Related
Here is the problem:
Given a string s and a non-empty string p, find all the start indices of p's anagrams in s.
Input: s: "cbaebabacd" p: "abc"
Output: [0, 6]
Input: s: "abab" p: "ab"
Output: [0, 1, 2]
Here is my solution
vector<int> findAnagrams(string s, string p) {
vector<int> res, s_map(26,0), p_map(26,0);
int s_len = s.size();
int p_len = p.size();
if (s_len < p_len) return res;
for (int i = 0; i < p_len; i++) {
++s_map[s[i] - 'a'];
++p_map[p[i] - 'a'];
}
if (s_map == p_map)
res.push_back(0);
for (int i = p_len; i < s_len; i++) {
++s_map[s[i] - 'a'];
--s_map[s[i - p_len] - 'a'];
if (s_map == p_map)
res.push_back(i - p_len + 1);
}
return res;
}
However, I think it is O(n^2) solution because I have to compare vectors s_map and p_map.
Does a O(n) solution exist for this problem?
lets say p has size n.
lets say you have an array A of size 26 that is filled with the number of a,b,c,... which p contains.
then you create a new array B of size 26 filled with 0.
lets call the given (big) string s.
first of all you initialize B with the number of a,b,c,... in the first n chars of s.
then you iterate through each word of size n in s always updating B to fit this n-sized word.
always B matches A you will have an index where we have an anagram.
to change B from one n-sized word to another, notice you just have to remove in B the first char of the previous word and add the new char of the next word.
Look at the example:
Input
s: "cbaebabacd"
p: "abc" n = 3 (size of p)
A = {1, 1, 1, 0, 0, 0, ... } // p contains just 1a, 1b and 1c.
B = {1, 1, 1, 0, 0, 0, ... } // initially, the first n-sized word contains this.
compare(A,B)
for i = n; i < size of s; i++ {
B[ s[i-n] ]--;
B[ s[ i ] ]++;
compare(A,B)
}
and suppose that compare(A,B) prints the index always A matches B.
the total complexity will be:
first fill of A = O(size of p)
first fill of B = O(size of s)
first comparison = O(26)
for-loop = |s| * (2 + O(26)) = |s| * O(28) = O(28|s|) = O(size of s)
____________________________________________________________________
2 * O(size of s) + O(size of p) + O(26)
which is linear in size of s.
Your solution is the O(n) solution. The size of the s_map and p_map vectors is a constant (26) that doesn't depend on n. So the comparison between s_map and p_map takes a constant amount of time regardless of how big n is.
Your solution takes about 26 * n integer comparisons to complete, which is O(n).
// In papers on string searching algorithms, the alphabet is often
// called Sigma, and it is often not considered a constant. Your
// algorthm works in (Sigma * n) time, where n is the length of the
// longer string. Below is an algorithm that works in O(n) time even
// when Sigma is too large to make an array of size Sigma, as long as
// values from Sigma are a constant number of "machine words".
// This solution works in O(n) time "with high probability", meaning
// that for all c > 2 the probability that the algorithm takes more
// than c*n time is 1-o(n^-c). This is a looser bound than O(n)
// worst-cast because it uses hash tables, which depend on randomness.
#include <functional>
#include <iostream>
#include <type_traits>
#include <vector>
#include <unordered_map>
#include <vector>
using namespace std;
// Finding a needle in a haystack. This works for any iterable type
// whose members can be stored as keys of an unordered_map.
template <typename T>
vector<size_t> AnagramLocations(const T& needle, const T& haystack) {
// Think of a contiguous region of an ordered container as
// representing a function f with the domain being the type of item
// stored in the container and the codomain being the natural
// numbers. We say that f(x) = n when there are n x's in the
// contiguous region.
