plus small triangles of area / each (base and height in ( )which applies only when is eventhe rectangles are shown to cover big rectangle of base / and height the lesson to be learned from proposition is that if we perform an algorithm with nested loops such that the operations in the inner loop increase by one each timethen the total number of operations is quadratic in the number of timesnwe perform the outer loop in particularthe number of operations is / / in this casewhich is little more than constant factor ( / times the quadratic function in other wordssuch an algorithm is only slightly better than an algorithm that uses operations each time the inner loop is performed this observation might at first seem nonintuitivebut it is nevertheless trueas shown in figure the cubic function and other polynomials continuing our discussion of functions that are powers of the inputwe consider the cubic functionf(nn