Why is it faster to process sorted array than an unsorted array ?
Here is a C++ and java code that illustrates that sorting the data miraculously makes the code faster than the unsorted version. Let’s try out sample C++ and java programs to understand the problem statement better.
Implementation:
CPP
// CPP program to demonstrate processing // time of sorted and unsorted array #include <iostream> #include <algorithm> #include <ctime> using namespace std; const int N = 100001; int main() { int arr[N]; // Assign random values to array for ( int i=0; i<N; i++) arr[i] = rand ()%N; // for loop for unsorted array int count = 0; double start = clock (); for ( int i=0; i<N; i++) if (arr[i] < N/2) count++; double end = clock (); cout << "Time for unsorted array :: " << ((end - start)/CLOCKS_PER_SEC) << endl; sort(arr, arr+N); // for loop for sorted array count = 0; start = clock (); for ( int i=0; i<N; i++) if (arr[i] < N/2) count++; end = clock (); cout << "Time for sorted array :: " << ((end - start)/CLOCKS_PER_SEC) << endl; return 0; } |
Java
// Java implementation for the above approach. import java.util.Arrays; public class Main { static final int N = 100001 ; public static void main(String[] args) { int [] arr = new int [N]; // Assign random values to array for ( int i = 0 ; i < N; i++) arr[i] = ( int )(Math.random() * N); // for loop for unsorted array int count = 0 ; long start = System.currentTimeMillis(); for ( int i = 0 ; i < N; i++) if (arr[i] < N/ 2 ) count++; long end = System.currentTimeMillis(); System.out.println( "Time for unsorted array :: " + (end - start) / 1000.0 ); Arrays.sort(arr); // for loop for sorted array count = 0 ; start = System.currentTimeMillis(); for ( int i = 0 ; i < N; i++) if (arr[i] < N/ 2 ) count++; end = System.currentTimeMillis(); System.out.println( "Time for sorted array :: " + (end - start) / 1000.0 ); } } // contributed my Rishabh |
Python3
import random import time N = 100001 # Assign random values to array arr = [random.randint( 0 , N) for i in range (N)] # for loop for unsorted array count = 0 start = time.time() for i in range (N): if arr[i] < N / 2 : count + = 1 end = time.time() print ( "Time for unsorted array ::" , end - start) arr.sort() # for loop for sorted array count = 0 start = time.time() for i in range (N): if arr[i] < N / 2 : count + = 1 end = time.time() print ( "Time for sorted array ::" , end - start) |
C#
using System; namespace Demo { class Program { const int N = 100001; static void Main( string [] args) { int [] arr = new int [N]; // Assign random values to array Random rand = new Random(); for ( int i = 0; i < N; i++) { arr[i] = rand.Next(N); } // for loop for unsorted array int count = 0; double start = DateTime.Now.Ticks / ( double )TimeSpan.TicksPerSecond; for ( int i = 0; i < N; i++) { if (arr[i] < N / 2) { count++; } } double end = DateTime.Now.Ticks / ( double )TimeSpan.TicksPerSecond; Console.WriteLine( "Time for unsorted array :: " + (end - start)); Array.Sort(arr); // for loop for sorted array count = 0; start = DateTime.Now.Ticks / ( double )TimeSpan.TicksPerSecond; for ( int i = 0; i < N; i++) { if (arr[i] < N / 2) { count++; } } end = DateTime.Now.Ticks / ( double )TimeSpan.TicksPerSecond; Console.WriteLine( "Time for sorted array :: " + (end - start)); Console.ReadKey(); } } } |
Javascript
const N = 100001; const arr = []; // Assign random values to array for (let i = 0; i < N; i++) { arr[i] = Math.floor(Math.random() * N); } // for loop for unsorted array let count = 0; let start = new Date().getTime(); for (let i = 0; i < N; i++) { if (arr[i] < N/2) { count++; } } let end = new Date().getTime(); console.log( "Time for unsorted array :: " + (end - start) / 1000.0); arr.sort(); // for loop for sorted array count = 0; start = new Date().getTime(); for (let i = 0; i < N; i++) { if (arr[i] < N/2) { count++; } } end = new Date().getTime(); console.log( "Time for sorted array :: " + (end - start) / 1000.0); // This code is contributed by shivhack999 |
Time for unsorted array :: 0.000844 Time for sorted array :: 0.00023
Observe that time taken for processing a sorted array is less as compared to unsorted array. The reason for this optimisation for sorted array is branch prediction.
What is branch prediction ?
In computer architecture, branch prediction means determining whether a conditional branch(jump) in the instruction flow of a program is likely to be taken or not. All the pipelined processors do branch prediction in some form, because they must guess the address of the next instruction to fetch before the current instruction has been executed.
How branch prediction in applicable on above case ?
The if condition checks that arr[i] < 5000, but if you observe in case of sorted array, after passing the number 5000 the condition is always false, and before that it is always true, compiler optimises the code here and skips the if condition which is referred as branch prediction.
Case 1 : Sorted array
T = if condition true F = if condition false arr[] = {0,1,2,3,4,5,6, .... , 4999,5000,5001, ... , 100000} {T,T,T,T,T,T,T, .... , T, F, F, ... , F }
We can observe that it is very easy to predict the branch in sorted array, as the sequence is TTTTTTTTTTTT………FFFFFFFFFFFFF
Case 2 : Unsorted array
T = if condition true F = if condition false arr[] = {5,0,5000,10000,17,13, ... , 3,21000,10} {T,T,F, F, T, T, ... , T, F, T}
It is very difficult to predict that if statement will be false or true, hence branch prediction don’t play any significant role here.
Branch prediction works on the pattern the algorithm is following or basically the history, how it got executed in previous steps. If the guess is correct, then CPU continue executing and if it goes wrong, then CPU need to flush the pipeline and roll back to the branch and restart from beginning.
In case compiler is not able to utilise branch prediction as a tool for improving performance, programmer can implement his own hacks to improve performance.