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The problem comes from Codility programming training and it sounds as follows:
we have an array (A[]) with n (ranging from 1 to 100,000) elements and these are our parameters. The elements of the array are integers from ā2,147,483,648 to 2,147,483,647, and we need to find smallest positive integer that is NOT in the array. Of course this could be done easily in O(n*log n) by sorting them all and going through the sorted array, looking for the missing posiitve number (this last operation has O(n) worst time complexity in my solution). But according to Codility, this ENTIRE problem can be done in O(n), and I cannot see any way to do that. Could someone give some tips to let me get un-stuck?
PS Here is a link to detailed description of the problem which I'm not allowed to copy - https://codility.com/c/intro/demo35UEXH-EAT
By pigeonhole principle, at least one of the numbers 1, 2, ..., n+1 is not in the array.
Let us create a boolean array b of size n+1 to store whether each of these numbers is present.
Now, we process the input array. If we find a number from 1 to n+1, we mark the corresponding entry in b. If the number we see does not fit into these bounds, just discard it and proceed to the next one. Both cases are O(1) per input entry, total O(n).
After we are done processing the input, we can find the first non-marked entry in our boolean array b trivially in O(n).
Simple solution 100% in Java.
Please note it is O(nlogn) solution but gives 100% result in codility.
public static int solution(final int[] A)
{
Arrays.sort(A);
int min = 1;
// Starting from 1 (min), compare all elements, if it does not match
// that would the missing number.
for (int i : A) {
if (i == min) {
min++;
}
}
return min;
}
wrote this today and got 100/100. not the most elegant solution, but easy to understand -
public int solution(int[] A) {
int max = A.length;
int threshold = 1;
boolean[] bitmap = new boolean[max + 1];
//populate bitmap and also find highest positive int in input list.
for (int i = 0; i < A.length; i++) {
if (A[i] > 0 && A[i] <= max) {
bitmap[A[i]] = true;
}
if (A[i] > threshold) {
threshold = A[i];
}
}
//find the first positive number in bitmap that is false.
for (int i = 1; i < bitmap.length; i++) {
if (!bitmap[i]) {
return i;
}
}
//this is to handle the case when input array is not missing any element.
return (threshold+1);
}
public int solutionMissingInteger(int[] A) {
int solution = 1;
HashSet<Integer> hashSet = new HashSet<>();
for(int i=0; i<A.length; ++i){
if(A[i]<1) continue;
if(hashSet.add(A[i])){
//this int was not handled before
while(hashSet.contains(solution)){
solution++;
}
}
}
return solution;
}
Simple Java soution. Scored 100/100 in correctness and performance.
public int solution(int[] A) {
int smallestMissingInteger = 1;
if (A.length == 0) {
return smallestMissingInteger;
}
Set<Integer> set = new HashSet<Integer>();
for (int i = 0; i < A.length; i++) {
if (A[i] > 0) {
set.add(A[i]);
}
}
while (set.contains(smallestMissingInteger)) {
smallestMissingInteger++;
}
return smallestMissingInteger;
}
Build a hash table of all the values. For the numbers 1 to n + 1, check if they are in the hash table. At least one of them is not. Print out the lowest such number.
This is O(n) expected time (you can get with high probability). See #Gassa's answer for how to avoid the hash table in favor of a lookup table of size O(n).
JavaScript 100%
function solution(A) {
let sortedOb = {};
let biggest = 0;
A.forEach(el => {
if (el > 0) {
sortedOb[el] = 0;
biggest = el > biggest ? el : biggest;
}
});
let arr = Object.keys(sortedOb).map(el => +el);
if (arr.length == 0) return 1;
for(let i = 1; i <= biggest; i++) {
if (sortedOb[i] === undefined) return i;
}
return biggest + 1;
}
100% Javascript
function solution(A) {
// write your code in JavaScript (Node.js 4.0.0)
var max = 0;
var array = [];
for (var i = 0; i < A.length; i++) {
if (A[i] > 0) {
if (A[i] > max) {
max = A[i];
}
array[A[i]] = 0;
}
}
var min = max;
if (max < 1) {
return 1;
}
for (var j = 1; j < max; j++) {
if (typeof array[j] === 'undefined') {
return j
}
}
if (min === max) {
return max + 1;
}
}
C# scored 100%,
Explanation: use of lookup table where we store already seen values from input array, we only care about values that are greater than 0 and lower or equal than length on input array
public static int solution(int[] A)
{
var lookUpArray = new bool[A.Length];
for (int i = 0; i < A.Length; i++)
if (A[i] > 0 && A[i] <= A.Length)
lookUpArray[A[i] - 1] = true;
for (int i = 0; i < lookUpArray.Length; i++)
if (!lookUpArray[i])
return i + 1;
return A.Length + 1;
}
This is my solution is Swift 4
public func solution(_ A: inout [Int]) -> Int {
var minNum = 1
var hashSet = Set<Int>()
for int in A {
if int > 0 {
hashSet.insert(int)
}
}
while hashSet.contains(minNum) {
minNum += 1
}
return minNum
}
var array = [1,3,6]
solution(&array)
// Answer: 2
100%: the Python sort routine is not regarded as cheating...
def solution(A):
"""
Sort the array then loop till the value is higher than expected
"""
missing = 1
for elem in sorted(A):
if elem == missing:
missing += 1
if elem > missing:
break
return missing
It worked for me. It is not O(n), but little simpler:
import java.util.stream.*;
class Solution {
public int solution(int[] A) {
A = IntStream.of(A)
.filter(x->x>0)
.distinct()
.sorted()
.toArray();
int min = 1;
for(int val : A)
{
if(val==min)
min++;
else
return min;
}
return min;
}
}
My solution. 100%. In Java.
