tabulation_2dim_triangular.md

layout	permalink	title	speed
page	/tabulation_2dim_triangular/	(partly) Space-efficient tabulation for 2-dim nonterminals	50

{% include tabulation_libs.html %}

The solution for the subword pair $(i..j,k..l)$ is stored at $M[adr(i,j),adr(k,l)]$ where $M$ is a two-dimensional matrix of size $(|w|+1)\cdot(|w|+2) / 2$ in both dimensions, and $adr(i,j) = i + (j\cdot(j+1)) \div 2$. This partially eliminates the space loss of the naive strategy -- while overlapping subwords still cause space loss (see the holes in the matrix).

Hint: Zoom out with your mouse scroll wheel for bigger word lengths!

{% include tabulation_speed_slider.html %}

{% include tabulation_length_slider.html %}

<script> Tabulation.prototype.adr = function(i,j) { return i + Math.floor((j*(j+1)) / 2); } Tabulation.prototype.solve = function(x1,x2,x3,x4,c) { this.addCubeDelayed(this.adr(x1,x2), this.adr(x3,x4), 0, c); } Tabulation.prototype.fill = function() { var len = this.len; var l = (len+1)*(len+2) / 2; this.addBoundingBox(l,l,1); this.addText(0, 0, -2, 0); this.addText(l-1, l-1, -2, 0); this.addText(0, -1.7, 0, 0); this.addText(l-1, -1.7, l-1, 0); var c = 0; for (var l=0; l<=len; l++) { for (var x1=0; x1<=len-l; x1++) { var x2 = x1 + l; for (var l2=0; l2<=l; l2++) { for (var x3=0; x3 <= (l==l2 ? x1 : len-l2); x3++) { var x4 = x3 + l2; if (x3 >= x2 || x4 <= x1) { this.solve(x1, x2, x3, x4,c); c++; if (!(x1 == x3 && x2 == x4)) { this.solve(x3, x4, x1, x2, c); c++; } } } } } } setTimeout(function(){console.log("subproblems: " + c)}, 100); } $(function() { var tab = new Tabulation($(".post-content")[0], $( "#slider" ).slider("value")); tab.speed = {{page.speed}}; tab.fill(); window.tab = tab; }); </script>