//
// Then two contiguous regions are anagrams when they have the same
// function. We can track how close they are to being anagrams by
// subtracting one function from the other, pointwise. When that
// difference is uniformly 0, then the regions are anagrams.
unordered_map<remove_const_t<remove_reference_t<decltype(*needle.begin())>>,
intmax_t> difference;
// As we iterate through the haystack, we track the lead (part
// closest to the end) and lag (part closest to the beginning) of a
// contiguous region in the haystack. When we move the region
// forward by one, one part of the function f is increased by +1 and
// one part is decreased by -1, so the same is true of difference.
auto lag = haystack.begin(), lead = haystack.begin();
// To compare difference to the uniformly-zero function in O(1)
// time, we make sure it does not contain any points that map to
// 0. The the property of being uniformly zero is the same as the
// property of having an empty difference.
const auto find = [&](const auto& x) {
difference[x]++;
if (0 == difference[x]) difference.erase(x);
};
const auto lose = [&](const auto& x) {
difference[x]--;
if (0 == difference[x]) difference.erase(x);
};
vector<size_t> result;
// First we initialize the difference with the first needle.size()
// items from both needle and haystack.
for (const auto& x : needle) {
lose(x);
find(*lead);
++lead;
if (lead == haystack.end()) return result;
}
size_t i = 0;
if (difference.empty()) result.push_back(i++);
// Now we iterate through the haystack with lead, lag, and i (the
// position of lag) updating difference in O(1) time at each spot.
for (; lead != haystack.end(); ++lead, ++lag, ++i) {
find(*lead);
lose(*lag);
if (difference.empty()) result.push_back(i);
}
return result;
}
int main() {
string needle, haystack;
cin >> needle >> haystack;
const auto result = AnagramLocations(needle, haystack);
for (auto x : result) cout << x << ' ';
}
import java.util.*;
public class FindAllAnagramsInAString_438{
public static void main(String[] args){
String s="abab";
String p="ab";
// String s="cbaebabacd";
// String p="abc";
System.out.println(findAnagrams(s,p));
}
public static List<Integer> findAnagrams(String s, String p) {
int i=0;
int j=p.length();
List<Integer> list=new ArrayList<>();
while(j<=s.length()){
//System.out.println("Substring >>"+s.substring(i,j));
if(isAnamgram(s.substring(i,j),p)){
list.add(i);
}
i++;
j++;
}
return list;
}
public static boolean isAnamgram(String s,String p){
HashMap<Character,Integer> map=new HashMap<>();
if(s.length()!=p.length()) return false;
for(int i=0;i<s.length();i++){
char chs=s.charAt(i);
char chp=p.charAt(i);
map.put(chs,map.getOrDefault(chs,0)+1);
map.put(chp,map.getOrDefault(chp,0)-1);
}
for(int val:map.values()){
if(val!=0) return false;
}
return true;
}
}
There is one question which is bugging me, and somehow, I cannot figure out what to do with it. Suppose an array {9,1,2,4,1,2,2} is given. The unique elements in the array are 9 and 4. The output array should be {1,2,1,2,2} .
My idea to preserve the order and find duplicates is to use a LinkedHashMap which will have the entries and the count of occurrence of the entries.
The problem is maintaining the order of the elements. Once I put the entries in the hashMap, the order will vanish.
There's nothing making the array vanish. Just iterate over the array, checking whether the value in the map is greater than one.
Just count elements and check if the total count of current element is greater than one.
Code example (C++11):
#include <iostream>
#include <unordered_map>
#include <vector>
int main() {
std::vector<int> to_split = {9, 1, 2, 4, 1, 2, 2};
std::vector<int> unique, not_unique;
std::unordered_map<int, int> counter;
for (int elem : to_split) {
++counter[elem];
}
for (int elem : to_split) {
if (counter[elem] > 1) {
not_unique.push_back(elem);
} else {
unique.push_back(elem);
}
}
std::cout << "Unique: " << std::endl;
for (int elem : unique) {
std::cout << elem << " ";
}
std::cout << std::endl;
std::cout << "Not unique:" << std::endl;
for (int elem : not_unique) {
std::cout << elem << " ";
}
std::cout << std::endl;
return 0;
}
Output:
Unique:
9 4
Not unique:
1 2 1 2 2
So an easy way to do this is to first count the number of each element (can be done in O(n)), iterate over the counter and put all elements with count = 1 in a set (also in O(n)).
