## Assignment 2 : Solution

### Exercise 1

```#include <stdio.h>
#include <math.h>

#define LIMIT 1000000

int main ()
{
double sum = 0, logn;
int n;

for (n = 1; n <= LIMIT; n++) {
sum += 1.0 / (double)(n);
if (n % 10000 == 0) {
logn = log(n);
printf("n = %7d, H_n = %12.9lf, ln n = %12.9lf, H_n - ln n = %12.9lf\n",
n, sum, logn, sum - logn);
}
}
}
```

### Sample output

```n =   10000, H_n =  9.787606036, ln n =  9.210340372, H_n - ln n =  0.577265664
n =   20000, H_n = 10.480728217, ln n =  9.903487553, H_n - ln n =  0.577240665
n =   30000, H_n = 10.886184992, ln n = 10.308952661, H_n - ln n =  0.577232331
n =   40000, H_n = 11.173862898, ln n = 10.596634733, H_n - ln n =  0.577228165
n =   50000, H_n = 11.397003949, ln n = 10.819778284, H_n - ln n =  0.577225665
n =   60000, H_n = 11.579323839, ln n = 11.002099841, H_n - ln n =  0.577223998
n =   70000, H_n = 11.733473329, ln n = 11.156250521, H_n - ln n =  0.577222808
n =   80000, H_n = 11.867003829, ln n = 11.289781914, H_n - ln n =  0.577221915
n =   90000, H_n = 11.984786170, ln n = 11.407564949, H_n - ln n =  0.577221220
n =  100000, H_n = 12.090146130, ln n = 11.512925465, H_n - ln n =  0.577220665
n =  110000, H_n = 12.185455855, ln n = 11.608235645, H_n - ln n =  0.577220210
n =  120000, H_n = 12.272466853, ln n = 11.695247022, H_n - ln n =  0.577219832
n =  130000, H_n = 12.352509240, ln n = 11.775289729, H_n - ln n =  0.577219511
n =  140000, H_n = 12.426616938, ln n = 11.849397702, H_n - ln n =  0.577219236
n =  150000, H_n = 12.495609571, ln n = 11.918390573, H_n - ln n =  0.577218998
n =  160000, H_n = 12.560147884, ln n = 11.982929094, H_n - ln n =  0.577218790
n =  170000, H_n = 12.620772322, ln n = 12.043553716, H_n - ln n =  0.577218606
n =  180000, H_n = 12.677930573, ln n = 12.100712130, H_n - ln n =  0.577218443
n =  190000, H_n = 12.731997648, ln n = 12.154779351, H_n - ln n =  0.577218296
n =  200000, H_n = 12.783290810, ln n = 12.206072646, H_n - ln n =  0.577218165
n =  210000, H_n = 12.832080856, ln n = 12.254862810, H_n - ln n =  0.577218046
n =  220000, H_n = 12.878600763, ln n = 12.301382825, H_n - ln n =  0.577217938
n =  230000, H_n = 12.923052427, ln n = 12.345834588, H_n - ln n =  0.577217839
n =  240000, H_n = 12.965611951, ln n = 12.388394202, H_n - ln n =  0.577217748
n =  250000, H_n = 13.006433862, ln n = 12.429216197, H_n - ln n =  0.577217665
n =  260000, H_n = 13.045654498, ln n = 12.468436910, H_n - ln n =  0.577217588
n =  270000, H_n = 13.083394755, ln n = 12.506177238, H_n - ln n =  0.577217517
n =  280000, H_n = 13.119762333, ln n = 12.542544882, H_n - ln n =  0.577217451
n =  290000, H_n = 13.154853591, ln n = 12.577636202, H_n - ln n =  0.577217389
n =  300000, H_n = 13.188755085, ln n = 12.611537754, H_n - ln n =  0.577217332
n =  310000, H_n = 13.221544854, ln n = 12.644327576, H_n - ln n =  0.577217278
n =  320000, H_n = 13.253293502, ln n = 12.676076275, H_n - ln n =  0.577217227
n =  330000, H_n = 13.284065113, ln n = 12.706847933, H_n - ln n =  0.577217180
n =  340000, H_n = 13.313918032, ln n = 12.736700897, H_n - ln n =  0.577217135
n =  350000, H_n = 13.342905527, ln n = 12.765688433, H_n - ln n =  0.577217093
n =  360000, H_n = 13.371076364, ln n = 12.793859310, H_n - ln n =  0.577217054
