# Stacking blocks

Given an input of a list of blocks to drop at certain points, output the height of the resulting "tower."

The best way to explain this challenge is by example. The input will be a list of 2n integers representing n blocks. The first integer is the block's x position, 0-indexed, and the second is how wide the block is. For example, an input of 2 4 represents the block (with x coordinates labeled below):

  ####
0123456789


Now, let's say the input is 2 4 4 6. That is, one block at x=2 with a width of 4, and one at x=4 with a width of 6:

    ######
####


Note that a.) blocks always "drop" from the very top of the tower and b.) blocks will never "fall over" (i.e. they will always balance). So, an input of 2 4 4 6 12 1 represents:

    ######
####      #


Note that the final block has fallen all the way to the "ground."

Your final output should be the maximum height of the tower at each x-value up to the largest. Hence, the input 2 4 4 6 12 1 should result in output 0011222222001:

    ######
####      #
0011222222001


Input may be given as either a whitespace-/comma-separated string, an array of integers, or function/command line arguments. The block positions (x values) will always be integers 0 or greater, the width will always be an integer 1 or greater, and there will always be at least one block.

Output may be given as a single string separated by non-numerical characters (ex. "0, 0, 1, ..."), a single string listing all the digits (ex. "001..."—the maximum height is guaranteed to be 9 or less), or an array of integers.

Since this is , the shortest code in bytes will win.

Test cases:

In                                   Out
---------------------------------------------------------
2 4 4 6 12 1                         0011222222001
0 5 9 1 6 4 2 5                      1133333222
0 5 9 1 2 5 6 4                      1122223333
0 5 2 5 6 4 9 1                      1122223334
20 1 20 1 20 1                       00000000000000000003
5 5                                  000011111
0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 4  123456789999

• Can we take input as an array of 2-tuples? Jan 27, 2016 at 0:35
• @ThomasKwa No, the input must be a 1-dimensional array. Jan 27, 2016 at 0:36

## Python 3, 89

def f(a):
h=[]
while a:x,w,*a=a;h[:x+w]=(h+[0]*x)[:x]+[max(h[x:x+w]+[0])+1]*w
return h


The function takes and returns a list of integers.

def f(a):                       # input as list of integers
h=[]                          # list of heights
while a:                      # while there's input left
x,w,*a=a;                   # pop first 2 integers as x and w

h[:x+w]=                    # change the heights between 0 and x+w
(h+[0]*x)[:x]+            # left of x -> unchanged but padded with zeros
[max(h[x:x+w]+[0])+1]*w   # between x and x+w -> set to the previous max + 1

return h                      # return the list of heights


## CJam, 34 30 bytes

Lq~2/{eeWf%e~_2$:).*:e>f*.e>}/  Input as a CJam-style array, output as a string of digits. Run all test cases. Here are two variants of another idea, but it's currently 2 bytes longer: Lq~2/{_:\3$><0+:e>)aeez.*e_.e>}/
LQ~2/{_:\3\$><0+:e>)aeez.+e~.e>}/


## Ruby, 88 87 bytes

f=->i{o=[]
(s,l,*i=i
r=s...s+l
o[r]=[([*o[r]]+[0]).max+1]*l
o.map! &:to_i)while i[0]
o}


Try it online.

Inspired by grc's answer, but in a different language and just slightly shorter.

Explanation:

f=->i                        # lambda with parameter i, expects array of ints
{
o=[]                     # output
(
s,l,*i=i             # pop start and length
r = s...s+l          # range is used twice, so shorten it to 1 char
o[r] =
[(
[*o[r]]  # o[r] returns nil if out of bounds, so splat it into another array
+[0]     # max doesn't like an empty array, so give it at least a 0
).max+1]*l       # repeat max+1 to fill length
o.map! &:to_i        # replace nil values with 0
) while i[0]             # i[0] returns nil when i is empty, which is falsy
o                        # return o
}


## APL, 79 bytes

{⊃{o←(z←(≢⍵)⌈a←+/⍺)↑⍵⋄e←(z↑(-a)↑⍺[1]⍴1)⋄o+0⌈o-⍨e×e⌈.+e×o}/⌽(⊂⍬),↓(⌽2,0.5×≢⍵)⍴⍵}


Input as an APL Array, output as an APL array of digits.

• {⊃{o←⍵↑⍨z←(≢⍵)⌈a←+/⍺⋄e←z↑(-a)↑⍺[1]⍴1⋄o+0⌈o-⍨e×e⌈.+e×o}/⌽(⊂⍬),↓⍵⍴⍨⌽2,.5×≢⍵} (My god, learn to use ⍨ right) Jul 31, 2017 at 22:06
• Please, be careful with your words... You don't seem to know the difference between ⊃ and 1↑ and because of this you give suggestions that cause the updated program to give the wrong result but I don't patronise you. Aug 2, 2017 at 9:39
• Yeah, I get like that sometimes when I see a bunch of things able to be golfed. But the other golfs should still apply, though. Aug 2, 2017 at 23:50
• They all do. And I've integrated your suggestions, hopefully with proper credits. Aug 3, 2017 at 8:48
• -- Did you? -- 0.5 Aug 3, 2017 at 10:36

### Java 1.8, 351 329 bytes

Not thrilled with this first attempt - I'm sure the double looping, and all those Integer.valueOf's can be golfed some more.

interface B{static void main(String[]x){Byte b=1;int i=0,s,c,m=0,h,a=x.length,t[];for(;i<a;){s=b.valueOf(x[i++]);c=b.valueOf(x[i++]);m=m>s+c?m:s+c;}t=new int[m];for(i=0;i<a;){h=0;s=b.valueOf(x[i++]);c=b.valueOf(x[i++]);for(m=s;m<s+c;m++)if(t[m]>=h)h=t[m]+1;for(m=s;m<s+c;)t[m++]=h;}for(i=0;i<t.length;)System.out.print(t[i++]);}}


### Ungolfed

interface B {
static void main(String[]x){
int start, count, maxWidth=0, height, args=x.length, totals[];
Byte b=1;
for (int i=0; i<args;){
start = b.valueOf(x[i++]);
count = b.valueOf(x[i++]);
maxWidth = maxWidth>start+count ? maxWidth : start+count;
}
totals=new int[maxWidth];
for (int i=0; i<args;){
height=0;
start = b.valueOf(x[i++]);
count = b.valueOf(x[i++]);
for (int j = start; j<start+count; j++) {
if (totals[j]>=height) {
height=totals[j]+1;
}
}
for (int j = start; j<start+count; j++) {
totals[j] = height;
}
}
for (int i=0;i<totals.length; i++){
System.out.print(totals[i]);
}
}
}