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
public class Solution {
public int solution(int[] A) {
Arrays.sort(A);
ArrayList<Integer> positive = new ArrayList<>();
for (int i = 0; i < A.length; i++) {
if(A[i] > 0)
positive.add(A[i]);
}
if(positive.isEmpty()) return 1;
if(positive.get(0) > 1) return 1;
for(int i = 0; i < positive.size() - 1; i++) {
if(positive.get(i + 1) - positive.get(i) > 1)
return positive.get(i) + 1;
}
return positive.get(positive.size() - 1) + 1;
}
public static void main(String[] args) {
Solution solution = new Solution();
int[] A = {-5,1,2,3,4,6,7,8,9,5};
System.out.println(solution.solution(A));
}
}
javascript 100% 100%
first sort the array, you just need to scan positive elements so find index of 1 (if there is no 1 in array then answer is 1). then search elements after 1 till find missing number.
function solution(A) {
// write your code in JavaScript (Node.js 6.4.0)
var missing = 1;
// sort the array.
A.sort(function(a, b) { return a-b });
// try to find the 1 in sorted array if there is no 1 so answer is 1
if ( A.indexOf(1) == -1) { return 1; }
// just search positive numbers to find missing number
for ( var i = A.indexOf(1); i < A.length; i++) {
if ( A[i] != missing) {
missing++;
if ( A[i] != missing ) { return missing; }
}
}
// if cant find any missing number return next integer number
return missing + 1;
}
I believe the solution is more involved than 'marking' corresponding values using a boolean array of n (100,000) elements. The boolean array of size n will not 'directly' map to the possible range of values (ā2,147,483,648 to 2,147,483,647).
This Java example I wrote attempts to map the 100K rows by mapping the value based on their offset from the max value. It also performs a modulus to reduce the resulting array to the same size as the sample element length.
/**
*
* This algorithm calculates the values from the min value and mods this offset with the size of the 100K sample size.
* This routine performs 3 scans.
* 1. Find the min/max
* 2. Record the offsets for the positive integers
* 3. Scan the offsets to find missing value.
*
* #author Paul Goddard
*
*/
public class SmallestPositiveIntMissing {
static int ARRAY_SIZE = 100000;
public static int solve(int[] array) {
int answer = -1;
Maxmin maxmin = getMaxmin(array);
int range = maxmin.max - maxmin.min;
System.out.println("min: " + maxmin.min);
System.out.println("max: " + maxmin.max);
System.out.println("range: " + range);
Integer[] values = new Integer[ARRAY_SIZE];
if (range == ARRAY_SIZE) {
System.out.println("No gaps");
return maxmin.max + 1;
}
for (int val: array) {
if (val > 0) {
int offset = val - maxmin.min;
int index = offset % ARRAY_SIZE;
values[index] = val;
}
}
for (int i = 0; i < ARRAY_SIZE; i++) {
if (values[i] == null) {
int missing = maxmin.min + i;
System.out.println("Missing: " + missing);
answer = missing;
break;
}
}
return answer;
}
public static Maxmin getMaxmin(int[] array) {
int max = Integer.MIN_VALUE;
int min = Integer.MAX_VALUE;
for (int val:array) {
if (val >=0) {
if (val > max) max = val;
if (val < min) min = val;
}
}
return new Maxmin(max,min);
}
public static void main(String[] args) {
int[] A = arrayBuilder();
System.out.println("Min not in array: " + solve(A));
}
public static int[] arrayBuilder() {
int[] array = new int[ARRAY_SIZE];
Random random = new Random();
System.out.println("array: ");
for (int i=0;i < ARRAY_SIZE; i++) {
array[i] = random.nextInt();
System.out.print(array[i] + ", ");
}
System.out.println(" array done.");
return array;
}
}
class Maxmin {
int max;
int min;
Maxmin(int max, int min) {
this.max = max;
this.min = min;
}
}
Sweet Swift version. 100% correct
public func solution(inout A : [Int]) -> Int {
//Create a Hash table
var H = [Int:Bool]()
// Create the minimum possible return value
var high = 1
//Iterate
for i in 0..<A.count {
// Get the highest element
high = A[i] > high ? A[i] : high
// Fill hash table
if (A[i] > 0){
H[A[i]] = true
}
}
// iterate through possible values on the hash table
for j in 1...high {
// If you could not find it on the hash, return it
if H[j] != true {
return j
} else {
// If you went through all values on the hash
// and can't find it, return the next higher value
// e.g.: [1,2,3,4] returns 5
if (j == high) {
return high + 1
}
}
}
return high
}
int[] copy = new int[A.length];
for (int i : A)
{
if (i > 0 && i <= A.length)
{
copy[i - 1] = 1;
}
}
for (int i = 0; i < copy.length; i++)
{
if (copy[i] == 0)
{
return i + 1;
}
}
return A.length + 1;
Swift 3 - 100%
public func solution(_ A : inout [Int]) -> Int {
// write your code in Swift 3.0 (Linux)
var solution = 1
var hashSet = Set<Int>()
for int in A
{
if int > 0
{
hashSet.insert(int)
while hashSet.contains(solution)
{
solution += 1
}
}
}
return solution
}
Thanks to Marian's answer above.
This is my solution using python:
def solution(A):
m = max(A)
if m <= 0:
return 1
if m == 1:
return 2
# Build a sorted list with all elements in A
s = sorted(list(set(A)))
b = 0
# Iterate over the unique list trying to find integers not existing in A
for i in xrange(len(s)):
x = s[i]
# If the current element is lte 0, just skip it
if x <= 0:
continue;
b = b + 1
# If the current element is not equal to the current position,
# it means that the current position is missing from A
if x != b:
return b
return m + 1
Scored 100%/100% https://codility.com/demo/results/demoDCU7CA-SBR/
Create a binary array bin of N+1 length (C uses 0 based indexing)
Traverse the binary array O(n)
If A[i] is within the bounds of bin then mark bin entry at index A[i] as present or true.
