The below question was asked in the atlassian company online test ,I don't have test cases , this is the below question I took from this link
find the number of ways you can form a string on size N, given an unlimited number of 0s and 1s. But
you cannot have D number of consecutive 0s and T number of consecutive 1s. N, D, T were given as inputs,
Please help me on this problem,any approach how to proceed with it
My approach for the above question is simply I applied recursion and tried for all possiblity and then I memoized it using hash map
But it seems to me there must be some combinatoric approach that can do this question in less time and space? for debugging purposes I am also printing the strings generated during recursion, if there is flaw in my approach please do tell me
#include <bits/stdc++.h>
using namespace std;
unordered_map<string,int>dp;
int recurse(int d,int t,int n,int oldd,int oldt,string s)
{
if(d<=0)
return 0;
if(t<=0)
return 0;
cout<<s<<"\n";
if(n==0&&d>0&&t>0)
return 1;
string h=to_string(d)+" "+to_string(t)+" "+to_string(n);
if(dp.find(h)!=dp.end())
return dp[h];
int ans=0;
ans+=recurse(d-1,oldt,n-1,oldd,oldt,s+'0')+recurse(oldd,t-1,n-1,oldd,oldt,s+'1');
return dp[h]=ans;
}
int main()
{
int n,d,t;
cin>>n>>d>>t;
dp.clear();
cout<<recurse(d,t,n,d,t,"")<<"\n";
return 0;
}
You are right, instead of generating strings, it is worth to consider combinatoric approach using dynamic programming (a kind of).
"Good" sequence of length K might end with 1..D-1 zeros or 1..T-1 of ones.
To make a good sequence of length K+1, you can add zero to all sequences except for D-1, and get 2..D-1 zeros for the first kind of precursors and 1 zero for the second kind
Similarly you can add one to all sequences of the first kind, and to all sequences of the second kind except for T-1, and get 1 one for the first kind of precursors and 2..T-1 ones for the second kind
Make two tables
Zeros[N][D] and Ones[N][T]
Fill the first row with zero counts, except for Zeros[1][1] = 1, Ones[1][1] = 1
Fill row by row using the rules above.
Zeros[K][1] = Sum(Ones[K-1][C=1..T-1])
for C in 2..D-1:
Zeros[K][C] = Zeros[K-1][C-1]
Ones[K][1] = Sum(Zeros[K-1][C=1..T-1])
for C in 2..T-1:
Ones[K][C] = Ones[K-1][C-1]
Result is sum of the last row in both tables.
Also note that you really need only two active rows of the table, so you can optimize size to Zeros[2][D] after debugging.
This can be solved using dynamic programming. I'll give a recursive solution to the same. It'll be similar to generating a binary string.
States will be:
i: The ith character that we need to insert to the string.
cnt: The number of consecutive characters before i
bit: The character which was repeated cnt times before i. Value of bit will be either 0 or 1.
Base case will: Return 1, when we reach n since we are starting from 0 and ending at n-1.
Define the size of dp array accordingly. The time complexity will be 2 x N x max(D,T)
#include<bits/stdc++.h>
using namespace std;
int dp[1000][1000][2];
int n, d, t;
int count(int i, int cnt, int bit) {
if (i == n) {
return 1;
}
int &ans = dp[i][cnt][bit];
if (ans != -1) return ans;
ans = 0;
if (bit == 0) {
ans += count(i+1, 1, 1);
if (cnt != d - 1) {
ans += count(i+1, cnt + 1, 0);
}
} else {
// bit == 1
ans += count(i+1, 1, 0);
if (cnt != t-1) {
ans += count(i+1, cnt + 1, 1);
}
}
return ans;
}
signed main() {
ios_base::sync_with_stdio(false), cin.tie(nullptr);
cin >> n >> d >> t;
memset(dp, -1, sizeof dp);
cout << count(0, 0, 0);
return 0;
}
Related
We need to find the maximum element in an array which is also equal to product of two elements in the same array. For example [2,3,6,8] , here 6=2*3 so answer is 6.
