1 00:00:04,530 --> 00:00:07,109 So now that we've seen Map and Filter, 2 00:00:07,109 --> 00:00:08,850 it should hopefully be easier to understand 3 00:00:08,850 --> 00:00:11,370 how Reduce works. I covered those two 4 00:00:11,370 --> 00:00:13,860 functions first because Reduce takes the 5 00:00:13,860 --> 00:00:15,870 same arguments and we now understand 6 00:00:15,870 --> 00:00:18,450 what they are. What reduce does though, 7 00:00:18,450 --> 00:00:20,910 is a bit harder to understand. It takes a 8 00:00:20,910 --> 00:00:23,640 function and a sequence, then reduces the 9 00:00:23,640 --> 00:00:26,490 sequence to a single value by repeatedly 10 00:00:26,490 --> 00:00:28,949 calling the function. The documentation 11 00:00:28,949 --> 00:00:30,060 is a really good example of 12 00:00:30,060 --> 00:00:32,009 documentation that's only useful 13 00:00:32,009 --> 00:00:34,710 after you already understand it. So we're going 14 00:00:34,710 --> 00:00:41,190 to just check that out briefly now. So 15 00:00:41,190 --> 00:00:42,690 the first thing to note there, in that 16 00:00:42,690 --> 00:00:44,820 link, is that Guido didn't remove it 17 00:00:44,820 --> 00:00:47,340 from Python, obviously, but he did get it 18 00:00:47,340 --> 00:00:49,379 removed to the functools module. 19 00:00:49,379 --> 00:00:51,809 You can see there, functools, and if we scroll 20 00:00:51,809 --> 00:00:53,129 down we can see here the functools 21 00:00:53,129 --> 00:00:55,559 dot reduce function. So he managed 22 00:00:55,559 --> 00:00:57,120 to get it moved into the functools module. 23 00:00:57,120 --> 00:00:59,219 So basically, Reduce is no longer 24 00:00:59,219 --> 00:01:01,680 a built-in function in Python 3. You have 25 00:01:01,680 --> 00:01:04,559 to import functools if you want to 26 00:01:04,559 --> 00:01:06,390 use it. Alright, so let's have a look at an 27 00:01:06,390 --> 00:01:08,070 example. We're going to start with the 28 00:01:08,070 --> 00:01:09,990 example in the documentation because 29 00:01:09,990 --> 00:01:12,630 it's quite simple. It uses a Lambda which 30 00:01:12,630 --> 00:01:14,130 we haven't covered yet, so I'm going to 31 00:01:14,130 --> 00:01:15,960 rewrite it using an ordinary 32 00:01:15,960 --> 00:01:19,049 function. I'll go back to IntelliJ, create a new 33 00:01:19,049 --> 00:01:21,720 file. This time, this new Python file, 34 00:01:21,720 --> 00:01:27,270 we'll call this reduceintro.py. Now let's 35 00:01:27,270 --> 00:01:28,409 add the code, so we'll start by 36 00:01:28,409 --> 00:01:33,090 typing import timeit and import func 37 00:01:33,090 --> 00:01:37,979 tools, and our first function on line 5, 38 00:01:37,979 --> 00:01:40,250 def calc underscore values 39 00:01:40,250 --> 00:01:44,270 parenthesis x comma space y colon int, 40 00:01:44,270 --> 00:01:46,560 then the closing right parenthesis and a 41 00:01:46,560 --> 00:01:49,020 colon. Then the value we want to return 42 00:01:49,020 --> 00:01:54,600 is x plus y. Okay and then on line 9 I'm 43 00:01:54,600 --> 00:01:57,840 going to type numbers equals left square 44 00:01:57,840 --> 00:02:04,229 bracket 2, 3, 5, 8, 13 and then on line 11, 45 00:02:04,229 --> 00:02:07,979 reduced underscore value equals and 46 00:02:07,979 --> 00:02:09,329 we're going to call our Reduce function. 47 00:02:09,329 --> 00:02:10,199 So it's going to be func 48 00:02:10,199 --> 00:02:15,330 tools dot reduce parentheses it's going to be 49 00:02:15,330 --> 00:02:19,450 calc underscore values comma space numbers 50 00:02:19,450 --> 00:02:22,100 and let's print that value out, print reduce 51 00:02:22,100 --> 00:02:24,709 underscore value. That should be calc 52 00:02:24,709 --> 00:02:26,840 underscore values, being the name of the 53 00:02:26,840 --> 00:02:32,770 function. Alright, run the program 54 00:02:32,770 --> 00:02:34,819 now we see that we've got the sum 55 00:02:34,819 --> 00:02:36,950 of all the numbers in the list, which is 31; 56 00:02:36,950 --> 00:02:41,209 2 plus 3 is 5, 5 is 10, 8 is 18 plus 13 57 00:02:41,209 --> 00:02:43,970 is 31, being the list on line 9. So we've 58 00:02:43,970 --> 00:02:46,790 got the sum of that list which is 31. 