Traverse the binary array again
Index of any bin entry that is not present or false is your missing integer
~
#include<stdio.h>
#include<stdlib.h>
#include<stdbool.h>
int solution(int A[], int N) {
// write your code in C99 (gcc 6.2.0)
int i;
bool *bin = (bool *)calloc((N+1),sizeof(bool));
for (i = 0; i < N; i++)
{
if (A[i] > 0 && A[i] < N+1)
{
bin[A[i]] = true;
}
}
for (i = 1; i < N+1; i++)
{
if (bin[i] == false)
{
break;
}
}
return i;
}
May be helpful, I am using arithmetic progression to calculate the sum, and using binary searach the element is fetched. checked with array of couple of hundred values works good. As there is one for loop and itression in step of 2, O(n/2) or less
def Missingelement (A):
B = [x for x in range(1,max(A)+1,1)]
n1 = len(B) - 1
begin = 0
end = (n1)//2
result = 0
print(A)
print(B)
if (len(A) < len(B)):
for i in range(2,n1,2):
if BinSum(A,begin,end) > BinSum(B,begin,end) :
end = (end + begin)//2
if (end - begin) <= 1 :
result=B[begin + 1 ]
elif BinSum(A,begin,end) == BinSum(B,begin,end):
r = end - begin
begin = end
end = (end + r)
if begin == end :
result=B[begin + 1 ]
return result
def BinSum(C,begin,end):
n = (end - begin)
if end >= len(C):
end = len(C) - 1
sum = n*((C[begin]+C[end])/2)
return sum
def main():
A=[1,2,3,5,6,7,9,10,11,12,14,15]
print ("smallest number missing is ",Missingelement(A))
if __name__ == '__main__': main()
Code for C, in fact, this can be used for any programming language without any change in the logic.
Logic is sum of N number is N*(N+1)/2.
int solution(int A[], int N) {
// write your code in C99
long long sum=0;
long long i;
long long Nsum=0;
for(i=0;i<N;i++){
sum=sum + (long long)A[i];
}
if (N%2==0){
Nsum= (N+1)*((N+2)/2);
return (int)(Nsum-sum);
}
else{
Nsum= ((N+1)/2)*(N+2);
return (int)(Nsum-sum);
}
}
This gave the 100/100 score.
This solution gets 100/100 on the test:
class Solution {
public int solution(int[] A) {
int x = 0;
while (x < A.length) {
// Keep swapping the values into the matching array positions.
if (A[x] > 0 && A[x] <= A.length && A[A[x]-1] != A[x]) {
swap(A, x, A[x] - 1);
} else {
x++; // Just need to increment when current element and position match.
}
}
for (int y=0; y < A.length; y++) {
// Find first element that doesn't match position.
// Array is 0 based while numbers are 1 based.
if (A[y] != y + 1) {
return y + 1;
}
}
return A.length + 1;
}
private void swap (int[] a, int i, int j) {
int t = a[i];
a[i] = a[j];
a[j] = t;
}
}
100% in PHP https://codility.com/demo/results/trainingKFXWKW-56V/
function solution($A){
$A = array_unique($A);
sort($A);
if (empty($A)) return 1;
if (max($A) <= 0) return 1;
if (max($A) == 1) return 2;
if (in_array(1, $A)) {
$A = array_slice($A, array_search(1, $A)); // from 0 to the end
array_unshift($A, 0); // Explanation 6a
if ( max($A) == array_search(max($A), $A)) return max($A) + 1; // Explanation 6b
for ($i = 1; $i <= count($A); $i++){
if ($A[$i] != $i) return $i; // Explanation 6c
}
} else {
return 1;
}
}
// Explanation
remove all duplicates
sort from min to max
if the array is empty return 1
if max of array is zero or less, return 1
if max of array is 1, return 2 // next positive integer
all other cases:
6a) split the array from value 1 to the end and add 0 before first number
6b) if the value of last element of array is the max of array, then the array is ascending so we return max + 1 // next positive integer
6c) if the array is not ascending, we find a missing number by a function for: if key of element is not as value the element but it should be (A = [0=>0, 1=>1,2=>3,...]), we return the key, because we expect the key and value to be equal.
Here is my solution, it Yields 88% in evaluation- Time is O(n), Correctness 100%, Performance 75%. REMEMBER - it is possible to have an array of all negative numbers, or numbers that exceed 100,000. Most of the above solutions (with actual code) yield much lower scores, or just do not work. Others seem to be irrelevant to the Missing Integer problem presented on Codility.
int compare( const void * arg1, const void * arg2 )
{
return *((int*)arg1) - *((int*)arg2);
}
solution( int A[], int N )
{
// Make a copy of the original array
// So as not to disrupt it's contents.
int * A2 = (int*)malloc( sizeof(int) * N );
memcpy( A2, A1, sizeof(int) * N );
// Quick sort it.
qsort( &A2[0], N, sizeof(int), compare );
// Start out with a minimum of 1 (lowest positive number)
int min = 1;
int i = 0;
// Skip past any negative or 0 numbers.
while( (A2[i] < 0) && (i < N )
{
i++;
}
// A variable to tell if we found the current minimum
int found;
while( i < N )
{
// We have not yet found the current minimum
found = 0;
while( (A2[i] == min) && (i < N) )
{
// We have found the current minimum
found = 1;
// move past all in the array that are that minimum
i++;
}
// If we are at the end of the array
if( i == N )
{
// Increment min once more and get out.
min++;
break;
}
// If we found the current minimum in the array
if( found == 1 )
{
// progress to the next minimum
min++;
}
else
{
// We did not find the current minimum - it is missing
// Get out - the current minimum is the missing one
break;
}
}
// Always free memory.
