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Task/Maximum-triangle-path-sum/REXX/maximum-triangle-path-sum.rexx

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+/*REXX program finds the max sum of a "column" of numbers in a triangle.*/
+@.   =
+@.1  =                           55
+@.2  =                         94 48
+@.3  =                        95 30 96
+@.4  =                      77 71 26 67
+@.5  =                     97 13 76 38 45
+@.6  =                   07 36 79 16 37 68
+@.7  =                  48 07 09 18 70 26 06
+@.8  =                18 72 79 46 59 79 29 90
+@.9  =               20 76 87 11 32 07 07 49 18
+@.10 =             27 83 58 35 71 11 25 57 29 85
+@.11 =            14 64 36 96 27 11 58 56 92 18 55
+@.12 =          02 90 03 60 48 49 41 46 33 36 47 23
+@.13 =         92 50 48 02 36 59 42 79 72 20 82 77 42
+@.14 =       56 78 38 80 39 75 02 71 66 66 01 03 55 72
+@.15 =      44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
+@.16 =    85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
+@.17 =   06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
+@.18 = 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93
+
+         do r=1  while  @.r\==''       /*build a version of the triangle*/
+             do k=1  for words(@.r)    /*build a row, number by number. */
+             #.r.k=word(@.r,k)         /*assign a number to an array num*/
+             end   /*k*/
+         end       /*r*/
+rows=r-1                               /*compute the number of rows.    */
+         do r=rows  by -1 to 2; p=r-1  /*traipse through triangle rows. */
+             do k=1  for p;     kn=k+1 /*re-calculate the previous row. */
+             #.p.k=max(#.r.k, #.r.kn)  +  #.p.k   /*replace previous #. */
+             end   /*k*/
+         end       /*r*/
+say 'maximum path sum:'  #.1.1         /*display the top (row 1) number.*/
+                                       /*stick a fork in it, we're done.*/