Three Dimensional Tables

The second type of multiple chart problem requires a form of three dimensional charts which are introduced next. Consider the PROGRAMING EXERCISES from PROBLEM 1.10: Example b. : Bill does a job in 5 hours. Together, Bill and Sue can do the job in 2 hours. How long would it take Sue to do the job alone? Example c. : Ben does a job in 5 days. Together, Ben and Marge do it in 3 days. How long would it take Marge to do the job alone? If we use plurals, we might produce a common table and program as below: Calculate rates: ------------------------------- | | rate | time |effort| ------------------------------- | Bill | | 5 | 1 | ------------------------------- | Sue | | | 1 | ------------------------------- |Bill&Sue| | 2 | 1 | ------------------------------- | Ben | | 5 | 1 | ------------------------------- | Marge | | | 1 | ------------------------------- |Ben&Marg| | 3 | 1 | ------------------------------- For Bill, Bill&Sue, Ben and Ben&Marg: rate$ = effort$ / time$. Sue's rate = Sue's effort / Sue's time; Marge's rate = Marge's effort / Marge's time; For Sue and Marge: time$ = effort$ / rate$. END. However, it is clear from the statements calculating Sue's and Marge's rate that additional plurals can be used if the tables are organized such that common formulas apply to facts aligned into rows and columns. This concept can be expanded by stacking the two problems behind one another to form a three dimensional table. A diagram of such an organization is sketched below showing only row and column labels. -------------------------------- / Ben / / | ----------- --------------------- | / Bill | rate | time | effort| /| ------------------------------------- | |first person | | | --------------- | |second person| | | --------------- | | combined | | / ------------------------------------- In this organization the plane label, "first person$" refers to Bill and Ben, "second person$" refers to Sue and Marge, and "Combined$" refers to Bill&Sue and Ben&Marg. Thus the sequential data parallel program is: For first person$ and combined$: rate$ = effort$ / time$. For second person$: rate$ = combined$ rate - first person$ rate; time$ = effort$ / rate$. The program is very compact, but how do you enter three dimensional data? - A plane at a time! The first plane is the diagram sketch given above. The second plane is the table for the first problem. The third plane is the table for the second problem. The entire data and program then is: Calculate times: ------------------------------------ | labels | rate | time |effort| ------------------------------------ |first person | | --------------- | |second person| | --------------- | | combined | | ------------------------------------ ------------------------------------ | table1 | rate | time |effort| ------------------------------------ | Bill | | 5 | 1 | ------------------------------------ | Sue | | | 1 | ------------------------------------ |Bill&Sue | | 2 | 1 | ------------------------------------ ------------------------------------ | table2 | rate | time |effort| ------------------------------------ | Ben | | 5 | 1 | ------------------------------------ | Marge | | | 1 | ------------------------------------ |Ben&Marg | | 3 | 1 | ------------------------------------ For first person$ and combined$: rate$ = effort$ / time$. For second person$: rate$ = combined$ rate - first person$ rate; time$ = effort$ / rate$. END. This format requires that the diagram sketch must be labeled with "labels" in the upper left hand corner. Labels on the other charts are optional. The diagram sketch must be first, the other planes may follow in any order. There may be any number of them, but all planes must have the same two dimensional layout.