free( A2 );
return min;
}
My 100/100 solution
public int solution(int[] A) {
Arrays.sort(A);
for (int i = 1; i < 1_000_000; i++) {
if (Arrays.binarySearch(A, i) < 0){
return i;
}
}
return -1;
}
static int spn(int[] array)
{
int returnValue = 1;
int currentCandidate = 2147483647;
foreach (int item in array)
{
if (item > 0)
{
if (item < currentCandidate)
{
currentCandidate = item;
}
if (item <= returnValue)
{
returnValue++;
}
}
}
return returnValue;
}
Can we do the run-length encoding in place(assuming the input array is very large)
We can do for the cases such as AAAABBBBCCCCDDDD
A4B4C4D4
But how to do it for the case such as ABCDEFG?
where the output would be A1B1C1D1E1F1G1
My first thought was to start encoding from the end, so we will use the free space (if any), after that we can shift the encoded array to the start. A problem with this approach is that it will not work for AAAAB, because there is no free space (it's not needed for A4B1) and we will try to write AAAAB1 on the first iteration.
Below is corrected solution:
(let's assume the sequence is AAABBC)
encode all groups with two or more elements and leave the rest unchanged (this will not increase length of the array) -> A3_B2C
shift everything right eliminating empty spaces after first step -> _A3B2C
encode the array from the start (reusing the already encoded groups of course) -> A3B2C1
Every step is O(n) and as far as I can see only constant additional memory is needed.
Limitations:
Digits are not supported, but that anyway would create problems with decoding as Petar Petrov mentioned.
We need some kind of "empty" character, but this can be worked around by adding zeros: A03 instead of A3_
C++ solution O(n) time O(1) space
string runLengthEncode(string str)
{
int len = str.length();
int j=0,k=0,cnt=0;
for(int i=0;i<len;i++)
{
j=i;
cnt=1;
while(i<len-1 && str[i]==str[i+1])
{
i++;
cnt++;
}
str[k++]=str[j];
string temp =to_string(cnt);
for(auto m:temp)
str[k++] = m;
}
str.resize(k);
return str;
}
null is used to indicate which items are empty and will be ignored for encoding. Also you can't encode digits (AAA2222 => A324 => 324 times 'A', but it's A3;24). Your question opens more questions.
Here's a "solution" in C#
public static void Encode(string[] input)
{
var writeIndex = 0;
var i = 0;
while (i < input.Length)
{
var symbol = input[i];
if (symbol == null)
{
break;
}
var nextIndex = i + 1;
var offset = 0;
var count = CountSymbol(input, symbol, nextIndex) + 1;
if (count == 1)
{
ShiftRight(input, nextIndex);
offset++;
}
input[writeIndex++] = symbol;
input[writeIndex++] = count.ToString();
i += count + offset;
}
Array.Clear(input, writeIndex, input.Length - writeIndex);
}
private static void ShiftRight(string[] input, int nextIndex)
{
var count = CountSymbol(input, null, nextIndex, (a, b) => a != b);
Array.Copy(input, nextIndex, input, nextIndex + 1, count);
}
private static int CountSymbol(string[] input, string symbol, int nextIndex)
{
return CountSymbol(input, symbol, nextIndex, (a, b) => a == b);
}
private static int CountSymbol(string[] input, string symbol, int nextIndex, Func<string, string, bool> cmp)
{
var count = 0;
var i = nextIndex;
while (i < input.Length && cmp(input[i], symbol))
{
count++;
i++;
}
return count;
}
The 1st solution does not take care of single characters. For example - 'Hi!' will not work. I've used totally different approach, used 'insert()' functions to add inplace. This take care of everything, whether the total 'same' character is > 10 or >100 or = 1.
#include<iostream>
#include<algorithm>
using namespace std;
int main(){
string name = "Hello Buddy!!";
int start = 0;
char distinct = name[0];
for(int i=1;i<name.length()+1;){
if(distinct!=name[i]){
string s = to_string(i-start);
name.insert(start+1,s);
name.erase(name.begin() + start + 1 + s.length(),name.begin() + s.length() + i);
i=start+s.length()+1;
start=i;
distinct=name[start];
continue;
}
i++;
}
cout<<name;
}
Suggest me if you find anything incorrect.
O(n), in-place RLE, I couldn't think better than this. It will not place a number, if chars occurence is just 1. Will also place a9a2, if the character comes 11 times.
void RLE(char *str) {
int len = strlen(str);
int count = 1, j = 0;
for (int i = 0; i < len; i++){
if (str[i] == str[i + 1])
count++;
else {
int times = count / 9;
int rem = count % 9;
for (int k = 0; k < times; k++) {
str[j++] = str[i];
_itoa(9, &str[j++], 10);
count = count - 9;
}
if (count > 1) {
str[j++] = str[i];
_itoa(rem, &str[j++], 10);
count = 1;
}
else
str[j++] = str[i];
}
}
cout << str;
}
I/P => aaabcdeeeefghijklaaaaa
O/P => a3bcde4fghijkla5
Inplace solution using c++ ( assumes length of encoding string is not more than actual string length):
#include <bits/stdc++.h>
#include<stdlib.h>
using namespace std;
void replacePattern(char *str)
{
int len = strlen(str);
if (len == 0)
return;
int i = 1, j = 1;
int count;
// for each character
while (str[j])
{
count = 1;
while (str[j] == str[j-1])
{
j = j + 1;
count++;
}
while(count > 0) {
int rem = count%10;
str[i++] = to_string(rem)[0];
count = count/10;
}
// copy character at current position j
// to position i and increment i and j
if (str[j])
str[i++] = str[j++];
}
// add a null character to terminate string
if(str[len-1] != str[len-2]) {
str[i] = '1';
i++;
}
str[i] = '\0';
}
// Driver code
int main()
{
char str[] = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabccccc";
replacePattern(str);
cout << str;
return 0;
}
I'm trying to construct an algorithm that runs at O(nb) time with the following input/question:
input: an array A[1..n] of n different integers and an integer b (i am assuming that the numbers in A are sequential, starting at 1 ending at n, i.e. for n=4 A[1,2,3,4].
question: in how many ways can b be written as the sum of elements of the array when elements in A[] can only be used once?
