Most efficient way to find smallest of 3 numbers Java

Question

I have an algorithm written in Java that I would like to make more efficient  A part that I think could be made more efficient is finding the smallest of 3 numbers  Currently I m using the Math min method as below   double smallest   Math min a  Math min b  c      How efficient is this  Would it be more efficient to replace with if statements like below   double smallest  if  a  lt   b  amp  amp  a  lt   c        smallest   a    else if  b  lt   c  amp  amp  b  lt   a        smallest   b    else       smallest   c      Or if any other way is more efficient  I m wondering if it is worth changing what I m currently using   Any speed increase would be greatly helpful

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double smallest   a  if  smallest  gt  b  smallest   b  if  smallest  gt  c  smallest   c    Not necessarily faster than your code

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Math min uses a simple comparison to do its thing  The only advantage to not using Math min is to save the extra function calls  but that is a negligible saving   If you have more than just three numbers  having a minimum method for any number of doubles might be valuable and would look something like   public static double min double     numbers        double min   numbers 0       for  int i 1   i lt numbers length   i              min    min  lt   numbers i     min   numbers i             return min      For three numbers this is the functional equivalent of Math min a  Math min b  c    but you save one method invocation

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Use the Arrays sort   method  the lowest value will be element0  In terms of performance  this should not be expensive since the sort operation is already optimised  Also has the advantage of being concise  private int min int     value        Arrays sort value       return value 0      Proof of concept     int   intArr    12  5  6  9  44  28  1  4  18  2  66  13  1  33  74  12       5  6  9  44  28  1  4  18  2  66  13           Sorting approach     long startTime   System currentTimeMillis        int minVal   min intArr       long endTime   System currentTimeMillis        System out println  quot Sorting  Min   gt   quot    minVal    quot  took   gt   quot     endTime -      startTime        System out println startTime    quot     quot     endTime       System out println  quot   quot            Scanning approach     minVal   100      startTime   System currentTimeMillis        for int val   intArr            if  val  lt  minVal              minVal   val            endTime   System currentTimeMillis        System out println  quot Iterating  Min   gt   quot    minVal    quot  took   gt   quot     endTime      - startTime        System out println startTime    quot     quot     endTime

User · Answer

For pure characters-of-code efficiency  I can t find anything better than  smallest   a lt b amp  amp a lt c a b lt c b c

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Simply use this math function   System out println Math min a b c      You will get the answer in single line

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I would use min max  and not worry otherwise      however  here is another  long hand  approach which may or may not be easier for some people to understand   I would not expect it to be faster or slower than the code in the post    int smallest  if  a  lt  b      if  a  gt  c        smallest   c      else      a  lt   c     smallest   a        else      a  gt   b   if  b  gt  c        smallest   c      else      b  lt   c     smallest   b          Just throwing it into the mix   Note that this is just the side-effecting variant of Abhishek s answer

