Solution 087 reduce factors

CocoaheadsCodeGolf.xcodeproj/project.pbxproj

@@ -11,6 +11,7 @@
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@@ -78,6 +80,7 @@
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@@ -218,6 +221,7 @@
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HeatWaves/CharacterCount.txt

@@ -1 +1 @@
-12 bytes.
+87 bytes.

HeatWaves/HeatWaves-readable.swift

@@ -0,0 +1,100 @@
+//
+//  HeatWaves-readable.swift
+//  HeatWaves
+//
+//  Solution by Udo Borkowski (2018-05-25)
+//
+//  FOR THE PUBLIC DOMAIN
+//
+
+// Background
+//
+// The Royal Netherlands Meteorological Institute defines a heat wave* as a
+// series of at least 5 consecutive days of ≥25°C weather (“summery weather”),
+// such that at least 3 of those days are ≥30°C (“tropical weather”).
+//
+// The tropical weather doesn't have to be measured consecutively: for example:
+// 30, 25, 30, 26, 27, 28, 32, 30 is a 8-day long heat wave with 4 days of
+// tropical weather.
+//
+// *(Well, by Dutch standards.)
+//
+// Challenge
+//
+// Given a non-empty list of positive integers representing Celsius temperature
+// measurements from successive days, decide whether that list contains a heat
+// wave (as per the above definition).
+//
+// The shortest answer in bytes wins.
+//
+// (This function contains the same code/algorithm as 'isHeatWaveIncludedIn'
+// in 'HeatWaves.swift' but is intended for a reader who wants to understand
+// the code better. So it includes comments, whitespaces, better names, ....)
+public func isHeatWaveIncludedIn_readable(waves w: [Int]) -> Bool {
+
+    // This solution uses a single array reduce to determine if the array contains
+    // a heat wave. When the reduce returns 0 we have a heat wave.
+    //
+    // The reduced value encodes the number of days ≥25°C (but <30°C) and days ≥30°C found
+    // so far in the current series.
+    //
+    // To encode these two counters in one number we use factors of prim numbers.
+    //
+    // (!!!1) When we found a heat wave the reduced value becomes 0.
+    //
+    // (!!!2) To represent n days ≥25°C (but <30°C) and m days ≥30°C we use the formula "2^n*3^m"
+    //
+    //         E.g. 2*3*3*3 = 108 means: 1 day ≥25°C (but <30°C) and 3 days ≥30°C
+    //
+    // (!!!3) 2^0*3^0 = 1 means: no days ≥25°C (or ≥30°C)
+    //
+
+    return w.reduce(
+        1,                          // initialize the reduce with no days (see !!!3)
+        {                           //
+            let n = $1 > 24 ?       // when the day's temperature was ≥ 25 (*)
+                $0 * (              //     we "increment" the counter by multiplying with the proper factor:
+                    $1>29 ?         //         when the day's temperature was ≥ 30 (*)
+                        3           //             we multiply with 3 (see !!!2)
+                        :           //         when the day's temperature was < 30 (but ≥ 25)
+                    2)              //             we multiply with 2 (see !!!2)
+                :                   // when the day's temperature was < 25
+                $0>0 ?              //     and we have not yet found a heat wave (see !!!1)
+                    1               //         we clear the counter to no days (see !!!3)
+                :                   //     when we have found a heat wave before (see !!!1)
+            0                       //         we keep this information, i.e. use 0.
+                                    //
+                                    // Now let's check if we found a heat wave:
+            return n % 27 == 0 &&   // When we have at least 3 days ≥30°C (**)
+                n > 81 ?            //              and 2 more days ≥25°C (***)
+                    0               //      we have a heat wave and return 0 (see !!!1)
+                :                   // Otherwise
+            n}                      //      we return the count (that may also be 0)
+                                    //
+        )<1                         // Finally we just need to check if the result of the reduce is 0
+                                    // to determine if we found a heat wave (****)
+
+
+
+    // (*)     instead of "...  >= intConst" use "... > intConst-1" to save 1 byte (">=" vs ">")
+    //
+    // (**)    3 days ≥30°C means 'n' contains at least the factors 3*3*3 == 27. To check this we
+    //         just need to divide 'n' by 27 and check if the remainder is 0 ("modulo").
+    //
+    // (***)   We already know we have at least 3 days ≥30°C, i.e. 'a' contains 3*3*3 (see **).
+    //         Now lets check some cases:
+    //
+    //         | # ≥25°C but <30°C | # ≥30°C |   n | isHeatWave? |
+    //         |-------------------+---------+-----+-------------|
+    //         | 0                 | 3       |  27 | false       |
+    //         | 1                 | 3       |  54 | false       |
+    //         | 2                 | 3       | 108 | true        |
+    //         | 0                 | 4       |  81 | false       |
+    //         | 1                 | 4       | 162 | true        |
+    //
+    //         As we can see, when n > 81 (and there are at least 3 days ≥30°C) we have a heat wave.
+    //
+    // (****)  instead of "== 0"" use "< 0" to save 1 byte ("==" vs "<").
+    //         This transformation is correct as the reduce will only return positive Ints and 0.
+
+}

HeatWaves/HeatWaves.swift

@@ -2,8 +2,9 @@
 //  HeatWaves.swift
 //  HeatWaves
 //
-//  Created by Sven Titgemeyer on 20.05.18.
-//  Copyright © 2018 Cocoaheads Aachen. All rights reserved.
+//  Solution by Udo Borkowski (2018-05-25)
+//
+//  FOR THE PUBLIC DOMAIN
 //
 
 // Background
@@ -25,6 +26,8 @@
 // wave (as per the above definition).
 //
 // The shortest answer in bytes wins.
+//
+// (see "HeatWaves-readable.swift" for a readable/commented version of this code)
 public func isHeatWaveIncludedIn(waves w: [Int]) -> Bool {
-    return false
+    return w.reduce(1,{let n=$1>24 ?$0*($1>29 ?3:2):$0>0 ?1:0;return n%27==0&&n>81 ?0:n})<1
 }