I've kind of hit a wall on this one. I'm looking for some kind of recursive solution, but I don't see how to avoid using repeat numbers. Like, for instance, if we started at 1 and stored all the ways to make one (just 1) then 2 (just 2) then three (3 or 2+1) etc, it shouldn't be hard to see how many ways we can make larger numbers. But if, for instance, we take 5, we will see that it can be broken into 4+1, and 4 can be further broken down into 3+1, so then we would see 2 solutions (4+1, and 3+1+1), but one of those has a repeat of a number. Am I missing something obvious? Thanks so much!
Recursive and dynamic solutions in C:
#include <stddef.h>
#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
typedef unsigned char uchar;
typedef unsigned int uint;
typedef struct tAddend
{
struct tAddend* pPrev;
uint Value;
} tAddend;
void findRecursiveSolution(uint n, uint maxAddend, tAddend* pPrevAddend)
{
uint i;
for (i = maxAddend; ; i--)
{
if (n == 0)
{
while (pPrevAddend != NULL)
{
printf("+%u", pPrevAddend->Value);
pPrevAddend = pPrevAddend->pPrev;
}
printf("\n");
return;
}
if (n >= i && i > 0)
{
tAddend a;
a.pPrev = pPrevAddend;
a.Value = i;
findRecursiveSolution(n - i, i - 1, &a);
}
if (i <= 1)
{
break;
}
}
}
void printDynamicSolution(uchar** pTable, uint n, uint idx, uint sum, tAddend* pPrevAddend)
{
uchar el = pTable[idx][sum];
assert((el != 0) && (el != 5) && (el != 7));
if (el & 2) // 2,3,6 - other(s)
{
printDynamicSolution(pTable,
n,
idx - 1,
sum,
pPrevAddend);
}
if (el & 4) // self + other(s)
{
tAddend a;
a.pPrev = pPrevAddend;
a.Value = idx + 1;
printDynamicSolution(pTable,
n,
idx - 1,
sum - (idx + 1),
&a);
}
if (el & 1) // self, found a solution
{
tAddend a;
a.pPrev = pPrevAddend;
a.Value = idx + 1;
pPrevAddend = &a;
while (pPrevAddend != NULL)
{
printf("+%u", pPrevAddend->Value);
pPrevAddend = pPrevAddend->pPrev;
}
printf("\n");
}
}
void findDynamicSolution(uint n)
{
uchar** table;
uint i, j;
if (n == 0)
{
return;
}
// Allocate the DP table
table = malloc(sizeof(uchar*) * n);
if (table == NULL)
{
printf("not enough memory\n");
return;
}
for (i = 0; i < n; i++)
{
table[i] = malloc(n + 1);
if (table[i] == NULL)
{
while (i > 0)
{
free(table[--i]);
}
free(table);
printf("not enough memory\n");
return;
}
}
// Fill in the DP table
for (i = 0; i < n; i++)
{
for (j = 0; j <= n; j++)
{
if (i == 0)
{
table[i][j] = (i + 1 == j); // self
}
else
{
table[i][j] = (i + 1 == j) + // self
2 * (table[i - 1][j] != 0) + // other(s)
4 * ((j >= i + 1) && (table[i - 1][j - (i + 1)] != 0)); // self + other(s)
}
}
}
printDynamicSolution(table, n, n - 1, n, NULL);
for (i = 0; i < n; i++)
{
free(table[i]);
}
free(table);
}
int main(int argc, char** argv)
{
uint n;
if (argc != 2 || sscanf(argv[1], "%u", &n) != 1)
{
n = 10;
}
printf("Recursive Solution:\n");
findRecursiveSolution(n, n, NULL);
printf("\nDynamic Solution:\n");
findDynamicSolution(n);
return 0;
}
Output:
for 10:
Recursive Solution:
+10
+1+9
+2+8
+3+7
+1+2+7
+4+6
+1+3+6
+1+4+5
+2+3+5
+1+2+3+4
Dynamic Solution:
+1+2+3+4
+2+3+5
+1+4+5
+1+3+6
+4+6
+1+2+7
+3+7
+2+8
+1+9
+10
See also on ideone.
Let F(x,i) be the number of ways elements of A[1:i] can be summed to get x.
F(x,i+1) = F(x-A[i+1],i) + F(x,i)
That is it!
This is not a dynamic programming solution though. Non-recursive.
Assumption that arr is sorted in your case like [i....j] where a[i] <= a[j]
That's easy enough
void summer(int[] arr, int n , int b)
{
int lowerbound = 0;
int upperbound = n-1;
while (lowerbound < upperbound)
{
if(arr[lowerbound]+arr[upperbound] == b)
{
// print arr[lowerbound] and arr[upperbound]
lowerbound++; upperbound--;
}
else if(arr[lowerbound]+arr[upperbound] < b)
lowerbound++;
else
upperbound--;
}
}
The above program is easily modifiable to a recursive you need to only change the function definition by passing lowerbound and upperbound.
Case for termination is still lowerbound < upperbound
Base case is if arr[lowerbound] +arr[upperbound] == b
Edited based on comments
You will need to use a modified version of integer knapsack problem. The values of [i,j] both need to be modified accordingly. You are having the problem because you are not most probably modifying your i carefully, Increase your i accordingly then their will not be repetition like the one you are having.
Can someone give an example for finding greatest common divisor algorithm for more than two numbers?