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Let me first repeat what others already said  by quoting from the article  quot Structured Programming with go to Statements quot  by Donald Knuth   We should forget about small efficiencies  say about 97  of the time  premature optimization is the root of all evil  Yet we should not pass up our opportunities in that critical 3   A good programmer will not be lulled into complacency by such reasoning  he will be wise to look carefully at the critical code  but only after that code has been identified    emphasis by me  So if you have identified that a seemingly trivial operation like the computation of the minimum of three numbers is the actual bottleneck  that is  the  quot critical 3  quot   in your application  then you may consider optimizing it  And in this case  this is actually possible  The Math min double double  method in Java has very special semantics   Returns the smaller of two double values  That is  the result is the value closer to negative infinity  If the arguments have the same value  the result is that same value  If either value is NaN  then the result is NaN  Unlike the numerical comparison operators  this method considers negative zero to be strictly smaller than positive zero  If one argument is positive zero and the other is negative zero  the result is negative zero   One can have a look at the implementation  and see that it s actually rather complex  public static double min double a  double b        if  a    a          return a       a is NaN     if   a    0 0d   amp  amp           b    0 0d   amp  amp           Double doubleToRawLongBits b     negativeZeroDoubleBits                Raw conversion ok since NaN can t map to -0 0          return b            return  a  lt   b    a   b      Now  it may be important to point out that this behavior is different from a simple comparison  This can easily be examined with the following example  public class MinExample       public static void main String   args                test 0 0  1 0           test 1 0  0 0           test -0 0  0 0           test Double NaN  1 0           test 1 0  Double NaN              private static void test double a  double b                double minA   Math min a  b           double minB   a  lt  b   a   b          System out println  quot a   quot  a           System out println  quot b   quot  b           System out println  quot minA  quot  minA           System out println  quot minB  quot  minB           if  Double doubleToRawLongBits minA                 Double doubleToRawLongBits minB                         System out println  quot  - gt  Different results  quot                      System out println              However  If the treatment of NaN and positive negative zero is not relevant for your application  you can replace the solution that is based on Math min with a solution that is based on a simple comparison  and see whether it makes a difference  This will  of course  be application dependent  Here is a simple  artificial microbenchmark  to be taken with a grain of salt   import java util Random   public class MinPerformance       public static void main String   args                bench               private static void bench                 int runs   1000          for  int size 10000  size lt  100000  size  10000                        Random random   new Random 0               double data     new double size               for  int i 0  i lt size  i                                  data i    random nextDouble                              benchA data  runs               benchB data  runs                        private static void benchA double data    int runs                long before   System nanoTime            double sum   0          for  int r 0  r lt runs  r                          for  int i 0  i lt data length-3  i                                  sum    minA data i   data i 1   data i 2                                    long after   System nanoTime            System out println  quot A  length  quot  data length  quot   time  quot   after-before  1e6  quot   result  quot  sum              private static void benchB double data    int runs                long before   System nanoTime            double sum   0          for  int r 0  r lt runs  r                          for  int i 0  i lt data length-3  i                                  sum    minB data i   data i 1   data i 2                                    long after   System nanoTime            System out println  quot B  length  quot  data length  quot   time  quot   after-before  1e6  quot   result  quot  sum              private static double minA double a  double b  double c                return Math min a  Math min b  c               private static double minB double a  double b  double c                if  a  lt  b                        if  a  lt  c                                return a                            return c                    if  b  lt  c                        return b                    return c            Disclaimer  Microbenchmarking in Java is an art  and for more reliable results  one should consider using JMH or Caliper   Running this with JRE 1 8 0 31 may result in something like      A  length 90000  time 545 929078  result 2 247805342620906E7 B  length 90000  time 441 999193  result 2 247805342620906E7 A  length 100000  time 608 046928  result 2 5032781001456387E7 B  length 100000  time 493 747898  result 2 5032781001456387E7  This at least suggests that it might be possible to squeeze out a few percent here  again  in a very artifical example    Analyzing this further  by looking at the hotspot disassembly output created with java -server -XX  UnlockDiagnosticVMOptions -XX  TraceClassLoading -XX  LogCompilation -XX  PrintAssembly MinPerformance  one can see the optimized versions of both methods  minA and minB  First  the output for the method that uses Math min  Decoding compiled method 0x0000000002992310  Code   Entry Point   Verified Entry Point   Constants       method   0x000000001c010910   amp apos minA amp apos   amp apos  DDD D amp apos  in  amp apos MinPerformance amp apos      parm0     xmm0 xmm0     double     parm1     xmm1 xmm1     double     parm2     xmm2 xmm2     double                sp 0x60    sp of caller    0x0000000002992480  mov     eax -0x6000  rsp    0x0000000002992487  push    rbp   0x0000000002992488  sub     0x50  rsp   0x000000000299248c  movabs  0x1c010cd0  rsi   0x0000000002992496  mov    0x8  rsi   edi   0x0000000002992499  add     0x8  edi   0x000000000299249c  mov     edi 0x8  rsi    0x000000000299249f  movabs  0x1c010908  rsi      metadata  method   0x000000001c010910   amp apos minA amp apos   amp apos  DDD D amp apos  in  amp apos MinPerformance amp apos      0x00000000029924a9  and     0x3ff8  edi   0x00000000029924af  cmp     0x0  edi   0x00000000029924b2  je     0x00000000029924e8    dload 0                           - MinPerformance  minA 0  line 58     0x00000000029924b8  vmovsd  xmm0 0x38  rsp    0x00000000029924be  vmovapd  xmm1  xmm0   0x00000000029924c2  vmovapd  xmm2  xmm1         invokestatic min                           - MinPerformance  minA 4  line 58     0x00000000029924c6  nop   0x00000000029924c7  callq  