Now run through the original list and print all elements that are not in your set (also O(n)). So the solution will run in O(n) time and space.
And here is 2 line solution in python:
from collections import Counter
arr = [9,1,2,4,1,2,2]
unique = {k for k, v in Counter(arr).iteritems() if v == 1}
print [i for i in arr if i not in unique]
I would do it like this:
create a
HashMap count =new HashMap();
iterate your array store the array-value as key and the count of the value as value in the hashmap
iterate the array a second time and remove value from the array if count to the key is one.
Just brainstorming a bit, but I somehow have to think about how an unstable sorting algorithm can be made stable: decorate, sort, undecorate.
Given your input list, you iterate over it, adding the position of the item to a list in a map.
for (i = 0; i < length; i++) {
value = list[i]
map[value].append(i)
}
Then, remove all items with count 1, and reconstruct the list (which you can do, because you have the indices in the map).
Thinking about it further: why not just do 1 loop counting, and then another loop to construct the filtered list? Probably even has better performance, I think O(n). (1 iteration to do the counts, 1 iteration to re-construct the new list)
Similar to fedekau's approach, but not counting:
int[]numbers = {9,1,2,4,1,2,2};
int guessedDistinct = (int)(2 * Math.sqrt(numbers.length));
final Map<Number, Boolean>
seenBefore = new HashMap<>(guessedDistinct);
for (int i : numbers)
seenBefore.put(i, seenBefore.containsKey(i));
int[] out = Arrays.stream(numbers)
.filter(i -> seenBefore.getOrDefault(i, false))
.toArray();
System.out.println(Arrays.toString(out));
(or try to avoid "finding i twice" in filling seenBefore:
for (int i : numbers)
seenBefore.compute(i, (k, seen) -> null != seen);
So i have some ranges like these:
2 4
1 9
4 5
4 7
For this the result should be
1 -> 1
2 -> 2
3 -> 2
4 -> 4
5 -> 3
6 -> 2
7 -> 2
8 -> 1
9 -> 1
The naive approach will be to loop through all the ranges but that would be very inefficient and the worst case would take O(n * n)
What would be the efficient approach probably in O(n) or O(log(n))
Here's the solution, in O(n):
The rationale is to add a range [a, b] as a +1 in a, and a -1 after b. Then, after adding all the ranges, then compute the accumulated sums for that array and display it.
If you need to perform queries while adding the values, a better choice would be to use a Binary Indexed Tree, but your question doesn't seem to require this, so I left it out.
#include <iostream>
#define MAX 1000
using namespace std;
int T[MAX];
int main() {
int a, b;
int min_index = 0x1f1f1f1f, max_index = 0;
while(cin >> a >> b) {
T[a] += 1;
T[b+1] -= 1;
min_index = min(min_index, a);
max_index = max(max_index, b);
}
for(int i=min_index; i<=max_index; i++) {
T[i] += T[i-1];
cout << i << " -> " << T[i] << endl;
}
}
UPDATE: Based on the "provocations" (in a good sense) by גלעד ברקן, you can also do this in O(n log n):
#include <iostream>
#include <map>
#define ull unsigned long long
#define miit map<ull, int>::iterator
using namespace std;
map<ull, int> T;
int main() {
ull a, b;
while(cin >> a >> b) {
T[a] += 1;
T[b+1] -= 1;
}
ull last;
int count = 0;
for(miit it = T.begin(); it != T.end(); it++) {
if (count > 0)
for(ull i=last; i<it->first; i++)
cout << i << " " << count << endl;
count += it->second;
last = it->first;
}
}
The advantage of this solution is being able to support ranges with much larger values (as long as the output isn't so large).