I believe programming language doesn't matter.
Start with the first pair and get their GCD, then take the GCD of that result and the next number. The obvious optimization is you can stop if the running GCD ever reaches 1. I'm watching this one to see if there are any other optimizations. :)
Oh, and this can be easily parallelized since the operations are commutative/associative.
The GCD of 3 numbers can be computed as gcd(a, b, c) = gcd(gcd(a, b), c). You can apply the Euclidean algorithm, the extended Euclidian or the binary GCD algorithm iteratively and get your answer. I'm not aware of any other (smarter?) ways to find a GCD, unfortunately.
A little late to the party I know, but a simple JavaScript implementation, utilising Sam Harwell's description of the algorithm:
function euclideanAlgorithm(a, b) {
if(b === 0) {
return a;
}
const remainder = a % b;
return euclideanAlgorithm(b, remainder)
}
function gcdMultipleNumbers(...args) { //ES6 used here, change as appropriate
const gcd = args.reduce((memo, next) => {
return euclideanAlgorithm(memo, next)}
);
return gcd;
}
gcdMultipleNumbers(48,16,24,96) //8
I just updated a Wiki page on this.
[https://en.wikipedia.org/wiki/Binary_GCD_algorithm#C.2B.2B_template_class]
This takes an arbitrary number of terms.
use GCD(5, 2, 30, 25, 90, 12);
template<typename AType> AType GCD(int nargs, ...)
{
va_list arglist;
va_start(arglist, nargs);
AType *terms = new AType[nargs];
// put values into an array
for (int i = 0; i < nargs; i++)
{
terms[i] = va_arg(arglist, AType);
if (terms[i] < 0)
{
va_end(arglist);
return (AType)0;
}
}
va_end(arglist);
int shift = 0;
int numEven = 0;
int numOdd = 0;
int smallindex = -1;
do
{
numEven = 0;
numOdd = 0;
smallindex = -1;
// count number of even and odd
for (int i = 0; i < nargs; i++)
{
if (terms[i] == 0)
continue;
if (terms[i] & 1)
numOdd++;
else
numEven++;
if ((smallindex < 0) || terms[i] < terms[smallindex])
{
smallindex = i;
}
}
// check for exit
if (numEven + numOdd == 1)
continue;
// If everything in S is even, divide everything in S by 2, and then multiply the final answer by 2 at the end.
if (numOdd == 0)
{
shift++;
for (int i = 0; i < nargs; i++)
{
if (terms[i] == 0)
continue;
terms[i] >>= 1;
}
}
// If some numbers in S are even and some are odd, divide all the even numbers by 2.
if (numEven > 0 && numOdd > 0)
{
for (int i = 0; i < nargs; i++)
{
if (terms[i] == 0)
continue;
if ((terms[i] & 1) == 0)
terms[i] >>= 1;
}
}
//If every number in S is odd, then choose an arbitrary element of S and call it k.
//Replace every other element, say n, with | nāk | / 2.
if (numEven == 0)
{
for (int i = 0; i < nargs; i++)
{
if (i == smallindex || terms[i] == 0)
continue;
terms[i] = abs(terms[i] - terms[smallindex]) >> 1;
}
}
} while (numEven + numOdd > 1);
// only one remaining element multiply the final answer by 2s at the end.
for (int i = 0; i < nargs; i++)
{
if (terms[i] == 0)
continue;
return terms[i] << shift;
}
return 0;
};
For golang, using remainder
func GetGCD(a, b int) int {
for b != 0 {
a, b = b, a%b
}
return a
}
func GetGCDFromList(numbers []int) int {
var gdc = numbers[0]
for i := 1; i < len(numbers); i++ {
number := numbers[i]
gdc = GetGCD(gdc, number)
}
return gdc
}
In Java (not optimal):
public static int GCD(int[] a){
int j = 0;
boolean b=true;
for (int i = 1; i < a.length; i++) {
if(a[i]!=a[i-1]){
b=false;
break;
}
}
if(b)return a[0];
j=LeastNonZero(a);
System.out.println(j);
for (int i = 0; i < a.length; i++) {
if(a[i]!=j)a[i]=a[i]-j;
}
System.out.println(Arrays.toString(a));
return GCD(a);
}
public static int LeastNonZero(int[] a){
int b = 0;
for (int i : a) {
if(i!=0){
if(b==0||i<b)b=i;
}
}
return b;
}
Given an array of characters which forms a sentence of words, give an efficient algorithm to reverse the order of the words (not characters) in it.
Example input and output:
>>> reverse_words("this is a string")
'string a is this'
It should be O(N) time and O(1) space (split() and pushing on / popping off the stack are not allowed).
The puzzle is taken from here.
A solution in C/C++:
void swap(char* str, int i, int j){
char t = str[i];
str[i] = str[j];
str[j] = t;
}
void reverse_string(char* str, int length){
for(int i=0; i<length/2; i++){
swap(str, i, length-i-1);
}
}
void reverse_words(char* str){
int l = strlen(str);
//Reverse string
reverse_string(str,strlen(str));
int p=0;
//Find word boundaries and reverse word by word
for(int i=0; i<l; i++){
if(str[i] == ' '){
reverse_string(&str[p], i-p);
p=i+1;
}
}
//Finally reverse the last word.
reverse_string(&str[p], l-p);
}
This should be O(n) in time and O(1) in space.
Edit: Cleaned it up a bit.
The first pass over the string is obviously O(n/2) = O(n). The second pass is O(n + combined length of all words / 2) = O(n + n/2) = O(n), which makes this an O(n) algorithm.
pushing a string onto a stack and then popping it off - is that still O(1)?
essentially, that is the same as using split()...
Doesn't O(1) mean in-place? This task gets easy if we can just append strings and stuff, but that uses space...
