Below, there are a few code fragments and the order of growth of their running times as a function of the number of input elements N.

The order of growth: linear.

```for (int N = 1; N <= 100; ++N)
{
outer = 0;
inner = 0;
for (int n = N; n > 0; n /= 2)
{
++outer;
for (int i = 0; i < n; ++i)
++inner;
}
// outer: ln(N)
// inner: 2N
Console.WriteLine(\$"N={N}\touter: ({N},{outer})\tinner: ({N},{inner})");
}
```

The order of growth: linear ("staircase")

```for (int N = 1; N <= 100; ++N)
{
outer = 0;
inner = 0;
for (int n = 1; n < N; n *= 2)
{
outer++;
for (int i = 0; i < n; ++i)
inner++;
}
// outer: ln(N)
// inner: N
Console.WriteLine(\$"N={N}\touter: ({N},{outer})\tinner: ({N},{inner})");
}```

The order of growth: linearithmic

```for (int N = 1; N <= 100; ++N)
{
outer = 0;
inner = 0;
for (int n = 1; n < N; n *= 2)
{
outer++;
for (int i = 0; i < N; ++i)
inner++;
}
// outer: ln(N)
// inner: N*ln(N)
Console.WriteLine(\$"N={N}\touter: ({N},{outer})\tinner: ({N},{inner})");
}```

The above linear "staircase" order of growth can be depicted as follows:

This is output from the above code fragments - the lists of points:

```N=1     outer: (1,1)    inner: (1,1)
N=2     outer: (2,2)    inner: (2,3)
N=3     outer: (3,2)    inner: (3,4)
N=4     outer: (4,3)    inner: (4,7)
N=5     outer: (5,3)    inner: (5,8)
N=6     outer: (6,3)    inner: (6,10)
N=7     outer: (7,3)    inner: (7,11)
N=8     outer: (8,4)    inner: (8,15)
N=9     outer: (9,4)    inner: (9,16)
N=10    outer: (10,4)   inner: (10,18)
N=11    outer: (11,4)   inner: (11,19)
N=12    outer: (12,4)   inner: (12,22)
N=13    outer: (13,4)   inner: (13,23)
N=14    outer: (14,4)   inner: (14,25)
N=15    outer: (15,4)   inner: (15,26)
N=16    outer: (16,5)   inner: (16,31)
N=17    outer: (17,5)   inner: (17,32)
N=18    outer: (18,5)   inner: (18,34)
N=19    outer: (19,5)   inner: (19,35)
N=20    outer: (20,5)   inner: (20,38)
N=21    outer: (21,5)   inner: (21,39)
N=22    outer: (22,5)   inner: (22,41)
N=23    outer: (23,5)   inner: (23,42)
N=24    outer: (24,5)   inner: (24,46)
N=25    outer: (25,5)   inner: (25,47)
N=26    outer: (26,5)   inner: (26,49)
N=27    outer: (27,5)   inner: (27,50)
N=28    outer: (28,5)   inner: (28,53)
N=29    outer: (29,5)   inner: (29,54)
N=30    outer: (30,5)   inner: (30,56)
N=31    outer: (31,5)   inner: (31,57)
N=32    outer: (32,6)   inner: (32,63)
N=33    outer: (33,6)   inner: (33,64)
N=34    outer: (34,6)   inner: (34,66)
N=35    outer: (35,6)   inner: (35,67)
N=36    outer: (36,6)   inner: (36,70)
N=37    outer: (37,6)   inner: (37,71)
N=38    outer: (38,6)   inner: (38,73)
N=39    outer: (39,6)   inner: (39,74)
N=40    outer: (40,6)   inner: (40,78)
N=41    outer: (41,6)   inner: (41,79)
N=42    outer: (42,6)   inner: (42,81)
N=43    outer: (43,6)   inner: (43,82)
N=44    outer: (44,6)   inner: (44,85)
N=45    outer: (45,6)   inner: (45,86)
N=46    outer: (46,6)   inner: (46,88)
N=47    outer: (47,6)   inner: (47,89)
N=48    outer: (48,6)   inner: (48,94)
N=49    outer: (49,6)   inner: (49,95)
N=50    outer: (50,6)   inner: (50,97)
N=51    outer: (51,6)   inner: (51,98)
N=52    outer: (52,6)   inner: (52,101)
N=53    outer: (53,6)   inner: (53,102)
N=54    outer: (54,6)   inner: (54,104)