0x00000000028c6360    OopMap off 76                            invokestatic min                           - MinPerformance  minA 4  line 58                               static call    0x00000000029924cc  vmovapd  xmm0  xmm1         invokestatic min                           - MinPerformance  minA 4  line 58     0x00000000029924d0  vmovsd 0x38  rsp   xmm0     invokestatic min                           - MinPerformance  minA 7  line 58     0x00000000029924d6  nop   0x00000000029924d7  callq  0x00000000028c6360    OopMap off 92                            invokestatic min                           - MinPerformance  minA 7  line 58                               static call    0x00000000029924dc  add     0x50  rsp   0x00000000029924e0  pop     rbp   0x00000000029924e1  test    eax -0x27623e7  rip           0x0000000000230100                              poll return    0x00000000029924e7  retq   0x00000000029924e8  mov     rsi 0x8  rsp    0x00000000029924ed  movq    0xffffffffffffffff   rsp    0x00000000029924f5  callq  0x000000000297e260    OopMap off 122                            synchronization entry                           - MinPerformance  minA -1  line 58                               runtime call    0x00000000029924fa  jmp    0x00000000029924b8   0x00000000029924fc  nop   0x00000000029924fd  nop   0x00000000029924fe  mov    0x298  r15   rax   0x0000000002992505  movabs  0x0  r10   0x000000000299250f  mov     r10 0x298  r15    0x0000000002992516  movabs  0x0  r10   0x0000000002992520  mov     r10 0x2a0  r15    0x0000000002992527  add     0x50  rsp   0x000000000299252b  pop     rbp   0x000000000299252c  jmpq   0x00000000028ec620     runtime call    0x0000000002992531  hlt   0x0000000002992532  hlt   0x0000000002992533  hlt   0x0000000002992534  hlt   0x0000000002992535  hlt   0x0000000002992536  hlt   0x0000000002992537  hlt   0x0000000002992538  hlt   0x0000000002992539  hlt   0x000000000299253a  hlt   0x000000000299253b  hlt   0x000000000299253c  hlt   0x000000000299253d  hlt   0x000000000299253e  hlt   0x000000000299253f  hlt  Stub Code    0x0000000002992540  nop                            no reloc    0x0000000002992541  nop   0x0000000002992542  nop   0x0000000002992543  nop   0x0000000002992544  nop   0x0000000002992545  movabs  0x0  rbx             static stub    0x000000000299254f  jmpq   0x000000000299254f     runtime call    0x0000000002992554  nop   0x0000000002992555  movabs  0x0  rbx             static stub    0x000000000299255f  jmpq   0x000000000299255f     runtime call   Exception Handler    0x0000000002992564  callq  0x000000000297b9e0     runtime call    0x0000000002992569  mov     rsp -0x28  rsp    0x000000000299256e  sub     0x80  rsp   0x0000000002992575  mov     rax 0x78  rsp    0x000000000299257a  mov     rcx 0x70  rsp    0x000000000299257f  mov     rdx 0x68  rsp    0x0000000002992584  mov     rbx 0x60  rsp    0x0000000002992589  mov     rbp 0x50  rsp    0x000000000299258e  mov     rsi 0x48  rsp    0x0000000002992593  mov     rdi 0x40  rsp    0x0000000002992598  mov     r8 0x38  rsp    0x000000000299259d  mov     r9 0x30  rsp    0x00000000029925a2  mov     r10 0x28  rsp    0x00000000029925a7  mov     r11 0x20  rsp    0x00000000029925ac  mov     r12 0x18  rsp    0x00000000029925b1  mov     r13 0x10  rsp    0x00000000029925b6  mov     r14 0x8  rsp    0x00000000029925bb  mov     r15   rsp    0x00000000029925bf  movabs  0x515db148  rcx      external word    0x00000000029925c9  movabs  0x2992569  rdx       internal word    0x00000000029925d3  mov     rsp  r8   0x00000000029925d6  and     0xfffffffffffffff0  rsp   0x00000000029925da  callq  0x00000000512a9020     runtime call    0x00000000029925df  hlt  Deopt Handler Code    0x00000000029925e0  movabs  0x29925e0  r10       section word    0x00000000029925ea  push    r10   0x00000000029925ec  jmpq   0x00000000028c7340     runtime call    0x00000000029925f1  hlt   0x00000000029925f2  hlt   0x00000000029925f3  hlt   0x00000000029925f4  hlt   0x00000000029925f5  hlt   0x00000000029925f6  hlt   0x00000000029925f7  hlt  One can see that the treatment of special cases involves some effort - compared to the output that uses simple comparisons  which is rather straightforward  Decoding compiled method 0x0000000002998790  Code   Entry Point   Verified Entry Point   Constants       method   0x000000001c0109c0   amp apos minB amp apos   amp apos  DDD D amp apos  in  amp apos MinPerformance amp apos      parm0     xmm0 xmm0     double     parm1     xmm1 xmm1     double     parm2     xmm2 xmm2     double                sp 0x20    sp of caller    0x00000000029988c0  sub     0x18  rsp   0x00000000029988c7  mov     rbp 0x10  rsp    synchronization entry                           - MinPerformance  minB -1  line 63     0x00000000029988cc  vucomisd  xmm0  xmm1   0x00000000029988d0  ja     0x00000000029988ee    ifge                           - MinPerformance  minB 3  line 63     0x00000000029988d2  vucomisd  xmm1  xmm2   0x00000000029988d6  ja     0x00000000029988de    ifge                           - MinPerformance  minB 22  line 71     0x00000000029988d8  vmovapd  xmm2  xmm0   0x00000000029988dc  jmp    0x00000000029988e2   0x00000000029988de  vmovapd  xmm1  xmm0   synchronization entry                           - MinPerformance  minB -1  line 63     0x00000000029988e2  add     0x10  rsp   0x00000000029988e6  pop     rbp   0x00000000029988e7  test    eax -0x27688ed  rip           0x0000000000230000                              poll return    0x00000000029988ed  retq   0x00000000029988ee  vucomisd  xmm0  xmm2   0x00000000029988f2  ja     0x00000000029988e2    ifge                           - MinPerformance  minB 10  line 65     0x00000000029988f4  vmovapd  xmm2  xmm0   0x00000000029988f8  jmp    0x00000000029988e2   0x00000000029988fa  hlt   0x00000000029988fb  hlt   0x00000000029988fc  hlt   0x00000000029988fd  hlt   0x00000000029988fe  hlt   0x00000000029988ff  hlt  Exception Handler   Stub Code    0x0000000002998900  jmpq   0x00000000028ec920       no reloc   Deopt Handler Code    0x0000000002998905  callq  0x000000000299890a   0x000000000299890a  subq    0x5   rsp    0x000000000299890f  jmpq   0x00000000028c7340     runtime call    0x0000000002998914  hlt   0x0000000002998915  hlt   0x0000000002998916  hlt   0x0000000002998917  hlt   Whether or not there are cases where such an optimization really makes a difference in an application is hard to tell  But at least  the bottom line is   The Math min double double  method is not the same as a simple comparison  and the treatment of the special cases does not come for free There are cases where the special case treatment that is done by Math min is not necessary  and then a comparison-based approach may be more efficient As already pointed out in other answers  In most cases  the performance difference will not matter  However  for this particular example  one should probably create a utility method min double double double  anyhow  for better convenience and readability  and then it would be easy to do two runs with the different implementations  and see whether it really affects the performance     Side note  The integer type methods  like Math min int int  actually are a simple comparison - so I would expect no difference for these