My approach was to sort the array and followed by a two pointer method which checked whether the product exist for each element. This is o(nlog(n)) + O(n^2) = O(n^2) approach. Is there a faster way to this ?
There is a slight better solution with O(n * sqrt(n)) if you are allowed to use O(M) memory M = max number in A[i]
Use an array of size M to mark every number while you traverse them from smaller to bigger number.
For each number try all its factors and see if those were already present in the array map.
Here is a pseudo code for that:
#define M 1000000
int array_map[M+2];
int ans = -1;
sort(A,A+n);
for(i=0;i<n;i++) {
for(j=1;j<=sqrt(A[i]);j++) {
int num1 = j;
if(A[i]%num1==0) {
int num2 = A[i]/num1;
if(array_map[num1] && array_map[num2]) {
if(num1==num2) {
if(array_map[num1]>=2) ans = A[i];
} else {
ans = A[i];
}
}
}
}
array_map[A[i]]++;
}
There is an ever better approach if you know how to find all possible factors in log(M) this just becomes O(n*logM). You have to use sieve and backtracking for that
#JerryGoyal 's solution is correct. However, I think it can be optimized even further if instead of using B pointer, we use binary search to find the other factor of product if arr[c] is divisible by arr[a]. Here's the modification for his code:
for(c=n-1;(c>1)&& (max==-1);c--){ // loop through C
for(a=0;(a<c-1)&&(max==-1);a++){ // loop through A
if(arr[c]%arr[a]==0) // If arr[c] is divisible by arr[a]
{
if(binary_search(a+1, c-1, (arr[c]/arr[a]))) //#include<algorithm>
{
max = arr[c]; // if the other factor x of arr[c] is also in the array such that arr[c] = arr[a] * x
break;
}
}
}
}
I would have commented this on his solution, unfortunately I lack the reputation to do so.
Try this.
Written in c++
#include <vector>
#include <algorithm>
using namespace std;
int MaxElement(vector< int > Input)
{
sort(Input.begin(), Input.end());
int LargestElementOfInput = 0;
int i = 0;
while (i < Input.size() - 1)
{
if (LargestElementOfInput == Input[Input.size() - (i + 1)])
{
i++;
continue;
}
else
{
if (Input[i] != 0)
{
LargestElementOfInput = Input[Input.size() - (i + 1)];
int AllowedValue = LargestElementOfInput / Input[i];
int j = 0;
while (j < Input.size())
{
if (Input[j] > AllowedValue)
break;
else if (j == i)
{
j++;
continue;
}
else
{
int Product = Input[i] * Input[j++];
if (Product == LargestElementOfInput)
return Product;
}
}
}
i++;
}
}
return -1;
}
Once you have sorted the array, then you can use it to your advantage as below.
One improvement I can see - since you want to find the max element that meets the criteria,
Start from the right most element of the array. (8)
Divide that with the first element of the array. (8/2 = 4).
Now continue with the double pointer approach, till the element at second pointer is less than the value from the step 2 above or the match is found. (i.e., till second pointer value is < 4 or match is found).
If the match is found, then you got the max element.
Else, continue the loop with next highest element from the array. (6).
Efficient solution:
2 3 8 6
Sort the array
keep 3 pointers C, B and A.
Keeping C at the last and A at 0 index and B at 1st index.
traverse the array using pointers A and B till C and check if A*B=C exists or not.
If it exists then C is your answer.
Else, Move C a position back and traverse again keeping A at 0 and B at 1st index.
Keep repeating this till you get the sum or C reaches at 1st index.
Here's the complete solution:
int arr[] = new int[]{2, 3, 8, 6};
Arrays.sort(arr);
int n=arr.length;
int a,b,c,prod,max=-1;
for(c=n-1;(c>1)&& (max==-1);c--){ // loop through C
for(a=0;(a<c-1)&&(max==-1);a++){ // loop through A
for(b=a+1;b<c;b++){ // loop through B
prod=arr[a]*arr[b];
if(prod==arr[c]){
System.out.println("A: "+arr[a]+" B: "+arr[b]);
max=arr[c];
break;
}
if(prod>arr[c]){ // no need to go further
break;
}
}
}
}
System.out.println(max);
I came up with below solution where i am using one array list, and following one formula:
divisor(a or b) X quotient(b or a) = dividend(c)
Sort the array.
