# RogerBW's Blog

 Perl Weekly Challenge 128: Maxima and Minima 03 September 2021 I’ve been doing the Weekly Challenges. The latest involved finding submatrices and counting trains. (Note that this is open until 5 September 2021.) TASK #1 › Maximum Sub-Matrix You are given m x n binary matrix having 0 or 1. Write a script to find out maximum sub-matrix having only 0. In other words, return the "maximum" rectangle that contains only 0 values. I chose to interpret "maximum" as the one with the largest area. Here's the Raku. ``````sub msm(@m) { `````` Establish the dimensions of the matrix. `````` my \$y=@m.elems; my \$x=@m[0].elems; `````` Maximum submatrix found so far: its area and dimensions. (Since it'll only contain 0 values, I will store just the dimensions, and recreate it at the end.) `````` my \$mxa=0; my @oc; `````` Any spot in the matrix might be the top left corner of the largest block of zeroes. `````` for (0..\$y-1) -> \$yi { for (0..\$x-1) -> \$xi { `````` …well, as long as it contains a zero itself. `````` if (@m[\$yi][\$xi]==0) { `````` Now I'm going to find the sizes of all the rectangles anchored on this this point. In each row, I iterate to the end, looking for a non-zero value. I stuff into `@rl` the minimum of (this row's count of zeroes) and (the lowest count of zeroes I've found so far). So the first entry in `@rl` will be the width of the N × 1 rectangle of zeroes anchored with `(xi,yi)` at top left, the second entry the width of the N × 2 rectangle, and so on. `````` my @rl; my \$mrl=\$x-\$xi; for (\$yi..\$y-1) -> \$yj { for (\$xi..min(\$xi+\$mrl,\$x)-1) -> \$xj { if (@m[\$yj][\$xj] != 0) { \$mrl=min(\$xj-\$xi,\$mrl); last; } } push @rl,\$mrl; } `````` So then I iterate through that list, derive the areas, and if there's a larger one than I already have, store that as the canonical largest area. (I'm using `>=` because one of the examples had both a 2×3 and a 3×2 as valid answers, but the 3×2, found later, is what's wanted.) (And yes, I could have done this in the earlier loop, but that happened not to be the way I thought when I was writing it.) `````` for (0..@rl.end) -> \$n { if (@rl[\$n]>0) { my \$a=@rl[\$n]*(\$n+1); if (\$a >= \$mxa) { \$mxa=\$a; @oc=(@rl[\$n],\$n+1); } } } } } } `````` Finally, build the actual array of zeroes that's asked for. `````` my @o; for (1..@oc[1]) -> \$y { push @o,[0 xx @oc[0]]; } return @o; } `````` TASK #2 › Minimum Platforms You are given two arrays of arrival and departure times of trains at a railway station. Write a script to find out the minimum number of platforms needed so that no train needs to wait. I've seen variants of this before, but usually with a series of tuples of (arrival time, departure time). Let's do this one in Perl. ``````sub mp { `````` `aa` and `da` are my arrival and departure time arrays. `````` my (\$aa,\$da)=@_; `````` I'm going to build an event list in `e`. `````` my %e; `````` An arrival has an event value of `+1`, a departure of `-1` (i.e. change in number of occupied platforms). The code for processing them is otherwise the same. `````` foreach my \$p ([\$aa,1],[\$da,-1]) { `````` For each timestamp in the list, `````` foreach my \$tm (@{\$p->[0]}) { `````` Parse it. `````` if (\$tm =~ /([0-9]+):([0-9]+)/) { `````` Store the event value, keyed with the numerical value of the timestamp. (This could be done with a string key instead, but then I'd have to validate for single-digit hours.) `````` \$e{\$1*60+\$2}+=\$p->[1]; } } } `````` So I now have a series of events, `+1` for a train arriving and `-1` for it departing. (If there's an arrival and a departure at the same moment, they'll cancel out; possibly not ideal, but the behaviour in this case is unspecified.) I run through these in time order, adding one to `pt` (platforms in use) when a train arrives and subtracting one when it departs. The maximum value is the number of platforms needed. `````` my \$pt=0; my \$pm=0; foreach my \$ts (sort {\$a <=> \$b} keys %e) { \$pt+=\$e{\$ts}; if (\$pt > \$pm) { \$pm=\$pt; } } return \$pm; } `````` Full code on github. Comments on this post are now closed. If you have particular grounds for adding a late comment, comment on a more recent post quoting the URL of this one. 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