Biochemical Digital Circuit

A biochemical digital circuit (BDC) is an artifact composed of a set of processing nodes. Each processing node is composed of a tiny receptacle for biochemical reagents, made of a biological substrate that acts as a digital electronic chip. Depending on the state of the reaction in the receptacle, the substrate generates two voltage levels. A reader coupled to the BDC is able to perform the reading of all the processing nodes of a BDC in a given instant, interpreting the two voltage levels as 0 or 1.

An experiment with the BDC is performed as follows. The processing nodes are loaded with substances of interest and appropriate reagents and, at every fixed interval of time (typically a few milliseconds), the processing nodes are read. Thus, the experiment results in a sequence of sets (vectors) of bits, each vector representing a measurement of the BDC.

An uninterrupted sequence of bits 1 of a same processing node along the time is called a toothpick. The length of a toothpick is the number of bits 1 that composes it (note that the length of the toothpick of an experiment may vary between one and the number of measurements made). An important feature of an experiment with the BDC is the amount and length of toothpicks generated. The figure below shows the result of an experiment conducted with a BDC of six processing nodes, in which four measurements were made, containing three toothpicks of length one, a toothpick of length two and one toothpick of length four.

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You've been hired to write a program to determine, given the outcome of an experiment, how many toothpicks of length equal to or greater than a certain value were generated.