Put array into Collection Col.(ex. which has faster lookup, and maintains insertion order)
Have 2 pointer a,c.
keep c at last, and a at 0.
try to follow (divisor(a or b) X quotient(b or a) = dividend(c)).
Check if a is divisor of c, if yes then check for b in col.(a
If a is divisor and list has b, then c is the answer.
else increase a by 1, follow step 5, 6 till c-1.
if max not found then decrease c index, and follow the steps 4 and 5.
Check this C# solution:
-Loop through each element,
-loop and multiply each element with other elements,
-verify if the product exists in the array and is the max
private static int GetGreatest(int[] input)
{
int max = 0;
int p = 0; //product of pairs
//loop through the input array
for (int i = 0; i < input.Length; i++)
{
for (int j = i + 1; j < input.Length; j++)
{
p = input[i] * input[j];
if (p > max && Array.IndexOf(input, p) != -1)
{
max = p;
}
}
}
return max;
}
Time complexity O(n^2)
I am trying to count two binary numbers from string. The maximum number of counting digits have to be 253. Short numbers works, but when I add there some longer numbers, the output is wrong. The example of bad result is "10100101010000111111" with "000011010110000101100010010011101010001101011100000000111000000000001000100101101111101000111001000101011010010111000110".
#include <iostream>
#include <stdlib.h>
using namespace std;
bool isBinary(string b1,string b2);
int main()
{
string b1,b2;
long binary1,binary2;
int i = 0, remainder = 0, sum[254];
cout<<"Get two binary numbers:"<<endl;
cin>>b1>>b2;
binary1=atol(b1.c_str());
binary2=atol(b2.c_str());
if(isBinary(b1,b2)==true){
while (binary1 != 0 || binary2 != 0){
sum[i++] =(binary1 % 10 + binary2 % 10 + remainder) % 2;
remainder =(binary1 % 10 + binary2 % 10 + remainder) / 2;
binary1 = binary1 / 10;
binary2 = binary2 / 10;
}
if (remainder != 0){
sum[i++] = remainder;
}
--i;
cout<<"Result: ";
while (i >= 0){
cout<<sum[i--];
}
cout<<endl;
}else cout<<"Wrong input"<<endl;
return 0;
}
bool isBinary(string b1,string b2){
bool rozhodnuti1,rozhodnuti2;
for (int i = 0; i < b1.length();i++) {
if (b1[i]!='0' && b1[i]!='1') {
rozhodnuti1=false;
break;
}else rozhodnuti1=true;
}
for (int k = 0; k < b2.length();k++) {
if (b2[k]!='0' && b2[k]!='1') {
rozhodnuti2=false;
break;
}else rozhodnuti2=true;
}
if(rozhodnuti1==false || rozhodnuti2==false){ return false;}
else{ return true;}
}
One of the problems might be here: sum[i++]
This expression, as it is, first returns the value of i and then increases it by one.
Did you do it on purporse?
Change it to ++i.
It'd help if you could also post the "bad" output, so that we can try to move backward through the code starting from it.
EDIT 2015-11-7_17:10
Just to be sure everything was correct, I've added a cout to check what binary1 and binary2 contain after you assing them the result of the atol function: they contain the integer numbers 547284487 and 18333230, which obviously dont represent the correct binary-to-integer transposition of the two 01 strings you presented in your post.
Probably they somehow exceed the capacity of atol.
Also, the result of your "math" operations bring to an even stranger result, which is 6011111101, which obviously doesnt make any sense.
What do you mean, exactly, when you say you want to count these two numbers? Maybe you want to make a sum? I guess that's it.
