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Learn about elementary instructions in algorithmic tasks, including variable assignments, testing conditions, and loops. Understand the concepts of variables, loops, and sequences in algorithms. Explore examples such as binary search.
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I.2Algorithmique Tasks Variables Elementary instructions Algorithmic culture SylvieBoldo 1
Elementary instructions: assignment variable ←value We change a variable’s value. ⇒ i ←17 ⇒ i ←i+1
Elementary instructions:test ifBooleantheninstructionsif notinstruction ⇒ Is one value ≥ 10? ⇒ Is a calculationlikely to exceedthe maximum/minimal values of the variable’s type? ⇒ Is itlikelythat I willbebeyond the chart?
Elementary instructions: thesequence • instruction ;instruction • For example: • assignment, thentest • assignment, thenloop, thentest • assignment, thenassignment, thenassignment, thenassignment
Elementary instructions: the loop The for loop: forvariable fromvaluetovalueDoinstructionn_for ⇒ browse a chart (search for a maximum, calculate an average, filling a chart. . .) The as long as loop(more general) : Aslongasbooleandoinstructionn_aslongas ⇒ convergent sequence ⇒ non boundediteration(terminationproblem)
Instructions ‹→algorithms • Take the desiredamount: • theséquence • thetest • The loop • Variable assignment • Mix well • You have all the algorithms in the world!
Example: binarysearch Entries/outputs Entries: classified chart t of integers, of a size n > 0 and one valuev Outputs: booleansaying if v appears in t inf ← 0; sup ← n−1; aslongas(inf ≤ sup)do i ←(inf+sup)/2; if(t[i] = v) thensendVRAI; if not if(t[i] > v) thensup ←i−1; If notinf ←i+1; n_if n_if n_aslongas sendFALSE;
Example: binarysearch I search for 5. 8
Example : binarysearch I search for 5. ↑ ↑ inf sup 8
Example : binarysearch I search for 5. ↑ ↑ ↑ inf sup i 8
Example : binarysearch I search for 5. ↑ ↑ inf sup 8
Example : binarysearch I search for 5. ↑ ↑ ↑ inf sup i 8
Example : binarysearch I search for 5. ↑ ↑ inf sup 8
Example : binarysearch I search for 5. ↑ ↑ inf,i sup 8
Example : binarysearch I search for 5. ↑ inf,i,sup 8
Example : binarysearch I search for 5. ↑ ↑ sup inf 8
Example : binarysearch I search for 5. ↑ ↑ sup inf donc 5 n'est pas dans letableau. 8
Example: binarysearch I search for 5. ↑ ↑ sup inf so5 is not in the chart. In fact(inf+sup)/2 shouldbeinf+(sup-inf)/2. 8