59 00:02:46,790 --> 00:02:48,050 Now I'll go through exactly what it's 60 00:02:48,050 --> 00:02:50,209 doing at the moment. Before that though, 61 00:02:50,209 --> 00:02:51,170 I want to refer back to 62 00:02:51,170 --> 00:02:53,510 Guido's comments that we saw earlier. 63 00:02:53,510 --> 00:02:55,070 So let's just go back and open it up again 64 00:02:55,070 --> 00:03:02,030 in a browser. You can see there's a few 65 00:03:02,030 --> 00:03:04,040 paragraphs down here. He's talking 66 00:03:04,040 --> 00:03:06,050 about the fact that Reduce - this is actually 67 00:03:06,050 --> 00:03:08,660 the one I've always hated most. Unless 68 00:03:08,660 --> 00:03:11,540 the function's trivial, as ours is, even Guido 69 00:03:11,540 --> 00:03:13,550 van Rossum struggles to understand 70 00:03:13,550 --> 00:03:15,739 what's going on. As he says, we already 71 00:03:15,739 --> 00:03:18,410 have a sum function to take care 72 00:03:18,410 --> 00:03:20,630 of addition. So back in our code, we can write 73 00:03:20,630 --> 00:03:24,220 what we've done there, quite simply, with 74 00:03:24,220 --> 00:03:27,890 print parentheses sum parentheses 75 00:03:27,890 --> 00:03:33,950 numbers. Click and run that, and obviously, we 76 00:03:33,950 --> 00:03:36,049 get the same result. So getting back 77 00:03:36,049 --> 00:03:39,049 to Guido's blog post, he talked about using 78 00:03:39,049 --> 00:03:41,540 product to calculate the product of a 79 00:03:41,540 --> 00:03:43,820 sequence - that didn't get added to Python. 80 00:03:43,820 --> 00:03:46,489 There is a product function in the 81 00:03:46,489 --> 00:03:49,220 itertools module, but that 82 00:03:49,220 --> 00:03:50,870 does something different. It calculates 83 00:03:50,870 --> 00:03:52,850 the Cartesian product which is useful 84 00:03:52,850 --> 00:03:55,850 when dealing with sets, for example. Guido 85 00:03:55,850 --> 00:03:57,859 proposed adding all and any to the 86 00:03:57,859 --> 00:03:59,750 built-in functions. That's been done and 87 00:03:59,750 --> 00:04:01,280 we'll look at those in a minute. 88 00:04:01,280 --> 00:04:03,200 The upshot of this discussion 89 00:04:03,200 --> 00:04:05,630 is that there's very rarely any need to use 90 00:04:05,630 --> 00:04:08,299 Reduce in your code. However, many people 91 00:04:08,299 --> 00:04:10,190 disagreed and there's a link to the 92 00:04:10,190 --> 00:04:11,630 comments at the bottom of the post, 93 00:04:11,630 --> 00:04:13,239 if you go down and have a look - 94 00:04:13,239 --> 00:04:15,799 118 comments there - so you can go ahead 95 00:04:15,799 --> 00:04:17,298 and check those and see why people have 96 00:04:17,298 --> 00:04:18,978 disagreed with it, if you want. Now going 97 00:04:18,978 --> 00:04:21,858 back to our code now, let's see how 98 00:04:21,858 --> 00:04:23,450 Reduce works so that you understand 99 00:04:23,450 --> 00:04:25,039 what's happening. You'll need to know 100 00:04:25,039 --> 00:04:26,990 what it's doing if you come across it in 101 00:04:26,990 --> 00:04:29,090 code that you have to maintain. Alright, 102 00:04:29,090 --> 00:04:31,190 so looking at our list on line 9, we've 103 00:04:31,190 --> 00:04:32,330 got five numbers. 104 00:04:32,330 --> 00:04:35,030 What reduce is doing, is calling our 105 00:04:35,030 --> 00:04:37,370 calc underscore values function with the 106 00:04:37,370 --> 00:04:39,440 first two items in the list, 2 and 107 00:04:39,440 --> 00:04:42,500 3, then returns the result 5. 108 00:04:42,500 --> 00:04:45,050 It uses that value and the next item in the 109 00:04:45,050 --> 00:04:47,090 list when it calls calc underscore 110 00:04:47,090 --> 00:04:49,909 values again. So that returns 10, so 111 00:04:49,909 --> 00:04:52,610 10 becomes the first argument in the next 112 00:04:52,610 --> 00:04:55,069 call, to the next call, of calc underscore 113 00:04:55,069 --> 00:04:57,139 values. So if you wanted to know what a 114 00:04:57,139 --> 00:04:58,669 long hand, or say a long-handed 115 00:04:58,669 --> 00:05:00,289 version of what's happening here, 116 00:05:00,289 --> 00:05:01,460 we could type that out. It'll be something 117 00:05:01,460 --> 00:05:05,900 along these lines; it'll be result equals 118 00:05:05,900 --> 00:05:10,240 calc underscore values 2 comma 3 119 00:05:10,240 --> 00:05:14,409 and let's just, actually, I'll do the next one, result 120 00:05:14,409 --> 00:05:16,729 equals and it's calc values again. This 121 00:05:16,729 --> 00:05:19,639 time it's result comma 5 and now 122 00:05:19,639 --> 00:05:21,349 I'll copy the lines, I'll copy the next two 123 00:05:21,349 --> 00:05:24,020 lines, and so it's result comma 5 124 00:05:24,020 --> 00:05:26,810 result comma 8 this time, then result 125 00:05:26,810 --> 00:05:31,719 comma 13, and then we can print result. 