Question

Exercises • Determine running time for the following code fragments: (a) a = b + c; d = a + e; (b) sum = 0; for (i=0; i<3; i++) for (j=0; j<n; j++) sum++; (c) sum=0; for (i=0; i<n<n; i++) sum++; (d) for (i=0; i < n-1; i++) for (j=i+1; j <n; j++) { tmp = A[i][j]; A[i][j] = A[j] [i]; A[j][i] = tmp; (e) sum = 0; for (i=1; i<=n; i++) for (j=1; j<=n; j+=2) sum++;

Answer 1

Answer:

take constant execute 2 . for will to adding ab+c date: a numbers time. Therefore, . time taken statements are constant. TODOW) . b) sumo for (izo; 13; i++) for Liao, san, sitt) Burrit; outer for loop will executes 3 iteration of outer loop inner executed for Ö times. time for loop for every gets enton = 30 3 S constant. Tim-OLN) - sum=o [nanan?. forciso, ent n;i++), sumit, for loop Egi- n=2 will for get loop executed gets for of times: executed for i times. To=0(M)]

d) for (P=0; iº4n4; i++) for (iaitu jangjitt) ^ :. temp- Ali][j]; [1] [j].: AC3] [1]; Alj] li] = temp; liec, i loop gets isl, loop gets ise, i executed. n-i'timesie n tones. nilan- i n -lo tienes -24-3 times. for s En2 i loop gels executed roups E X+2 -1 9-40-2.), -1 teme. cdn2-1 . Surn of first Time (N1) complexity Natural will be Numbers. ' inetn-Lfn-3+:, :,:41 = (n=1) 10{+2) = n(n+1) = 0 1T0-0102)

e) sum=o for liali Pean, itt) for (j'<!; 342n;*32) Sum + outer for loop gets executed n times every iteration of outer loop, inner gets executed for logn times.... for loop T(n)= nulogn - blogn TuTime O Cologn)}