The solution would be pretty simple:
generate two lists with the indices of all starting and ending indices of the ranges and sort them.
Generate a counter for the number of ranges that cover the current index. Start at the first item that is at any range and iterate over all numbers to the last element that is in any range. Now if an index is either part of the list of starting-indices, we add 1 to the counter, if it's an element of the ending-indices, we substract 1 from the counter.
Implementation:
vector<int> count(int** ranges , int rangecount , int rangemin , int rangemax)
{
vector<int> res;
set<int> open, close;
for(int** r = ranges ; r < ranges + sizeof(int*) * rangecount ; r++)
{
open.add((*r)[0]);
close.add((*r)[1]);
}
int rc = 0;
for(int i = rangemin ; i < rangemax ; i++)
{
if(open.count(i))
++rc;
res.add(rc);
if(close.count(i))
--rc;
}
return res;
}
Paul's answer still counts from "the first item that is at any range and iterate[s] over all numbers to the last element that is in any range." But what is we could aggregate overlapping counts? For example, if we have three (or say a very large number of) overlapping ranges [(2,6),[1,6],[2,8] the section (2,6) could be dependent only on the number of ranges, if we were to label the overlaps with their counts [(1),3(2,6),(7,8)]).
Using binary search (once for the start and a second time for the end of each interval), we could split the intervals and aggregate the counts in O(n * log m * l) time, where n is our number of given ranges and m is the number of resulting groups in the total range and l varies as the number of disjoint updates required for a particular overlap (the number of groups already within that range). Notice that at any time, we simply have a sorted list grouped as intervals with labeled count.
2 4
1 9
4 5
4 7
=>
(2,4)
(1),2(2,4),(5,9)
(1),2(2,3),3(4),2(5),(6,9)
(1),2(2,3),4(4),3(5),2(6,7),(8,9)
So you want the output to be an array, where the value of each element is the number of input ranges that include it?
Yeah, the obvious solution would be to increment every element in the range by 1, for each range.
I think you can get more efficient if you sort the input ranges by start (primary), end (secondary). So for 32bit start and end, start:end can be a 64bit sort key. Actually, just sorting by start is fine, we need to sort the ends differently anyway.
Then you can see how many ranges you enter for an element, and (with a pqueue of range-ends) see how many you already left.
# pseudo-code with possible bugs.
# TODO: peek or put-back the element from ranges / ends
# that made the condition false.
pqueue ends; // priority queue
int depth = 0; // how many ranges contain this element
for i in output.len {
while (r = ranges.next && r.start <= i) {
ends.push(r.end);
depth++;
}
while (ends.pop < i) {
depth--;
}
output[i] = depth;
}
assert ends.empty();
Actually, we can just sort the starts and ends separately into two separate priority queues. There's no need to build the pqueue on the fly. (Sorting an array of integers is more efficient than sorting an array of structs by one struct member, because you don't have to copy around as much data.)
I'm trying to write an algorithm for finding the index of the closest value that is lesser than or equal to the search value in a sorted array. In the example of the array [10, 20, 30], the following search values should output these indexes:
searchValue: 9, index: -1
searchValue: 10, index: 0
searchValue: 28, index: 1
searchValue: 55555, index: 2
I want to use binary search for logarithmic runtime. I have an algorithm in C-esque psuedocode, but it has 3 base cases. Can these 3 base cases be condensed into 1 for a more elegant solution?
int function indexOfClosestLesser(array, searchValue, startIndex, endIndex) {
if (startIndex == endIndex) {
if (searchValue >= array[startIndex]) {
return startIndex;
} else {
return -1;
}
}
// In the simplistic case of searching for 2 in [0, 2], the midIndex
// is always 0 due to int truncation. These checks are to avoid recursing
// infinitely from index 0 to index 1.
if (startIndex == endIndex - 1) {
if (searchValue >= array[endIndex]) {
return endIndex;
} else if (searchValue >= array[startIndex]) {
return startIndex;
} else {
return -1;
}
}
// In normal binary search, this would be the only base case
if (startIndex < endIndex) {
return -1;
}
int midIndex = endIndex / 2 + startIndex / 2;
int midValue = array[midIndex];
if (midValue > searchValue) {
return indexOfClosestLesser(array, searchValue, startIndex, midIndex - 1);
} else if (searchValue >= midValue) {
// Unlike normal binary search, we don't start on midIndex + 1.