n =  370000, H_n = 13.398475301, ln n = 12.821258285, H_n - ln n =  0.577217016
n =  380000, H_n = 13.425143512, ln n = 12.847926532, H_n - ln n =  0.577216981
n =  390000, H_n = 13.451118965, ln n = 12.873902018, H_n - ln n =  0.577216947
n =  400000, H_n = 13.476436741, ln n = 12.899219826, H_n - ln n =  0.577216915
n =  410000, H_n = 13.501129323, ln n = 12.923912439, H_n - ln n =  0.577216884
n =  420000, H_n = 13.525226846, ln n = 12.948009990, H_n - ln n =  0.577216855
n =  430000, H_n = 13.548757315, ln n = 12.971540488, H_n - ln n =  0.577216828
n =  440000, H_n = 13.571746807, ln n = 12.994530006, H_n - ln n =  0.577216801
n =  450000, H_n = 13.594219638, ln n = 13.017002862, H_n - ln n =  0.577216776
n =  460000, H_n = 13.616198520, ln n = 13.038981768, H_n - ln n =  0.577216752
n =  470000, H_n = 13.637704702, ln n = 13.060487974, H_n - ln n =  0.577216729
n =  480000, H_n = 13.658758089, ln n = 13.081541383, H_n - ln n =  0.577216707
n =  490000, H_n = 13.679377355, ln n = 13.102160670, H_n - ln n =  0.577216685
n =  500000, H_n = 13.699580042, ln n = 13.122363377, H_n - ln n =  0.577216665
n =  510000, H_n = 13.719382650, ln n = 13.142166005, H_n - ln n =  0.577216645
n =  520000, H_n = 13.738800717, ln n = 13.161584091, H_n - ln n =  0.577216626
n =  530000, H_n = 13.757848894, ln n = 13.180632286, H_n - ln n =  0.577216608
n =  540000, H_n = 13.776541009, ln n = 13.199324419, H_n - ln n =  0.577216591
n =  550000, H_n = 13.794890131, ln n = 13.217673557, H_n - ln n =  0.577216574
n =  560000, H_n = 13.812908620, ln n = 13.235692063, H_n - ln n =  0.577216558
n =  570000, H_n = 13.830608182, ln n = 13.253391640, H_n - ln n =  0.577216542
n =  580000, H_n = 13.847999909, ln n = 13.270783383, H_n - ln n =  0.577216527
n =  590000, H_n = 13.865094328, ln n = 13.287877816, H_n - ln n =  0.577216512
n =  600000, H_n = 13.881901432, ln n = 13.304684934, H_n - ln n =  0.577216498
n =  610000, H_n = 13.898430721, ln n = 13.321214236, H_n - ln n =  0.577216485
n =  620000, H_n = 13.914691228, ln n = 13.337474757, H_n - ln n =  0.577216471
n =  630000, H_n = 13.930691557, ln n = 13.353475098, H_n - ln n =  0.577216459
n =  640000, H_n = 13.946439901, ln n = 13.369223455, H_n - ln n =  0.577216446
n =  650000, H_n = 13.961944076, ln n = 13.384727642, H_n - ln n =  0.577216434
n =  660000, H_n = 13.977211536, ln n = 13.399995114, H_n - ln n =  0.577216422
n =  670000, H_n = 13.992249403, ln n = 13.415032991, H_n - ln n =  0.577216411
n =  680000, H_n = 14.007064477, ln n = 13.429848077, H_n - ln n =  0.577216400
n =  690000, H_n = 14.021663266, ln n = 13.444446877, H_n - ln n =  0.577216390
n =  700000, H_n = 14.036051993, ln n = 13.458835614, H_n - ln n =  0.577216379
n =  710000, H_n = 14.050236618, ln n = 13.473020249, H_n - ln n =  0.577216369
n =  720000, H_n = 14.064222850, ln n = 13.487006491, H_n - ln n =  0.577216359
n =  730000, H_n = 14.078016163, ln n = 13.500799813, H_n - ln n =  0.577216350
n =  740000, H_n = 14.091621806, ln n = 13.514405465, H_n - ln n =  0.577216341
n =  750000, H_n = 14.105044817, ln n = 13.527828486, H_n - ln n =  0.577216332
n =  760000, H_n = 14.118290035, ln n = 13.541073712, H_n - ln n =  0.577216323
n =  770000, H_n = 14.131362108, ln n = 13.554145794, H_n - ln n =  0.577216314