But then, again, what you got there is two signed integer numbers and not two binaries, which means those %10 and %2 operations are (probably) misused.
EDIT 2015-11-07_17:20
I've tried to use your program with small binary strings and it actually works; with small binary strings.
It's a fact(?), at this point, that atol cant handle numerical strings that long.
My suggestion: use char arrays instead of strings and replace 0 and 1 characters with numerical values (if (bin1[i]){bin1[i]=1;}else{bin1[i]=0}) with which you'll be able to perform all the math operations you want (you've already written a working sum function, after all).
Once done with the math, you can just convert the char array back to actual characters for 0 and 1 and cout it on the screen.
EDIT 2015-11-07_17:30
Tested atol on my own: it correctly converts only strings that are up to 10 characters long.
Anything beyond the 10th character makes the function go crazy.
Here's a problem:
Given string A and a substring B, remove the first occurence of substring B in string A till it is possible to do so. Note that removing a substring, can further create a new same substring. Ex. removing 'hell' from 'hehelllloworld' once would yield 'helloworld' which after removing once more would become 'oworld', the desired string.
Write a program for the above for input constraints of length 10^6 for A, and length 100 for B.
This question was asked to me in an interview, I gave them a simple algorithm to solve it that was to do exactly what the statement was and remove it iteratievly(to decresae over head calls), I later came to know there's a better solution for it that's much faster what would it be ? I've thought of a few optimizations but it's still not as fast as the fastest soln for the problem(acc. the company), so can anyone tell me of a faster way to solve the problem ?
P.S> I know of stackoverflow rules and that having code is better, but for this problem, I don't think that having code would be in any way beneficial...
Your approach has a pretty bad complexity. In a very bad case the string a will be aaaaaaaaabbbbbbbbb, and the string b will be ab, in which case you will need O(|a|) searches, each taking O(|a| + |b|) (assuming using some sophisticated search algorithm), resulting in a total complexity of O(|a|^2 + |a| * |b|), which with their constraints is years.
For their constraints a good complexity to aim for would be O(|a| * |b|), which is around 100 million operations, will finish in subsecond. Here's one way to approach it. For each position i in the string a let's compute the largest length n_i, such that the a[i - n_i : i] = b[0 : n_i] (in other words, the longest suffix of a at that position which is a prefix of b). We can compute it in O(|a| + |b|) by using Knuth-Morris-Pratt algorithm.
After we have n_i computed, finding the first occurrence of b in a is just a matter of finding the first n_i that is equal to |b|. This will be the right end of one of the occurrences of b in a.
Finally, we will need to modify Knuth-Morris-Pratt slightly. We will be logically removing occurrences of b as soon as we compute an n_i that is equal to |b|. To account for the fact that some letters were removed from a we will rely on the fact that Knuth-Morris-Pratt only relies on the last value of n_i (and those computed for b), and the current letter of a, so we just need a fast way of retrieving the last value of n_i after we logically remove an occurrence of b. That can be done with a deque, that stores all the valid values of n_i. Each value will be pushed into the deque once, and popped from it once, so that complexity of maintaining it is O(|a|), while the complexity of the Knuth-Morris-Pratt is O(|a| + |b|), resulting in O(|a| + |b|) total complexity.
Here's a C++ implementation. It could have some off-by-one errors, but it works on your sample, and it flies for the worst case that I described at the beginning.