// We're not sure whether the midValue can be excluded yet
return indexOfClosestLesser(array, searchValue, midIndex, endIndex);
}
}
Based on your recursive approach, I would suggest the following c++ snippet that reduces the number of different cases a bit:
int search(int *array, int start_idx, int end_idx, int search_val) {
if( start_idx == end_idx )
return array[start_idx] <= search_val ? start_idx : -1;
int mid_idx = start_idx + (end_idx - start_idx) / 2;
if( search_val < array[mid_idx] )
return search( array, start_idx, mid_idx, search_val );
int ret = search( array, mid_idx+1, end_idx, search_val );
return ret == -1 ? mid_idx : ret;
}
Basically it performs a normal binary search. It only differs in the return statement of the last case to fulfill the additional requirement.
Here is a short test program:
#include <iostream>
int main( int argc, char **argv ) {
int array[3] = { 10, 20, 30 };
std::cout << search( array, 0, 2, 9 ) << std::endl;
std::cout << search( array, 0, 2, 10 ) << std::endl;
std::cout << search( array, 0, 2, 28 ) << std::endl;
std::cout << search( array, 0, 2, 55555 ) << std::endl;
return 0;
}
The output is as desired:
-1
0
1
2
Frankly speaking, I find the logic of finding a number greater than a given number a lot easier than the logic needed to find numbers less than or equal to a given number. Obviously, the reason behind that is the extra logic (that forms the edge cases) required to handle the duplicate numbers (of given num) present in the array.
public int justGreater(int[] arr, int val, int s, int e){
// Returns the index of first element greater than val.
// If no such value is present, returns the size of the array.
if (s >= e){
return arr[s] <= N ? s+1 : s;
}
int mid = (s + e) >> 1;
if (arr[mid] < val) return justGreater(arr, val, mid+1, e);
return justGreater(arr, val, s, mid);
}
and then to find the index of the closest value that is lesser than or equal to the search value in a sorted array, just subtract the returned value by 1:
ans = justGreater(arr, val, 0, arr.length-1) - 1;
Trick
The trick here is to search for searchValue + 1 and return the the found index as index - 1 which is left - 1 in the code below
For example if we search for 9 in [10, 20, 30]. The code will look for 10 and return that it's present at 0th index and we return 0-1 which is -1
Similarly if we try to search for 10 in the above example it will search for 10 + 1 and return 1st index and we return 1-1 which is 0
Code
def binary_search(array, searchValue, startIndex=0, endIndex=2 ** 32):
"""
Binary search for the closest value less than or equal to the search value
:param array: The given sorted list
:param searchValue: Value to be found in the array
:param startIndex: Initialized with 0
:param endIndex: Initialized with 2**32
:return: Returns the index closest value less than or equal to the search value
"""
left = max(0, startIndex)
right = min(len(array), endIndex)
while left < right:
mid = (left + right) // 2
if array[mid] < searchValue + 1:
left = mid + 1
else:
right = mid
return left - 1
It can also be done in a single line with the standard library.
import bisect
def standard_binary_search(array, searchVal):
return bisect.bisect_left(array, searchVal + 1) - 1
Testing
Testing the test cases provided by OP
array = [10, 20, 30]
print(binary_search(array, 9))
print(binary_search(array, 10))
print(binary_search(array, 28))
print(binary_search(array, 5555))
Results
-1
0
1
2
I created a linear search to test the binary search.
def linear_search(array, searchVal):
ans = -1
for i, num in enumerate(array):
if num > searchVal:
return ans
ans = i
return ans
And a function to test all the binary search functions above.