N=55    outer: (55,6)   inner: (55,105)
N=56    outer: (56,6)   inner: (56,109)
N=57    outer: (57,6)   inner: (57,110)
N=58    outer: (58,6)   inner: (58,112)
N=59    outer: (59,6)   inner: (59,113)
N=60    outer: (60,6)   inner: (60,116)
N=61    outer: (61,6)   inner: (61,117)
N=62    outer: (62,6)   inner: (62,119)
N=63    outer: (63,6)   inner: (63,120)
N=64    outer: (64,7)   inner: (64,127)
N=65    outer: (65,7)   inner: (65,128)
N=66    outer: (66,7)   inner: (66,130)
N=67    outer: (67,7)   inner: (67,131)
N=68    outer: (68,7)   inner: (68,134)
N=69    outer: (69,7)   inner: (69,135)
N=70    outer: (70,7)   inner: (70,137)
N=71    outer: (71,7)   inner: (71,138)
N=72    outer: (72,7)   inner: (72,142)
N=73    outer: (73,7)   inner: (73,143)
N=74    outer: (74,7)   inner: (74,145)
N=75    outer: (75,7)   inner: (75,146)
N=76    outer: (76,7)   inner: (76,149)
N=77    outer: (77,7)   inner: (77,150)
N=78    outer: (78,7)   inner: (78,152)
N=79    outer: (79,7)   inner: (79,153)
N=80    outer: (80,7)   inner: (80,158)
N=81    outer: (81,7)   inner: (81,159)
N=82    outer: (82,7)   inner: (82,161)
N=83    outer: (83,7)   inner: (83,162)
N=84    outer: (84,7)   inner: (84,165)
N=85    outer: (85,7)   inner: (85,166)
N=86    outer: (86,7)   inner: (86,168)
N=87    outer: (87,7)   inner: (87,169)
N=88    outer: (88,7)   inner: (88,173)
N=89    outer: (89,7)   inner: (89,174)
N=90    outer: (90,7)   inner: (90,176)
N=91    outer: (91,7)   inner: (91,177)
N=92    outer: (92,7)   inner: (92,180)
N=93    outer: (93,7)   inner: (93,181)
N=94    outer: (94,7)   inner: (94,183)
N=95    outer: (95,7)   inner: (95,184)
N=96    outer: (96,7)   inner: (96,190)
N=97    outer: (97,7)   inner: (97,191)
N=98    outer: (98,7)   inner: (98,193)
N=99    outer: (99,7)   inner: (99,194)
N=100   outer: (100,7)  inner: (100,197)
```
```N=1     outer: (1,0)    inner: (1,0)
N=2     outer: (2,1)    inner: (2,1)
N=3     outer: (3,2)    inner: (3,3)
N=4     outer: (4,2)    inner: (4,3)
N=5     outer: (5,3)    inner: (5,7)
N=6     outer: (6,3)    inner: (6,7)
N=7     outer: (7,3)    inner: (7,7)
N=8     outer: (8,3)    inner: (8,7)
N=9     outer: (9,4)    inner: (9,15)
N=10    outer: (10,4)   inner: (10,15)
N=11    outer: (11,4)   inner: (11,15)
N=12    outer: (12,4)   inner: (12,15)
N=13    outer: (13,4)   inner: (13,15)
N=14    outer: (14,4)   inner: (14,15)
N=15    outer: (15,4)   inner: (15,15)
N=16    outer: (16,4)   inner: (16,15)
N=17    outer: (17,5)   inner: (17,31)
N=18    outer: (18,5)   inner: (18,31)
N=19    outer: (19,5)   inner: (19,31)
N=20    outer: (20,5)   inner: (20,31)
N=21    outer: (21,5)   inner: (21,31)
N=22    outer: (22,5)   inner: (22,31)
N=23    outer: (23,5)   inner: (23,31)
N=24    outer: (24,5)   inner: (24,31)
N=25    outer: (25,5)   inner: (25,31)
N=26    outer: (26,5)   inner: (26,31)
N=27    outer: (27,5)   inner: (27,31)
N=28    outer: (28,5)   inner: (28,31)
N=29    outer: (29,5)   inner: (29,31)
N=30    outer: (30,5)   inner: (30,31)
N=31    outer: (31,5)   inner: (31,31)
N=32    outer: (32,5)   inner: (32,31)
N=33    outer: (33,6)   inner: (33,63)
N=34    outer: (34,6)   inner: (34,63)
N=35    outer: (35,6)   inner: (35,63)
N=36    outer: (36,6)   inner: (36,63)
N=37    outer: (37,6)   inner: (37,63)