#include <deque>
#include <string>
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
int main() {
string a, b;
cin >> a >> b;
size_t blen = b.size();
// make a = b$a
a = b + "$" + a;
vector<size_t> n(a.size()); // array for knuth-morris-pratt
vector<bool> removals(a.size()); // positions of right ends at which we remove `b`s
deque<size_t> lastN;
n[0] = 0;
// For the first blen + 1 iterations just do vanilla knuth-morris-pratt
for (size_t i = 1; i < blen + 1; ++ i) {
size_t z = n[i - 1];
while (z && a[i] != a[z]) {
z = n[z - 1];
}
if (a[i] != a[z]) n[i] = 0;
else n[i] = z + 1;
lastN.push_back(n[i]);
}
// For the remaining iterations some characters could have been logically
// removed from `a`, so use lastN to get last value of n instaed
// of actually getting it from `n[i - 1]`
for (size_t i = blen + 1; i < a.size(); ++ i) {
size_t z = lastN.back();
while (z && a[i] != a[z]) {
z = n[z - 1];
}
if (a[i] != a[z]) n[i] = 0;
else n[i] = z + 1;
if (n[i] == blen) // found a match
{
removals[i] = true;
// kill last |b| - 1 `n_i`s
for (size_t j = 0; j < blen - 1; ++ j) {
lastN.pop_back();
}
}
else {
lastN.push_back(n[i]);
}
}
string ret;
size_t toRemove = 0;
for (size_t pos = a.size() - 1; a[pos] != '$'; -- pos) {
if (removals[pos]) toRemove += blen;
if (toRemove) -- toRemove;
else ret.push_back(a[pos]);
}
reverse(ret.begin(), ret.end());
cout << ret << endl;
return 0;
}
[in] hehelllloworld
[in] hell
[out] oworld
[in] abababc
[in] ababc
[out] ab
[in] caaaaa ... aaaaaabbbbbb ... bbbbc
[in] ab
[out] cc
This is a question from one of the online coding challenge (which has completed).
I just need some logic for this as to how to approach.
Problem Statement:
We have two strings A and B with the same super set of characters. We need to change these strings to obtain two equal strings. In each move we can perform one of the following operations:
1. swap two consecutive characters of a string
2. swap the first and the last characters of a string
A move can be performed on either string.
What is the minimum number of moves that we need in order to obtain two equal strings?
Input Format and Constraints:
The first and the second line of the input contains two strings A and B. It is guaranteed that the superset their characters are equal.
1 <= length(A) = length(B) <= 2000
All the input characters are between 'a' and 'z'
Output Format:
Print the minimum number of moves to the only line of the output
Sample input:
aab
baa
Sample output:
1
Explanation:
Swap the first and last character of the string aab to convert it to baa. The two strings are now equal.
EDIT : Here is my first try, but I'm getting wrong output. Can someone guide me what is wrong in my approach.
int minStringMoves(char* a, char* b) {
int length, pos, i, j, moves=0;
char *ptr;
length = strlen(a);
for(i=0;i<length;i++) {
// Find the first occurrence of b[i] in a
ptr = strchr(a,b[i]);
pos = ptr - a;
// If its the last element, swap with the first
if(i==0 && pos == length-1) {
swap(&a[0], &a[length-1]);
moves++;
}
// Else swap from current index till pos
else {
for(j=pos;j>i;j--) {
swap(&a[j],&a[j-1]);
moves++;
}
}
// If equal, break
if(strcmp(a,b) == 0)
break;
}
return moves;
}
Take a look at this example:
aaaaaaaaab
abaaaaaaaa
Your solution: 8
aaaaaaaaab -> aaaaaaaaba -> aaaaaaabaa -> aaaaaabaaa -> aaaaabaaaa ->
aaaabaaaaa -> aaabaaaaaa -> aabaaaaaaa -> abaaaaaaaa
Proper solution: 2
aaaaaaaaab -> baaaaaaaaa -> abaaaaaaaa
You should check if swapping in the other direction would give you better result.
But sometimes you will also ruin the previous part of the string. eg:
caaaaaaaab
cbaaaaaaaa
caaaaaaaab -> baaaaaaaac -> abaaaaaaac
You need another swap here to put back the 'c' to the first place.
The proper algorithm is probably even more complex, but you can see now what's wrong in your solution.
The A* algorithm might work for this problem.
The initial node will be the original string.
The goal node will be the target string.
Each child of a node will be all possible transformations of that string.
The current cost g(x) is simply the number of transformations thus far.
The heuristic h(x) is half the number of characters in the wrong position.