n =  780000, H_n = 14.144265505, ln n = 13.567049199, H_n - ln n =  0.577216306
n =  790000, H_n = 14.157004522, ln n = 13.579788224, H_n - ln n =  0.577216298
n =  800000, H_n = 14.169583297, ln n = 13.592367007, H_n - ln n =  0.577216290
n =  810000, H_n = 14.182005809, ln n = 13.604789527, H_n - ln n =  0.577216282
n =  820000, H_n = 14.194275894, ln n = 13.617059619, H_n - ln n =  0.577216275
n =  830000, H_n = 14.206397247, ln n = 13.629180980, H_n - ln n =  0.577216267
n =  840000, H_n = 14.218373431, ln n = 13.641157171, H_n - ln n =  0.577216260
n =  850000, H_n = 14.230207882, ln n = 13.652991628, H_n - ln n =  0.577216253
n =  860000, H_n = 14.241903915, ln n = 13.664687668, H_n - ln n =  0.577216246
n =  870000, H_n = 14.253464730, ln n = 13.676248491, H_n - ln n =  0.577216240
n =  880000, H_n = 14.264893420, ln n = 13.687677186, H_n - ln n =  0.577216233
n =  890000, H_n = 14.276192968, ln n = 13.698976742, H_n - ln n =  0.577216227
n =  900000, H_n = 14.287366263, ln n = 13.710150042, H_n - ln n =  0.577216220
n =  910000, H_n = 14.298416093, ln n = 13.721199878, H_n - ln n =  0.577216214
n =  920000, H_n = 14.309345157, ln n = 13.732128949, H_n - ln n =  0.577216208
n =  930000, H_n = 14.320156068, ln n = 13.742939865, H_n - ln n =  0.577216203
n =  940000, H_n = 14.330851351, ln n = 13.753635154, H_n - ln n =  0.577216197
n =  950000, H_n = 14.341433455, ln n = 13.764217264, H_n - ln n =  0.577216191
n =  960000, H_n = 14.351904749, ln n = 13.774688563, H_n - ln n =  0.577216186
n =  970000, H_n = 14.362267531, ln n = 13.785051350, H_n - ln n =  0.577216180
n =  980000, H_n = 14.372524026, ln n = 13.795307851, H_n - ln n =  0.577216175
n =  990000, H_n = 14.382676392, ln n = 13.805460222, H_n - ln n =  0.577216170
n = 1000000, H_n = 14.392726723, ln n = 13.815510558, H_n - ln n =  0.577216165
```

### Exercise 2

```#include <stdio.h>
#include <stdlib.h>

int main ()
{
int a, i, max, min;

srand((unsigned int)time(NULL));

i = 1;
while (1) {
a = (rand() % 105) - 5;
printf("Iteration %3d: new entry = %3d, ", i, a);
if (a < 0) { printf("...quitting...\n\n\n"); exit(0); }
if (i == 1) max = min = a;
else {
if (a > max) max = a;
if (a < min) min = a;
}
printf("max = %3d, min = %3d\n", max, min);
++i;
}
}
```

### Sample output

```Iteration   1: new entry =  81, max =  81, min =  81
Iteration   2: new entry =  89, max =  89, min =  81
Iteration   3: new entry =  45, max =  89, min =  45
Iteration   4: new entry =   2, max =  89, min =   2
Iteration   5: new entry =  18, max =  89, min =   2
Iteration   6: new entry =   4, max =  89, min =   2
Iteration   7: new entry =   2, max =  89, min =   2
Iteration   8: new entry =  77, max =  89, min =   2
Iteration   9: new entry =  82, max =  89, min =   2
Iteration  10: new entry =  47, max =  89, min =   2
Iteration  11: new entry =  80, max =  89, min =   2
Iteration  12: new entry =  63, max =  89, min =   2
Iteration  13: new entry =   1, max =  89, min =   1
Iteration  14: new entry =  53, max =  89, min =   1
Iteration  15: new entry =   3, max =  89, min =   1
Iteration  16: new entry =  64, max =  89, min =   1
Iteration  17: new entry =  59, max =  89, min =   1
Iteration  18: new entry =  38, max =  89, min =   1
Iteration  19: new entry =  -2, ...quitting...