EDIT: Thomas Watnedal is right. The following algorithm is O(n) in time and O(1) in space:
reverse string in-place (first iteration over string)
reverse each (reversed) word in-place (another two iterations over string)
find first word boundary
reverse inside this word boundary
repeat for next word until finished
I guess we would need to prove that step 2 is really only O(2n)...
#include <string>
#include <boost/next_prior.hpp>
void reverse(std::string& foo) {
using namespace std;
std::reverse(foo.begin(), foo.end());
string::iterator begin = foo.begin();
while (1) {
string::iterator space = find(begin, foo.end(), ' ');
std::reverse(begin, space);
begin = boost::next(space);
if (space == foo.end())
break;
}
}
Here is my answer. No library calls and no temp data structures.
#include <stdio.h>
void reverse(char* string, int length){
int i;
for (i = 0; i < length/2; i++){
string[length - 1 - i] ^= string[i] ;
string[i] ^= string[length - 1 - i];
string[length - 1 - i] ^= string[i];
}
}
int main () {
char string[] = "This is a test string";
char *ptr;
int i = 0;
int word = 0;
ptr = (char *)&string;
printf("%s\n", string);
int length=0;
while (*ptr++){
++length;
}
reverse(string, length);
printf("%s\n", string);
for (i=0;i<length;i++){
if(string[i] == ' '){
reverse(&string[word], i-word);
word = i+1;
}
}
reverse(&string[word], i-word); //for last word
printf("\n%s\n", string);
return 0;
}
In pseudo code:
reverse input string
reverse each word (you will need to find word boundaries)
#Daren Thomas
Implementation of your algorithm (O(N) in time, O(1) in space) in D (Digital Mars):
#!/usr/bin/dmd -run
/**
* to compile & run:
* $ dmd -run reverse_words.d
* to optimize:
* $ dmd -O -inline -release reverse_words.d
*/
import std.algorithm: reverse;
import std.stdio: writeln;
import std.string: find;
void reverse_words(char[] str) {
// reverse whole string
reverse(str);
// reverse each word
for (auto i = 0; (i = find(str, " ")) != -1; str = str[i + 1..length])
reverse(str[0..i]);
// reverse last word
reverse(str);
}
void main() {
char[] str = cast(char[])("this is a string");
writeln(str);
reverse_words(str);
writeln(str);
}
Output:
this is a string
string a is this
in Ruby
"this is a string".split.reverse.join(" ")
In C: (C99)
#include <stdio.h>
#include <string.h>
void reverseString(char* string, int length)
{
char swap;
for (int i = 0; i < length/2; i++)
{
swap = string[length - 1 - i];
string[length - 1 - i] = string[i];
string[i] = swap;
}
}
int main (int argc, const char * argv[]) {
char teststring[] = "Given an array of characters which form a sentence of words, give an efficient algorithm to reverse the order of the words (not characters) in it.";
printf("%s\n", teststring);
int length = strlen(teststring);
reverseString(teststring, length);
int i = 0;
while (i < length)
{
int wordlength = strspn(teststring + i, "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz");
reverseString(teststring + i, wordlength);
i += wordlength + 1;
}
printf("%s\n", teststring);
return 0;
}
This gives output:
Given an array of characters which
form a sentence of words, give an
efficient algorithm to reverse the
order of the words (not characters) in
it.
.it in )characters not( words the
of order the reverse to algorithm
efficient an give ,words of sentence a
form which characters of array an
Given
This takes at most 4N time, with small constant space.
Unfortunately, It doesn't handle punctuation or case gracefully.
O(N) in space and O(N) in time solution in Python:
def reverse_words_nosplit(str_):
"""
>>> f = reverse_words_nosplit
>>> f("this is a string")
'string a is this'
"""
iend = len(str_)
s = ""
while True:
ispace = str_.rfind(" ", 0, iend)
if ispace == -1:
s += str_[:iend]
break
s += str_[ispace+1:iend]
s += " "
iend = ispace
return s
You would use what is known as an iterative recursive function, which is O(N) in time as it takes N (N being the number of words) iterations to complete and O(1) in space as each iteration holds its own state within the function arguments.
(define (reverse sentence-to-reverse)
(reverse-iter (sentence-to-reverse ""))
(define (reverse-iter(sentence, reverse-sentence)
(if (= 0 string-length sentence)
reverse-sentence
( reverse-iter( remove-first-word(sentence), add-first-word(sentence, reverse-sentence)))
Note: I have written this in scheme which I am a complete novice, so apologies for lack of correct string manipulation.
remove-first-word finds the first word boundary of sentence, then takes that section of characters (including space and punctuation) and removes it and returns new sentence
add-first-word finds the first word boundary of sentence, then takes that section of characters (including space and punctuation) and adds it to reverse-sentence and returns new reverse-sentence contents.
THIS PROGRAM IS TO REVERSE THE SENTENCE USING POINTERS IN "C language" By Vasantha kumar & Sundaramoorthy from KONGU ENGG COLLEGE, Erode.
NOTE: Sentence must end with dot(.)
because NULL character is not assigned automatically
at the end of the sentence*
#include<stdio.h>
#include<string.h>
int main()
{
char *p,*s="this is good.",*t;
int i,j,a,l,count=0;
l=strlen(s);
p=&s[l-1];
t=&s[-1];
while(*t)
{
if(*t==' ')
count++;
t++;
}
a=count;
while(l!=0)
{
for(i=0;*p!=' '&&t!=p;p--,i++);
p++;
for(;((*p)!='.')&&(*p!=' ');p++)
printf("%c",*p);
printf(" ");
if(a==count)
{
p=p-i-1;
l=l-i;
}
else
{
p=p-i-2;
l=l-i-1;
}
count--;
}
return 0;
}
Push each word onto a stack. Pop all the words off the stack.
using System;
namespace q47407
{
class MainClass
{
public static void Main(string[] args)
{
string s = Console.ReadLine();
string[] r = s.Split(' ');
for(int i = r.Length-1 ; i >= 0; i--)
Console.Write(r[i] + " ");
Console.WriteLine();
}
}
}
edit: i guess i should read the whole question... carry on.