Since h(x) is admissible (because a single transformation can't put more than 2 characters in their correct positions), the path to the target string will give the least number of transformations possible.
However, an elementary implementation will likely be too slow. Calculating all possible transformations of a string would be rather expensive.
Note that there's a lot of similarity between a node's siblings (its parent's children) and its children. So you may be able to just calculate all transformations of the original string and, from there, simply copy and recalculate data involving changed characters.
You can use dynamic programming. Go over all swap possibilities while storing all the intermediate results along with the minimal number of steps that took you to get there. Actually, you are going to calculate the minimum number of steps for every possible target string that can be obtained by applying given rules for a number times. Once you calculate it all, you can print the minimum number of steps, which is needed to take you to the target string. Here's the sample code in JavaScript, and its usage for "aab" and "baa" examples:
function swap(str, i, j) {
var s = str.split("");
s[i] = str[j];
s[j] = str[i];
return s.join("");
}
function calcMinimumSteps(current, stepsCount)
{
if (typeof(memory[current]) !== "undefined") {
if (memory[current] > stepsCount) {
memory[current] = stepsCount;
} else if (memory[current] < stepsCount) {
stepsCount = memory[current];
}
} else {
memory[current] = stepsCount;
calcMinimumSteps(swap(current, 0, current.length-1), stepsCount+1);
for (var i = 0; i < current.length - 1; ++i) {
calcMinimumSteps(swap(current, i, i + 1), stepsCount+1);
}
}
}
var memory = {};
calcMinimumSteps("aab", 0);
alert("Minimum steps count: " + memory["baa"]);
Here is the ruby logic for this problem, copy this code in to rb file and execute.
str1 = "education" #Sample first string
str2 = "cnatdeiou" #Sample second string
moves_count = 0
no_swap = 0
count = str1.length - 1
def ends_swap(str1,str2)
str2 = swap_strings(str2,str2.length-1,0)
return str2
end
def swap_strings(str2,cp,np)
current_string = str2[cp]
new_string = str2[np]
str2[cp] = new_string
str2[np] = current_string
return str2
end
def consecutive_swap(str,current_position, target_position)
counter=0
diff = current_position > target_position ? -1 : 1
while current_position!=target_position
new_position = current_position + diff
str = swap_strings(str,current_position,new_position)
# p "-------"
# p "CP: #{current_position} NP: #{new_position} TP: #{target_position} String: #{str}"
current_position+=diff
counter+=1
end
return counter,str
end
while(str1 != str2 && count!=0)
counter = 1
if str1[-1]==str2[0]
# p "cross match"
str2 = ends_swap(str1,str2)
else
# p "No match for #{str2}-- Count: #{count}, TC: #{str1[count]}, CP: #{str2.index(str1[count])}"
str = str2[0..count]
cp = str.rindex(str1[count])
tp = count
counter, str2 = consecutive_swap(str2,cp,tp)
count-=1
end
moves_count+=counter
# p "Step: #{moves_count}"
# p str2
end
p "Total moves: #{moves_count}"
Please feel free to suggest any improvements in this code.
Try this code. Hope this will help you.
public class TwoStringIdentical {
static int lcs(String str1, String str2, int m, int n) {
int L[][] = new int[m + 1][n + 1];
int i, j;
for (i = 0; i <= m; i++) {
for (j = 0; j <= n; j++) {
if (i == 0 || j == 0)
L[i][j] = 0;
else if (str1.charAt(i - 1) == str2.charAt(j - 1))
L[i][j] = L[i - 1][j - 1] + 1;
else
L[i][j] = Math.max(L[i - 1][j], L[i][j - 1]);
}
}
return L[m][n];
}
static void printMinTransformation(String str1, String str2) {
int m = str1.length();
int n = str2.length();
int len = lcs(str1, str2, m, n);
System.out.println((m - len)+(n - len));
}
public static void main(String[] args) {
Scanner scan = new Scanner(System.in);
String str1 = scan.nextLine();
String str2 = scan.nextLine();
printMinTransformation("asdfg", "sdfg");
}
}
I was implementing quicksort and I wished to set the pivot to be the median or three numbers. The three numbers being the first element, the middle element, and the last element.
