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+1
+00:00:00,025 --> 00:00:02,900
+Okay, so now we're going to answer the question. So if we want
+
+2
+00:00:02,900 --> 00:00:06,520
+to consider all these inputs, and run them all on the software,
+
+3
+00:00:06,520 --> 00:00:09,490
+let's see how it will work. Let's assume that these are, 32
+
+4
+00:00:09,490 --> 00:00:12,280
+bit integers. So at this point what we will have is, a
+
+5
+00:00:12,280 --> 00:00:15,130
+number of combination, which is 2 to the 32, times 2 to
+
+6
+00:00:15,130 --> 00:00:18,390
+the 32. They're two integers. This is equal to 2 to the
+
+7
+00:00:18,390 --> 00:00:21,910
+64, which in turn, is more or less equal, to 10 to
+
+8
+00:00:21,910 --> 00:00:25,110
+the 19. So 10 to the 19 is the number of tests that
+
+9
+00:00:25,110 --> 00:00:27,960
+we need to run to cover the whole domain. Now let's assume
+
+10
+00:00:27,960 --> 00:00:31,400
+that we can run one test per nanosecond. So what that means
+
+11
+00:00:31,400 --> 00:00:34,290
+is that we can run 10 to the 9 tests per second,
+
+12
+00:00:34,290 --> 00:00:37,240
+and that's a lot. If we do the math, that results in 10
+
+13
+00:00:37,240 --> 00:00:40,750
+to the 10 seconds over all, because we have 10 to the
+
+14
+00:00:40,750 --> 00:00:43,760
+19 tests, we could run 10 to the 9 tests per second
+
+15
+00:00:43,760 --> 00:00:46,630
+so, we do the math, and we can run all these tests
+
+16
+00:00:46,630 --> 00:00:50,340
+in 10 to the 10 seconds. And what that corresponds to, it's about
+
+17
+00:00:50,340 --> 00:00:54,470
+600 years, so a lot of time. So even for such
+
+18
+00:00:54,470 --> 00:00:57,710
+a simple problem, a problem that takes two integers and adds them,
+
+19
+00:00:57,710 --> 00:01:00,990
+it will take more than 500 years to test it exhaustively. So
+
+20
+00:01:00,990 --> 00:01:04,690
+the bottom line here is that we just can't do exhaustive testing.