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5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Chapter 6.1, Problem 37ES

Textbook Problem

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Trace the action of Algorithm 6,1,1 on the variables *I, j, found, *and *answer *for *m *= 4, *n *= 4, and sets *A *and *B *represented as the arrays

To determine

**To trace:**

The action of Algorithm 6.1.1 on the variables i, j, found and answer for m = 4,

n = 4.

**Given information:**

For m = 4, n = 4 and sets A and B represented as the arrays

**Calculation:**

Input:

We also initialize i as 1 and we initialize answer as

i | 1 |

j | |

found | |

answer |

Next, the algorithm will enter the outer while-loop.

We first assign the value 1 to j and the value “no” to found.

i | 1 | 1 |

j | 1 | |

found | no | |

answer |

Since,

We increase the value of j by 1.

Since

i | 1 | 1 | 1 |

j | 1 | 2 | |

found | no | yes | |

answer |

Since, found is set to “yes”, the inner while-loop stops executing and we then increase i by 1.

Next, we start the second iteration of the outer while-loop, which re-initializes j as 1 and found as “no”.

i | 1 | 1 | 1 | 2 |

j | 1 | 2 | 1 | |

found | no | yes | no | |

answer |

Since,

We increase the value of j by 1.

Since,

i | 1 | 1 | 1 | 2 | 2 |

j | 1 | 2 | 1 | 2 | |

found | no | yes | no | no | |

answer |

We increase the value of j by 1.

Since

i | 1 | 1 | 1 | 2 | 2 | 2 |

j | 1 | 2 | 1 | 2 | 3 | |

found | no | yes | no | no | no | |

answer |

We increase the value of j by 1.

Since

i | 1 | 1 | 1 | 2 | 2 | 2 | 2 |

j | 1 | 2 | 1 | 2 | 3 | 4 | |

found | no | yes | no | no | no | no | |

answer |

We increase the value of j by 1.

Since j = 5 > 4 = n, the inner while-loop stops executing.

Since found is still set to “no”, answer is changed to

i | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |

j | 1 | 2 | 1 | 2 | 3 | 4 | 5 | |

found | no | yes | no | no | no | no | no | |

answer |

Next, we increase i by 1. We then start the third iteration of the outer while-loop, which re-initializes j as 1 and found as “no”

i | 3 |

j | 1 |

found | no |

answer |

Since

We increase the value of j by 1.

Since

i | 3 | 3 |

j | 1 | 2 |

found | no | no |

answer |

We increase the value of j by 1.

Since

i | 3 | 3 | 3 |

j | 1 | 2 | 3 |

found | no | no | no |

answer |

We increase the value of j by 1.

Since

i | 3 | 3 | 3 | 3 |

j | 1 | 2 | 3 | 4 |

found | no | no | no | no |

answer |

We increase the value of j by 1.

Since j = 5 > 4 = n, the inner while-loop stops executing.

Since found is still set to “no”, answer is set to

i | 3 | 3 | 3 | 3 | 3 |

j | 1 | 2 | 3 | 4 | 5 |

found | no | no | no | no | no |

answer |

Next, we increase i by 1

Discrete Mathematics With Applications

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