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Abstract

The problem of the Dutch national flag was formulated by Dijkstra (1976) as follows: There is a row of buckets numbered from 1 to n. It is given that: P1: each bucket contains one pebble P2: each pebble is either red, white, or blue. A minicomputer is placed in front of this row of buckets and has to be programmed in such a way that it will rearrange (if necessary) the pebbles in the order of the Dutch national flag. The minicomputer in question should perform this rearrangement using two commands: swap i j for 1≤i≤n and 1≤j≤n exchanges the pebbles stored in the buckets numbered i and j; read (i) for 1≤i≤n returns the colour of the pebble currently lying in bucket number i. Dijkstra originally named this operation buck. © Cambridge University Press 2011.