N=38    outer: (38,6)   inner: (38,63)
N=39    outer: (39,6)   inner: (39,63)
N=40    outer: (40,6)   inner: (40,63)
N=41    outer: (41,6)   inner: (41,63)
N=42    outer: (42,6)   inner: (42,63)
N=43    outer: (43,6)   inner: (43,63)
N=44    outer: (44,6)   inner: (44,63)
N=45    outer: (45,6)   inner: (45,63)
N=46    outer: (46,6)   inner: (46,63)
N=47    outer: (47,6)   inner: (47,63)
N=48    outer: (48,6)   inner: (48,63)
N=49    outer: (49,6)   inner: (49,63)
N=50    outer: (50,6)   inner: (50,63)
N=51    outer: (51,6)   inner: (51,63)
N=52    outer: (52,6)   inner: (52,63)
N=53    outer: (53,6)   inner: (53,63)
N=54    outer: (54,6)   inner: (54,63)
N=55    outer: (55,6)   inner: (55,63)
N=56    outer: (56,6)   inner: (56,63)
N=57    outer: (57,6)   inner: (57,63)
N=58    outer: (58,6)   inner: (58,63)
N=59    outer: (59,6)   inner: (59,63)
N=60    outer: (60,6)   inner: (60,63)
N=61    outer: (61,6)   inner: (61,63)
N=62    outer: (62,6)   inner: (62,63)
N=63    outer: (63,6)   inner: (63,63)
N=64    outer: (64,6)   inner: (64,63)
N=65    outer: (65,7)   inner: (65,127)
N=66    outer: (66,7)   inner: (66,127)
N=67    outer: (67,7)   inner: (67,127)
N=68    outer: (68,7)   inner: (68,127)
N=69    outer: (69,7)   inner: (69,127)
N=70    outer: (70,7)   inner: (70,127)
N=71    outer: (71,7)   inner: (71,127)
N=72    outer: (72,7)   inner: (72,127)
N=73    outer: (73,7)   inner: (73,127)
N=74    outer: (74,7)   inner: (74,127)
N=75    outer: (75,7)   inner: (75,127)
N=76    outer: (76,7)   inner: (76,127)
N=77    outer: (77,7)   inner: (77,127)
N=78    outer: (78,7)   inner: (78,127)
N=79    outer: (79,7)   inner: (79,127)
N=80    outer: (80,7)   inner: (80,127)
N=81    outer: (81,7)   inner: (81,127)
N=82    outer: (82,7)   inner: (82,127)
N=83    outer: (83,7)   inner: (83,127)
N=84    outer: (84,7)   inner: (84,127)
N=85    outer: (85,7)   inner: (85,127)
N=86    outer: (86,7)   inner: (86,127)
N=87    outer: (87,7)   inner: (87,127)
N=88    outer: (88,7)   inner: (88,127)
N=89    outer: (89,7)   inner: (89,127)
N=90    outer: (90,7)   inner: (90,127)
N=91    outer: (91,7)   inner: (91,127)
N=92    outer: (92,7)   inner: (92,127)
N=93    outer: (93,7)   inner: (93,127)
N=94    outer: (94,7)   inner: (94,127)
N=95    outer: (95,7)   inner: (95,127)
N=96    outer: (96,7)   inner: (96,127)
N=97    outer: (97,7)   inner: (97,127)
N=98    outer: (98,7)   inner: (98,127)
N=99    outer: (99,7)   inner: (99,127)
N=100   outer: (100,7)  inner: (100,127)
```
```N=1     outer: (1,0)    inner: (1,0)
N=2     outer: (2,1)    inner: (2,2)
N=3     outer: (3,2)    inner: (3,6)
N=4     outer: (4,2)    inner: (4,8)
N=5     outer: (5,3)    inner: (5,15)
N=6     outer: (6,3)    inner: (6,18)
N=7     outer: (7,3)    inner: (7,21)
N=8     outer: (8,3)    inner: (8,24)
N=9     outer: (9,4)    inner: (9,36)
N=10    outer: (10,4)   inner: (10,40)
N=11    outer: (11,4)   inner: (11,44)
N=12    outer: (12,4)   inner: (12,48)
N=13    outer: (13,4)   inner: (13,52)
N=14    outer: (14,4)   inner: (14,56)
N=15    outer: (15,4)   inner: (15,60)
N=16    outer: (16,4)   inner: (16,64)
N=17    outer: (17,5)   inner: (17,85)
N=18    outer: (18,5)   inner: (18,90)
N=19    outer: (19,5)   inner: (19,95)
