計算量

. .. . . . ....... I, Summer 2009.. .. . . . ... .1 : .. .2 1 () () ()..

. .. . . . .: XXXXXXXX: XXXXXXXXXX: XXXXXXXXXX1: XXXXXXXXXXXXXXXXXXXXXXXXXXXX2: XXXXXXXXXXXXXXXXXXXXXXXXXXXX3: . . .n-1: XXXXXXXXXXXXXXXXXXXXXXXXXXXXn : XXXXXXXXXXXXXXXXXXXXXXXXXXXX.. .. . . . ....??.......

. .. . . . ... .1 : .. .2 1 () () ().. .. . . . ...: ? n O(n) n 2 O(n 2 ) 4 n f (n)

. .. . . . .1 1 rowsum: 1 A = (a 1 , a 2 , · · · , a m ): A ()1: Total := 0;2: i 1 m :Total := Total + a i ;3: Total() ;..... () m f m f = 1 + m + 1 m ..... .. . . . . () () tablesumSS⎛: m n A = ⎜⎝⎞a 11 a 12 · · · a 1na 21 a 22 · · · a 2n.. . ..⎟. ⎠a m1 a m2 · · · a mn: A ()1: Total := 0;2: i 1 m :3: SubTotal := 0;4: j 1 n :5 SubTotal := SubTotal + a ij ;6 Total := Total + SubTotal;7: Total() ;..

. .. . . . . () () tablesum⎛⎞a 11 a 12 · · · a 1na 21 a 22 · · · a 2n: n m A = ⎜⎝.. . ..⎟. ⎠a m1 a m2 · · · a mn: A ()1: Total := 0;2: i 1 m :3: j 1 n :4: Total := Total + a ij ;5: Total() ;.. .. . . . . () ()..... tablesum1: Total := 0;2: i 1 m :3: j 1 n :4: Total := Total + a ij ;5: Total() ; n n f n m 2 3 ?.....

. .. . . . ....1 rowsum () 2 ? tablesum 2 ? tablesum 2 ?........