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It all looks ok  your code will be fine  unless you re doing this in a tight loop  I also would consider  double min  min    a lt b    a   b  min    min lt c    min   c

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If you will call min   around 1kk times with different a  b  c  then use my method   Here only two comparisons  There is no way to calc faster  P  public static double min double a  double b  double c        if  a  gt  b          if true  min   b         if  b  gt  c      if true  min   c             return c            else         else min   b             return b                              else min   a     if  a  gt  c        if true  min c         return c        else           return a

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double smallest  if a lt b  amp  amp  a lt c       smallest   a   else if b lt c  amp  amp  b lt a       smallest   b   else      smallest   c      can be improved to   double smallest  if a lt b  amp  amp  a lt c   smallest   a   else if b lt c       smallest   b   else      smallest   c

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Works with an arbitrary number of input values   public static double min double    doubles        double m   Double MAX VALUE      for  double d   doubles            m   Math min m  d             return m

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Write a method minimum3 that returns the smallest of three floating-point numbers  Use the Math min method to implement minimum3  Incorporate the method into an application that reads three values from the user  determines the smallest value and displays the result

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For a lot of utility-type methods  the apache commons libraries have solid implementations that you can either leverage or get additional insight from  In this case  there is a method for finding the smallest of three doubles available in org apache commons lang math NumberUtils  Their implementation is actually nearly identical to your initial thought   public static double min double a  double b  double c        return Math min Math min a  b   c

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No  it s seriously not worth changing  The sort of improvements you re going to get when fiddling with micro-optimisations like this will not be worth it  Even the method call cost will be removed if the min function is called enough   If you have a problem with your algorithm  your best bet is to look into macro-optimisations   big picture  stuff like algorithm selection or tuning  - you ll generally get much better performance improvements there   And your comment that removing Math pow gave improvements may well be correct but that s because it s a relatively expensive operation  Math min will not even be close to that in terms of cost

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OP s efficient code has a bug    when a    b  and a  or b   lt  c  the code will pick c instead of a or b

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You can use ternary operator as follows   smallest  a lt b    a lt c  a c    b lt c  b c     Which takes only one assignment and minimum two comparisons   But I think that these statements would not have any effect on execution time  your initial logic will take same time as of mine and all of others

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For those who find this topic much later   If you have just three values to compare there is no significant difference  But if you have to find min of  say  thirty or sixty values   min  could be easier for anyone to read in the code next year   int smallest   smallest   min a1  a2   smallest   min smallest  a3   smallest   min smallest  a4       smallest   min smallest  a37     But if you think of speed  maybe better way would be to put values into list  and then find min of that   List lt Integer gt  mySet   Arrays asList a1  a2  a3       a37    int smallest   Collections min mySet     Would you agree

[java] Most efficient way to find smallest of 3 numbers Java?

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