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# An Introduction to Algol 68 through Problems by A. Learner

By A. Learner

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Problems for Chapter 3 1. Write a program whose input is a sequence of integers, all less than 400, and whose output is their equivalent in Roman numerals. 2. Given a square grid of heights above sea level, including a mountain top, find a possible path for a river from the mountain top to the lowest point on the grid. (Water does not run uphill but may run diagonally relative to the grid. Assume a path does exist). 3. Write a program to form the rna trix product of two matrices, one mxp and the other pxn.

All unary (one-operand) operators, such as not and unary - have priority IO; for example -3t2 is (-3) 2 =9, whereas 0-3t2 equals -3 2 = -9. Priorities are included in the list of standard operators in 56 AN INTRODUCTION TO ALGOL 68 Appendix I. The BNF of priority declarations is (identity decl) : := prio ( opsymbol) = (nonzero digit ) We now construct an algorithm to transform simple unbracketed arithmetic expressions into postfix form. The input is a string made up of single letters or digits as operands, operators +,-,*j,t, spaces to be ignored, and £ as terminating symbol, and is mathematically wellformed.

In! 2 However, the main point of the declaration is that structures, like multiples, can be treated as single objects. 'date := (12, "JUL", 1984)' assigns to 'date' the display on the right-hand side, which is a row of denotations of values of the types and in the order that the structure declaration specified. Then 'day of date plusab 13; month of date :="DEC'' ' makes 'date' now refer to Christmas day 1984. The fields of a structure may be of any type, including other structures, and there may be any number ;;;,:1 of fields.