Iteration   1: new entry =  64, max =  64, min =  64
Iteration   2: new entry =  82, max =  82, min =  64
Iteration   3: new entry =  98, max =  98, min =  64
Iteration   4: new entry =  -1, ...quitting...

Iteration   1: new entry =   0, max =   0, min =   0
Iteration   2: new entry =  48, max =  48, min =   0
Iteration   3: new entry =  48, max =  48, min =   0
Iteration   4: new entry =   3, max =  48, min =   0
Iteration   5: new entry =  43, max =  48, min =   0
Iteration   6: new entry =  60, max =  60, min =   0
Iteration   7: new entry =  29, max =  60, min =   0
Iteration   8: new entry =  79, max =  79, min =   0
Iteration   9: new entry =  82, max =  82, min =   0
Iteration  10: new entry =  55, max =  82, min =   0
Iteration  11: new entry =  59, max =  82, min =   0
Iteration  12: new entry =  49, max =  82, min =   0
Iteration  13: new entry =  75, max =  82, min =   0
Iteration  14: new entry =  33, max =  82, min =   0
Iteration  15: new entry =  82, max =  82, min =   0
Iteration  16: new entry =  53, max =  82, min =   0
Iteration  17: new entry =  91, max =  91, min =   0
Iteration  18: new entry =  93, max =  93, min =   0
Iteration  19: new entry =  56, max =  93, min =   0
Iteration  20: new entry =  94, max =  94, min =   0
Iteration  21: new entry =   1, max =  94, min =   0
Iteration  22: new entry =  32, max =  94, min =   0
Iteration  23: new entry =  83, max =  94, min =   0
Iteration  24: new entry =  63, max =  94, min =   0
Iteration  25: new entry =  79, max =  94, min =   0
Iteration  26: new entry =  -2, ...quitting...

Iteration   1: new entry =  55, max =  55, min =  55
Iteration   2: new entry =   5, max =  55, min =   5
Iteration   3: new entry =  14, max =  55, min =   5
Iteration   4: new entry =  74, max =  74, min =   5
Iteration   5: new entry =  73, max =  74, min =   5
Iteration   6: new entry =  79, max =  79, min =   5
Iteration   7: new entry =  41, max =  79, min =   5
Iteration   8: new entry =  79, max =  79, min =   5
Iteration   9: new entry =  51, max =  79, min =   5
Iteration  10: new entry =  14, max =  79, min =   5
Iteration  11: new entry =  90, max =  90, min =   5
Iteration  12: new entry =  37, max =  90, min =   5
Iteration  13: new entry =  83, max =  90, min =   5
Iteration  14: new entry =  71, max =  90, min =   5
Iteration  15: new entry =  84, max =  90, min =   5
Iteration  16: new entry =  32, max =  90, min =   5
Iteration  17: new entry =  16, max =  90, min =   5
Iteration  18: new entry =  89, max =  90, min =   5
Iteration  19: new entry =  41, max =  90, min =   5
Iteration  20: new entry =  38, max =  90, min =   5
Iteration  21: new entry =  48, max =  90, min =   5
Iteration  22: new entry =   9, max =  90, min =   5
Iteration  23: new entry =  31, max =  90, min =   5
Iteration  24: new entry =  96, max =  96, min =   5
Iteration  25: new entry =  66, max =  96, min =   5
Iteration  26: new entry =  17, max =  96, min =   5
Iteration  27: new entry =  17, max =  96, min =   5
Iteration  28: new entry =  53, max =  96, min =   5
Iteration  29: new entry =  53, max =  96, min =   5
Iteration  30: new entry =  -2, ...quitting...

Iteration   1: new entry =  14, max =  14, min =  14
Iteration   2: new entry =  19, max =  19, min =  14
Iteration   3: new entry =  74, max =  74, min =  14
Iteration   4: new entry =   8, max =  74, min =   8
Iteration   5: new entry =  -1, ...quitting...
```