Check for correctness
def check_correctness(array, searchVal):
assert binary_search(array, searchVal) == linear_search(array, searchVal)
assert binary_search(array, searchVal) == standard_binary_search(array, searchVal)
return binary_search(array, searchVal)
Driver Function
nums = sorted(
[460, 4557, 1872, 2698, 4411, 1730, 3870, 4941, 77, 7789, 8553, 6011, 9882, 9597, 8060, 1518, 8210, 380, 6822, 9022,
8255, 8977, 2492, 5918, 3710, 4253, 8386, 9660, 2933, 7880, 615, 1439, 9311, 3526, 5674, 1899, 1544, 235, 3369,
519, 8018, 8489, 3093, 2547, 4903, 1836, 2447, 570, 7666, 796, 7149, 9623, 681, 1869, 4381, 2711, 9882, 4348, 4617,
7852, 5897, 4135, 9471, 4202, 6630, 3037, 9694, 9693, 7779, 3041, 3160, 4911, 8022, 7909, 297, 7258, 4379, 3216,
9474, 8876, 6108, 7814, 9484, 2868, 882, 4206, 3986, 3038, 3659, 3287, 2152, 2964, 7057, 7122, 261, 2716, 4845,
3709, 3562, 1928]
)
for num in range(10002):
ans = check_correctness(nums, num)
if ans != -1:
print(num, nums[check_correctness(nums, num)])
The driver function ran without any assert errors. This proves the correctness of the above two functions.
Commented version in typescript. Based on this answer but modified to return less than or equal to.
/**
* Binary Search of a sorted array but returns the closest smaller value if the
* needle is not in the array.
*
* Returns null if the needle is not in the array and no smaller value is in
* the array.
*
* #param haystack the sorted array to search #param needle the need to search
* for in the haystack #param compareFn classical comparison function, return
* -1 if a is less than b, 0 if a is equal to b, and 1 if a is greater than b
*/
export function lessThanOrEqualBinarySearch<T>(
haystack: T[],
needle: T,
compareFn: (a: T, b: T) => number
): T | null {
let lo = 0;
let hi = haystack.length - 1;
let lowestFound: T | null = null;
// iteratively search halves of the array but when we search the larger
// half keep track of the largest value in the smaller half
while (lo <= hi) {
let mid = (hi + lo) >> 1;
let cmp = compareFn(needle, haystack[mid]);
// needle is smaller than middle
// search in the bottom half
if (cmp < 0) {
hi = mid - 1;
continue;
}
// needle is larger than middle
// search in the top half
else if (cmp > 0) {
lo = mid + 1;
lowestFound = haystack[mid];
} else if (cmp === 0) {
return haystack[mid];
}
}
return lowestFound;
}
Here's a PHP version, based on user0815's answer.
Adapted it to take a function, not just an array, and made it more efficient by avoiding evaluation of $mid_idx twice.
function binarySearchLessOrEqual($start_idx, $end_idx, $search_val, $valueFunction)
{
//N.B. If the start index is bigger or equal to the end index, we've reached the end!
if( $start_idx >= $end_idx )
{
return $valueFunction($end_idx) <= $search_val ? $end_idx : -1;
}
$mid_idx = intval($start_idx + ($end_idx - $start_idx) / 2);
if ( $valueFunction($mid_idx) > $search_val ) //If the function is too big, we search in the bottom half
{
return binarySearchLessOrEqual( $start_idx, $mid_idx-1, $search_val, $valueFunction);
}
else //If the function returns less than OR equal, we search in the top half
{
$ret = binarySearchLessOrEqual($mid_idx+1, $end_idx, $search_val, $valueFunction);
//If nothing is suitable, then $mid_idx was actually the best one!