Could I possibly find the median in less no. of comparisons?
median(int a[], int p, int r)
{
int m = (p+r)/2;
if(a[p] < a[m])
{
if(a[p] >= a[r])
return a[p];
else if(a[m] < a[r])
return a[m];
}
else
{
if(a[p] < a[r])
return a[p];
else if(a[m] >= a[r])
return a[m];
}
return a[r];
}
If the concern is only comparisons, then this should be used.
int getMedian(int a, int b , int c) {
int x = a-b;
int y = b-c;
int z = a-c;
if(x*y > 0) return b;
if(x*z > 0) return c;
return a;
}
int32_t FindMedian(const int n1, const int n2, const int n3) {
auto _min = min(n1, min(n2, n3));
auto _max = max(n1, max(n2, n3));
return (n1 + n2 + n3) - _min - _max;
}
You can't do it in one, and you're only using two or three, so I'd say you've got the minimum number of comparisons already.
Rather than just computing the median, you might as well put them in place. Then you can get away with just 3 comparisons all the time, and you've got your pivot closer to being in place.
T median(T a[], int low, int high)
{
int middle = ( low + high ) / 2;
if( a[ middle ].compareTo( a[ low ] ) < 0 )
swap( a, low, middle );
if( a[ high ].compareTo( a[ low ] ) < 0 )
swap( a, low, high );
if( a[ high ].compareTo( a[ middle ] ) < 0 )
swap( a, middle, high );
return a[middle];
}
I know that this is an old thread, but I had to solve exactly this problem on a microcontroller that has very little RAM and does not have a h/w multiplication unit (:)). In the end I found the following works well:
static char medianIndex[] = { 1, 1, 2, 0, 0, 2, 1, 1 };
signed short getMedian(const signed short num[])
{
return num[medianIndex[(num[0] > num[1]) << 2 | (num[1] > num[2]) << 1 | (num[0] > num[2])]];
}
If you're not afraid to get your hands a little dirty with compiler intrinsics you can do it with exactly 0 branches.
The same question was discussed before on:
Fastest way of finding the middle value of a triple?
Though, I have to add that in the context of naive implementation of quicksort, with a lot of elements, reducing the amount of branches when finding the median is not so important because the branch predictor will choke either way when you'll start tossing elements around the the pivot. More sophisticated implementations (which don't branch on the partition operation, and avoid WAW hazards) will benefit from this greatly.
remove max and min value from total sum
int med3(int a, int b, int c)
{
int tot_v = a + b + c ;
int max_v = max(a, max(b, c));
int min_v = min(a, min(b, c));
return tot_v - max_v - min_v
}
There is actually a clever way to isolate the median element from three using a careful analysis of the 6 possible permutations (of low, median, high). In python:
def med(a, start, mid, last):
# put the median of a[start], a[mid], a[last] in the a[start] position
SM = a[start] < a[mid]
SL = a[start] < a[last]
if SM != SL:
return
ML = a[mid] < a[last]
m = mid if SM == ML else last
a[start], a[m] = a[m], a[start]
Half the time you have two comparisons otherwise you have 3 (avg 2.5). And you only swap the median element once when needed (2/3 of the time).
Full python quicksort using this at:
https://github.com/mckoss/labs/blob/master/qs.py
You can write up all the permutations:
1 0 2
1 2 0
0 1 2
2 1 0
0 2 1
2 0 1
Then we want to find the position of the 1. We could do this with two comparisons, if our first comparison could split out a group of equal positions, such as the first two lines.
The issue seems to be that the first two lines are different on any comparison we have available: a<b, a<c, b<c. Hence we have to fully identify the permutation, which requires 3 comparisons in the worst case.
Using a Bitwise XOR operator, the median of three numbers can be found.
def median(a,b,c):
m = max(a,b,c)
n = min(a,b,c)
ans = m^n^a^b^c
return ans