, 2, 2, 1 );
#b = ( 1, 3, 8, 8, 8 );
$d{$_}++ for(#a);
$d{$_}-- for(#b);
print"added = ";
for(keys %d){print "$_ " x (-$d{$_}) if($d{$_}<0)}
print"\n";
print"removed = ";
for(keys %d){print "$_ " x ($d{$_}) if($d{$_}>0)}
print"\n";
result:
$ ./inout.pl
added = 8 8 3
removed = 7 2 2
In Groovy:
def before = [8, 7, 2, 1, 1, 1], after = [1, 3, 8, 8, 8]
def added = before.countBy{it}
def result = after.inject(added){map, a -> map[a] ? map << [(a):map[a] - 1]: map << [(a):-1]}
.inject([:]){m, k, v -> v == 0 ? (m << [:]) : (v < 0 ? m << [(k):"added ${v.abs()} times"] : m << [(k):"removed ${v.abs()} times"])}
println "before $before\nafter $after"
println "result: $result"
Result:
before [8, 7, 2, 1, 1, 1]
after [1, 3, 8, 8, 8]
result: [8:added 2 times, 7:removed 1 times, 2:removed 1 times, 1:removed 2 times, 3:added 1 times]
For countBy I got insipred from Some groovy magic post
In groovy inject is like reduce in other functional languages.
I also refer Groovy collection api slides from Trygve Amundsen with really good table with functional methods
Second solution:
def before = [8, 7, 2, 1, 1, 1], after = [1, 3, 8, 8, 8]
def sb = before.countBy{it}
def sa = after.countBy{it}
def result = sa.inject(sb){m, k, v -> m[k] ? m << [(k): m[k] - v] : m << [(k): -v]}
.inject([:]){m, k, v -> v == 0 ? (m << [:]) : (v < 0 ? m << [(k):"added ${v.abs()} times"] : m << [(k):"removed ${v.abs()} times"])}

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