return $ret == -1 ? $mid_idx : $ret;
}
}
Rather than taking an array, it takes a int-indexed function. You could easily adapt it to take an array instead, or simply use it as below:
function indexOfClosestLesser($array, $searchValue)
{
return binarySearchLessOrEqual(
0,
count($array)-1,
$searchValue,
function ($n) use ($array)
{
return $array[$n];
}
);
}
Tested:
$array = [ 10, 20, 30 ];
echo "0: " . indexOfClosestLesser($array, 0) . "<br>"; //-1
echo "5: " . indexOfClosestLesser($array, 5) . "<br>"; //-1
echo "10: " . indexOfClosestLesser($array, 10) . "<br>"; //0
echo "15: " . indexOfClosestLesser($array, 15) . "<br>"; //0
echo "20: " . indexOfClosestLesser($array, 20) . "<br>"; //1
echo "25: " . indexOfClosestLesser($array, 25) . "<br>"; //1
echo "30: " . indexOfClosestLesser($array, 30) . "<br>"; //2
echo "35: " . indexOfClosestLesser($array, 35) . "<br>"; //2
Try using a pair of global variables, then reference those variables inside the COMPARE function for bsearch
In RPGIV we can call c functions.
The compare function with global variables looks like this:
dcl-proc compInvHdr;
dcl-pi compInvHdr int(10);
elmPtr1 pointer value;
elmPtr2 pointer value;
end-pi;
dcl-ds elm1 based(elmPtr1) likeds(invHdr_t);
dcl-ds elm2 based(elmPtr2) likeds(elm1);
dcl-s low int(10) inz(-1);
dcl-s high int(10) inz(1);
dcl-s equal int(10) inz(0);
select;
when elm1.rcd.RECORDNO < elm2.rcd.RECORDNO;
lastHiPtr = elmPtr2;
return low;
when elm1.rcd.RECORDNO > elm2.rcd.RECORDNO;
lastLoPtr = elmPtr2;
return high;
other;
return equal;
endsl;
end-proc;
Remember, that in bsearch the first element is the search key and the second element is the actual storage element in your array/memory, that is why the COMPARE procedure is using elmPtr2;
the call to bsearch looks like this:
// lastLoPtr and LastHiPtr are global variables
// basePtr points to the beginning of the array
lastLoPtr = basePtr;
lastHiPtr = basePtr + ((numRec - 1) * sizRec));
searchKey = 'somevalue';
hitPtr = bsearch(%addr(searchkey)
:basePtr
:numRec
:sizRec
:%PADDR('COMPINVHDR'));
if hitPtr <> *null;
//? not found
hitPtr = lastLoPtr;
else;
//? found
endif;
So if the key is not found then the hitPtr is set to the key of the closest match, effectively archiving a "Less than or Equal key".
If you want the opposite, the next greater key. Then use lastHiPtr to reference the first key greater than the search key.
Note: protect the global variables against race conditions (if applicable).
Wanted to provide a non-binary search way of doing this, in C#. The following finds the closest value to X, without being greater than X, but it can be equal to X. My function also does not need the list to be sorted. It is also theoretically faster than O(n), but only in the event that the exact target number is found, in which case it terminates early and returns the integer.
public static int FindClosest(List<int> numbers, int target)
{
int current = 0;
int difference = Int32.MaxValue;
foreach(int integer in numbers)
{
if(integer == target)
{
return integer;
}
int diff = Math.Abs(target - integer);
if(integer <= target && integer >= current && diff < difference)
{
current = integer;
difference = diff;
}
}
return current;
}
I tested this with the following setup, and it appears to be working flawlessly:
List<int> values = new List<int>() {1,24,32,6,14,9,11,22 };
int target = 21;
int closest = FindClosest(values,target);
Console.WriteLine("Closest: " + closest);
7 years later, I hope to provide some intuition:
If search_val <= arr[mid], we know for the sure that the solution resides in the interval [lo, mid], inclusive. So, we set right=mid (we probably can set right=mid-1 if mid is not included). Note that if search_val < arr[mid], we in fact know that the solution resides in [lo, mid), mid not inclusive. This is because search_val won't fall back on mid and use mid as the closest value <= search value if it is less than arr[mid].