N=20    outer: (20,5)   inner: (20,100)
N=21    outer: (21,5)   inner: (21,105)
N=22    outer: (22,5)   inner: (22,110)
N=23    outer: (23,5)   inner: (23,115)
N=24    outer: (24,5)   inner: (24,120)
N=25    outer: (25,5)   inner: (25,125)
N=26    outer: (26,5)   inner: (26,130)
N=27    outer: (27,5)   inner: (27,135)
N=28    outer: (28,5)   inner: (28,140)
N=29    outer: (29,5)   inner: (29,145)
N=30    outer: (30,5)   inner: (30,150)
N=31    outer: (31,5)   inner: (31,155)
N=32    outer: (32,5)   inner: (32,160)
N=33    outer: (33,6)   inner: (33,198)
N=34    outer: (34,6)   inner: (34,204)
N=35    outer: (35,6)   inner: (35,210)
N=36    outer: (36,6)   inner: (36,216)
N=37    outer: (37,6)   inner: (37,222)
N=38    outer: (38,6)   inner: (38,228)
N=39    outer: (39,6)   inner: (39,234)
N=40    outer: (40,6)   inner: (40,240)
N=41    outer: (41,6)   inner: (41,246)
N=42    outer: (42,6)   inner: (42,252)
N=43    outer: (43,6)   inner: (43,258)
N=44    outer: (44,6)   inner: (44,264)
N=45    outer: (45,6)   inner: (45,270)
N=46    outer: (46,6)   inner: (46,276)
N=47    outer: (47,6)   inner: (47,282)
N=48    outer: (48,6)   inner: (48,288)
N=49    outer: (49,6)   inner: (49,294)
N=50    outer: (50,6)   inner: (50,300)
N=51    outer: (51,6)   inner: (51,306)
N=52    outer: (52,6)   inner: (52,312)
N=53    outer: (53,6)   inner: (53,318)
N=54    outer: (54,6)   inner: (54,324)
N=55    outer: (55,6)   inner: (55,330)
N=56    outer: (56,6)   inner: (56,336)
N=57    outer: (57,6)   inner: (57,342)
N=58    outer: (58,6)   inner: (58,348)
N=59    outer: (59,6)   inner: (59,354)
N=60    outer: (60,6)   inner: (60,360)
N=61    outer: (61,6)   inner: (61,366)
N=62    outer: (62,6)   inner: (62,372)
N=63    outer: (63,6)   inner: (63,378)
N=64    outer: (64,6)   inner: (64,384)
N=65    outer: (65,7)   inner: (65,455)
N=66    outer: (66,7)   inner: (66,462)
N=67    outer: (67,7)   inner: (67,469)
N=68    outer: (68,7)   inner: (68,476)
N=69    outer: (69,7)   inner: (69,483)
N=70    outer: (70,7)   inner: (70,490)
N=71    outer: (71,7)   inner: (71,497)
N=72    outer: (72,7)   inner: (72,504)
N=73    outer: (73,7)   inner: (73,511)
N=74    outer: (74,7)   inner: (74,518)
N=75    outer: (75,7)   inner: (75,525)
N=76    outer: (76,7)   inner: (76,532)
N=77    outer: (77,7)   inner: (77,539)
N=78    outer: (78,7)   inner: (78,546)
N=79    outer: (79,7)   inner: (79,553)
N=80    outer: (80,7)   inner: (80,560)
N=81    outer: (81,7)   inner: (81,567)
N=82    outer: (82,7)   inner: (82,574)
N=83    outer: (83,7)   inner: (83,581)
N=84    outer: (84,7)   inner: (84,588)
N=85    outer: (85,7)   inner: (85,595)
N=86    outer: (86,7)   inner: (86,602)
N=87    outer: (87,7)   inner: (87,609)
N=88    outer: (88,7)   inner: (88,616)
N=89    outer: (89,7)   inner: (89,623)
N=90    outer: (90,7)   inner: (90,630)
N=91    outer: (91,7)   inner: (91,637)
N=92    outer: (92,7)   inner: (92,644)
N=93    outer: (93,7)   inner: (93,651)
N=94    outer: (94,7)   inner: (94,658)
N=95    outer: (95,7)   inner: (95,665)
N=96    outer: (96,7)   inner: (96,672)
N=97    outer: (97,7)   inner: (97,679)
N=98    outer: (98,7)   inner: (98,686)
N=99    outer: (99,7)   inner: (99,693)
N=100   outer: (100,7)  inner: (100,700)
```