Efficient in terms of my time: took under 2 minutes to write in REBOL:
reverse_words: func [s [string!]] [form reverse parse s none]
Try it out:
reverse_words "this is a string"
"string a is this"
A C++ solution:
#include <string>
#include <iostream>
using namespace std;
string revwords(string in) {
string rev;
int wordlen = 0;
for (int i = in.length(); i >= 0; --i) {
if (i == 0 || iswspace(in[i-1])) {
if (wordlen) {
for (int j = i; wordlen--; )
rev.push_back(in[j++]);
wordlen = 0;
}
if (i > 0)
rev.push_back(in[i-1]);
}
else
++wordlen;
}
return rev;
}
int main() {
cout << revwords("this is a sentence") << "." << endl;
cout << revwords(" a sentence with extra spaces ") << "." << endl;
return 0;
}
A Ruby solution.
# Reverse all words in string
def reverse_words(string)
return string if string == ''
reverse(string, 0, string.size - 1)
bounds = next_word_bounds(string, 0)
while bounds.all? { |b| b < string.size }
reverse(string, bounds[:from], bounds[:to])
bounds = next_word_bounds(string, bounds[:to] + 1)
end
string
end
# Reverse a single word between indices "from" and "to" in "string"
def reverse(s, from, to)
half = (from - to) / 2 + 1
half.times do |i|
s[from], s[to] = s[to], s[from]
from, to = from.next, to.next
end
s
end
# Find the boundaries of the next word starting at index "from"
def next_word_bounds(s, from)
from = s.index(/\S/, from) || s.size
to = s.index(/\s/, from + 1) || s.size
return { from: from, to: to - 1 }
end
in C#, in-place, O(n), and tested:
static char[] ReverseAllWords(char[] in_text)
{
int lindex = 0;
int rindex = in_text.Length - 1;
if (rindex > 1)
{
//reverse complete phrase
in_text = ReverseString(in_text, 0, rindex);
//reverse each word in resultant reversed phrase
for (rindex = 0; rindex <= in_text.Length; rindex++)
{
if (rindex == in_text.Length || in_text[rindex] == ' ')
{
in_text = ReverseString(in_text, lindex, rindex - 1);
lindex = rindex + 1;
}
}
}
return in_text;
}
static char[] ReverseString(char[] intext, int lindex, int rindex)
{
char tempc;
while (lindex < rindex)
{
tempc = intext[lindex];
intext[lindex++] = intext[rindex];
intext[rindex--] = tempc;
}
return intext;
}
This problem can be solved with O(n) in time and O(1) in space. The sample code looks as mentioned below:
public static string reverseWords(String s)
{
char[] stringChar = s.ToCharArray();
int length = stringChar.Length, tempIndex = 0;
Swap(stringChar, 0, length - 1);
for (int i = 0; i < length; i++)
{
if (i == length-1)
{
Swap(stringChar, tempIndex, i);
tempIndex = i + 1;
}
else if (stringChar[i] == ' ')
{
Swap(stringChar, tempIndex, i-1);
tempIndex = i + 1;
}
}
return new String(stringChar);
}
private static void Swap(char[] p, int startIndex, int endIndex)
{
while (startIndex < endIndex)
{
p[startIndex] ^= p[endIndex];
p[endIndex] ^= p[startIndex];
p[startIndex] ^= p[endIndex];
startIndex++;
endIndex--;
}
}
Algorithm:
1).Reverse each word of the string.
2).Reverse resultant String.
public class Solution {
public String reverseWords(String p) {
String reg=" ";
if(p==null||p.length()==0||p.equals(""))
{
return "";
}
String[] a=p.split("\\s+");
StringBuilder res=new StringBuilder();;
for(int i=0;i<a.length;i++)
{
String temp=doReverseString(a[i]);
res.append(temp);
res.append(" ");
}
String resultant=doReverseString(res.toString());
System.out.println(res);
return resultant.toString().replaceAll("^\\s+|\\s+$", "");
}
public String doReverseString(String s)`{`
char str[]=s.toCharArray();
int start=0,end=s.length()-1;
while(start<end)
{
char temp=str[start];
str[start]=str[end];
str[end]=temp;
start++;
end--;
}
String a=new String(str);
return a;
}
public static void main(String[] args)
{
Solution r=new Solution();
String main=r.reverseWords("kya hua");
//System.out.println(re);
System.out.println(main);
}
}
A one liner:
l="Is this as expected ??"
" ".join(each[::-1] for each in l[::-1].split())
Output:
'?? expected as this Is'
The algorithm to solve this problem is based on two steps process, first step will reverse the individual words of string,then in second step, reverse whole string. Implementation of algorithm will take O(n) time and O(1) space complexity.
#include <stdio.h>
#include <string.h>
void reverseStr(char* s, int start, int end);
int main()
{
char s[] = "This is test string";
int start = 0;
int end = 0;
int i = 0;
while (1) {
if (s[i] == ' ' || s[i] == '\0')
{
reverseStr(s, start, end-1);
start = i + 1;
end = start;
}
else{
end++;
}
if(s[i] == '\0'){
break;
}
i++;
}
reverseStr(s, 0, strlen(s)-1);
printf("\n\noutput= %s\n\n", s);
return 0;
}
void reverseStr(char* s, int start, int end)
{
char temp;
int j = end;
int i = start;
for (i = start; i < j ; i++, j--) {
temp = s[i];
s[i] = s[j];
s[j] = temp;
}
}