On the other hand, search_val >= arr[mid]. In this case, we know that the solution resides in [mid, hi]. In fact, even if search_val > arr[mid], the solution is still [mid, hi]. This means that we should set left = mid. HOWEVER, in binary search, left is usually always set to mid + 1 to avoid infinite loops. But this means, when the loops at left==right, it is possible we are 1 index over the solution. Thus, we do a check at the very end to return either the left or left-1, that you can see in the other solutions.
Practice Problem: Search a 2D Matrix
Write an efficient algorithm that searches for a value target in an m x n integer matrix matrix. This matrix has the following properties:
Integers in each row are sorted from left to right.
The first integer of each row is greater than the last integer of the
previous row.
The smart solution to this problem is to treat the two-dimensional array as an one-dimensional one and use regular binary search. But I wrote a solution that first locates the correct row. The process of finding the correct row in this problem is basically the same as finding the closest value less than equal to the search value.
Additionally link on binary search: Useful Insights into Binary Search
a non-recursive way using loop, I'm using this in javascript so I'll just post in javascript:
let left = 0
let right = array.length
let mid = 0
while (left < right) {
mid = Math.floor((left + right) / 2)
if (searchValue < array[mid]) {
right = mid
} else {
left = mid + 1
}
}
return left - 1
since general guideline tells us to look at the middle pointer, many fail to see that the actual answer is the left pointer's final value.
This is question asked in one of the interview. Please suggest some view.
Given an array containing all positive integers. You have to arrange elements in such a way that odd elements are at odd position and even elements are at even positions.
PS. No extra space. O(N) solution
Iterate over the even positions until you find an odd number. Iterate over the odd positions until you find and even number (using a different index). Swap the two numbers, and repeat.
Are you allowed to double the size of the array? Otherwise, the question doesn't make sense. Why?!? assume you are given an array full of odd numbers, can you think of any solution then? No, there is not.
So, I assume that you are allowed to double the size of the array. Then for any i, put the i-element ( a(i) ) into the location 2*i or 2*i +1 depending on whether a(i) is even or odd resp.
Two two new Arrays OddArray and EvenArray of same size as that of given array. Traverse through the given array and keep sending all the odd to OddArray and keep at odd positions and even number to EvenArray keeping numbers at even positions.
The efficiency will be O(n) and extra memory will be 2n where n is the size of original array.
list1 = [5, 7, 6, 8, 10, 3, 4, 9, 2, 1, 12]
odd_list = []
even_list = []
for i in range(len(list1)):
if((list1[i] % 2) == 0):
even_list.append(list1[i])
else:
odd_list.append(list1[i])
print(list1)
j = 0
k = 0
for i in range(0, len(list1)):
if((i % 2 == 0) and (j < len(odd_list))):
list1[i] = odd_list[j]
j += 1
elif(k < len(even_list)):
list1[i] = even_list[k]
k += 1
print(list1)
//Putting even number on even position and odd number on odd position
package com.learnJava;
public class ArrangeArray {
private int [] array={2,5,7,8,1,6,9};
private int len=array.length;
public static void main(String [] args)
{
ArrangeArray a=new ArrangeArray();
a.print();
a.arrange();
a.print();
}
public void print()
{
for(int i=0;i<array.length;i++)
{
System.out.print(array[i] + " ");
}
System.out.println();
}
public void arrange()
{
int oddinx=1;
int evenidx=0;
while(true)
{
while(evenidx<len && array[evenidx]%2==0)
{
evenidx+=2;
}
while(oddinx<len && array[oddinx]%2==1)
{
oddinx+=2;
}
if (evenidx < len && oddinx < len)
swap (evenidx, oddinx);
else
break;
}
}
public void swap(int a,int b)
{
int tmp=array[b];
array[b]=array[a];
array[a]=tmp;
}
}