126 00:05:31,719 --> 00:05:35,180 We can run that, and you can see we've 127 00:05:35,180 --> 00:05:37,520 got the same value there. So each time 128 00:05:37,520 --> 00:05:39,800 around, the function is called with the 129 00:05:39,800 --> 00:05:41,960 result from the previous call and the 130 00:05:41,960 --> 00:05:44,270 next item in the list, and you can see 131 00:05:44,270 --> 00:05:45,979 that when I ran the program, we got 31 132 00:05:45,979 --> 00:05:48,199 returned for a third time. Alright so 133 00:05:48,199 --> 00:05:50,180 addition's easy but the sum function is a 134 00:05:50,180 --> 00:05:52,240 much easier way to do the same thing. 135 00:05:52,240 --> 00:05:54,800 Multiplication is also trivial, so if I 136 00:05:54,800 --> 00:05:56,389 go ahead and change our calc underscore 137 00:05:56,389 --> 00:05:58,789 values function to perform multiplication 138 00:05:58,789 --> 00:06:00,680 instead, by changing the plus to a 139 00:06:00,680 --> 00:06:03,889 multiplication, which is the star. 140 00:06:03,889 --> 00:06:06,889 of course. If I run that again now, 141 00:06:06,889 --> 00:06:10,069 this time we get the value 3120. The sum 142 00:06:10,069 --> 00:06:11,479 is still 31, of course, and there's no 143 00:06:11,479 --> 00:06:12,830 built-in function to calculate 144 00:06:12,830 --> 00:06:15,289 the product of a list. If you wanted to 145 00:06:15,289 --> 00:06:17,210 calculate the product without using 146 00:06:17,210 --> 00:06:19,909 Reduce, then you'd have to use a loop. 147 00:06:19,909 --> 00:06:22,099 So what I can do is comment out the call, 148 00:06:22,099 --> 00:06:26,479 the call to sum there - comment that out. So 149 00:06:26,479 --> 00:06:32,319 result equals 1 for x in numbers colon 150 00:06:32,319 --> 00:06:38,599 result star equals x and then we can 151 00:06:38,599 --> 00:06:40,780 print result. 152 00:06:40,780 --> 00:06:43,600 We could run that, and then we get the 153 00:06:43,600 --> 00:06:46,750 value of 3120 again. Basically, all 154 00:06:46,750 --> 00:06:50,110 three methods are giving the same answer. We've 155 00:06:50,110 --> 00:06:51,610 been discussing comprehensions in this 156 00:06:51,610 --> 00:06:52,930 section and I mentioned that every 157 00:06:52,930 --> 00:06:55,450 comprehension can be re-written as a 158 00:06:55,450 --> 00:06:58,780 loop. The opposite though, isn't true. 159 00:06:58,780 --> 00:06:59,860 You may be expecting me to write 160 00:06:59,860 --> 00:07:01,540 a comprehension that does the same thing 161 00:07:01,540 --> 00:07:03,580 as Reduce - we did that with Map and 162 00:07:03,580 --> 00:07:05,980 Filter after all - but you can't 163 00:07:05,980 --> 00:07:08,950 replace Reduce with a comprehension. Well that's 164 00:07:08,950 --> 00:07:10,900 not strictly true - you can pretty much do 165 00:07:10,900 --> 00:07:12,940 anything you want with enough code. 166 00:07:12,940 --> 00:07:15,100 If you search for solutions online, you'll 167 00:07:15,100 --> 00:07:17,110 find some. You'll also see their authors 168 00:07:17,110 --> 00:07:18,940 describing the solutions as insane, 169 00:07:18,940 --> 00:07:21,490 and not in a good way. You should now be 170 00:07:21,490 --> 00:07:23,170 able to work out what reduce is doing 171 00:07:23,170 --> 00:07:24,940 though, if you come across it in code 172 00:07:24,940 --> 00:07:26,860 that you have to use or maintain, 173 00:07:26,860 --> 00:07:28,870 and we'll leave it up to you to decide 174 00:07:28,870 --> 00:07:31,090 whether to use it in your own code. So 175 00:07:31,090 --> 00:07:33,010 let's finish this video here, and in the 176 00:07:33,010 --> 00:07:33,610 next one, 177 00:07:33,610 --> 00:07:36,070 we'll take a look at All and Any. See you 178 00:07:36,070 --> 00:07:38,790 in the next video.