문제 설명
파일로부터 n개의 실수 데이터를 1차원 배열로 입력받아 오름차순으로 정렬하는 3가지 알고리즘(삽입정렬, 퀵정렬, 힙정렬)들을 구현한 후 정렬 결과와 원소의 실제 실행 시간(또는 비교 횟수)를 구해서 화면에 출력한다.
삽입 정렬
정렬되어 있는 앞 부분에 새로운 레코드를 올바른 위치에 삽입하는 과정을 반복하는 정렬이다. 최선의 경우 비교 횟수는 n-1번이며 최악의 경우는 n(n-1)/2번으로 오더가 n^2이다.
퀵 정렬
평균적으로 가장 빠른 정렬 방법으로 분할정복 기법을 이용한다. 축값(pivot)을 중심으로 하나의 리스트를 축값보다 작은 부분리스트와 축값보다 큰 부분리스트로 분할하고, 각 부분리스트를 다시 퀵정렬하는 재귀호출 과정을 통해 정렬한다. 최선의 경우 패스 수는 nlog2n이며, 각 패스 안에서의 비교횟수는 n으로 총 비교횟수는 nlog2n이다. 극도로 불균등하게 부분리스트로 분할되는 최악의 경우 패스 수는 n이며, 각 패스 안에서의 비교횟수도 n으로 총 비교 횟수는 n^2이 된다.
힙 정렬
힙을 이용하여 정렬한다. 먼저 정렬해야 할 n개의 원소들을 최대 힙으로 구성한 후 루트(최대값)과 가장 마지막 원소를 교환한 다음, 마지막 원소(최대값)을 제외하고 downheap을 반복적으로 수행하며 정렬한다. n개의 원소를 최대 힙으로 구성하기 위해서는 o(n)만큼의 시간이 소요되고, downheap 연산을 n-1번 수행해야 하므로의 시간이 걸린다. 따라서 전체적으로 O(nlogn2) 시간이 걸린다.
코드
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#define SWAP(a, b, c){c = a; a = b; b = c;} //a와 b의 데이터를 바꿈
void insert(int n, double list[], int *pcom) { // 삽입정렬
int i, j; //왼쪽 인덱스는 정렬이 안되고 오른쪽 인덱스는 정렬됨
double key;
for (i = 2; i <= n; i++) {
key = list[i]; //정렬안된 왼쪽 인덱스의 가장 첫 원소를 key로 정함
for (j = i - 1; (*pcom)++ >= 0&& j >= 1 && list[j] > key; j--) { //정렬된 오른쪽 원소들과 비교하며
list[j + 1] = list[j]; //key값의 올바른 위치 정함
}
list[j + 1] = key;
}
}
int partition(double list[], int **ppcom, int left, int right) { //퀵정렬
double temp = 0;
int low = left;
int high = right + 1;
double pivot = list[left]; //가장 왼쪽 데이터 pivot으로 정한 후
do {
do
low++;
while ((**ppcom)++ >= 0 && (low <= right) && (list[low] < pivot)); //왼쪽에서 pivot보다 큰 수 찾음
do
high--;
while ((**ppcom)++ >= 0 && (high >= left) && (list[high] > pivot)); //오른쪽에서 pivot보다 작은 수 찾아서
if (low < high) SWAP(list[low], list[high], temp); //바꿈
} while (low < high); //low가 high보다 작을 때 반복하며
SWAP(list[left], list[high], temp); //마지막으로 high와 pivot값 바꿔서 pivot을 올바른 위치에 정렬함
return high; //정렬된 pivot index 반환함
}
void quick(double list[], int *pcom, int left, int right) { //퀵정렬
if (left < right) {
int q = partition(list, &pcom, left, right); //pivot 정렬 후 위치 반환 받음
quick(list, pcom, left, (q - 1)); //pivot의 왼쪽 list에 대해 다시 퀵정렬
quick(list, pcom, (q + 1), right); //pivot의 오른쪽 list에 대해 다시 퀵정렬
}
}
void adjust(double list[], int root, int n, int **ppcom) { //힙정렬
double rootkey = list[root]; //rootkey설정
int child = 2 * root; //root의 왼쪽 자식 노드
while (child <= n) { //root가 오른쪽 자식 노드도 있으면
if ((child < n) && ((**ppcom)++ >= 0) && (list[child] < list[(child + 1)])) //왼쪽자식노드와 오른쪽 자식 노드 중
child++; //더 큰 값 선택
if (((**ppcom)++ >= 0) && (rootkey > list[child])) break; //자식 노드가 rootkey보다 크다면
else {
list[(child / 2)] = list[child]; //자식노드의 데이터 부모노드에 저장
child = 2 * child; //다음 자식노드와 rootkey 다시 비교
}
}
list[(child / 2)] = rootkey; //rootkey 올바른 자리에 정렬
}
void heap(double list[], int n, int *pcom) { //힙정렬
int i;
double temp = 0;
for (i = (n / 2); i >= 1; i--) //작은 heap부터
adjust(list, i, n, &pcom); //최대힙 정렬을 함
for (i = (n - 1); i >= 1; i--) {
SWAP(list[1], list[i + 1], temp); //최대값(첫 인덱스)을 정렬 안 된 부분의 가장 끝 데이터와 바꾸고
adjust(list, 1, i, &pcom); //첫 인덱스로 올라온 데이터를 downheap으로 정렬함
}
}
int main(void) {
FILE *fp = NULL; //파일 포인터 변수
int n, com_i = 0, com_q = 0, com_h = 0; // 비교 횟수
double *list_i = NULL; //insert 정렬 데이터 담을 list
double *list_q = NULL; //quick 정렬 데이터 담을 list
double *list_h = NULL; //heap 정렬 데이터 담을 list
double d = 0;
char filename[] = "r_data3.txt"; // 파일 열고
fp = fopen("c://r_data3.txt", "r");
fscanf(fp, "%d", &n); //첫 데이터(데이터 수) 입력 받은 후
list_i = (double*)malloc(sizeof(double)*(n + 1)); //데이터수 + 1 만큼 배열 생성
list_q = (double*)malloc(sizeof(double)*(n + 1));
list_h = (double*)malloc(sizeof(double)*(n + 1));
for (int i = 1; i <= n; i++) { //인덱스의 1번부터 데이터 수 만큼
fscanf(fp, "%lf", &d); //데이터 저장
list_i[i] = d;
list_q[i] = d;
list_h[i] = d;
}
insert(n, list_i, &com_i); //삽입정렬
quick(list_q, &com_q, 1, n);
heap(list_h, n, &com_h);
fclose(fp); //파일 닫고
printf("========== 삽입정렬 ==========\n"); //정렬된 데이터 출력
printf("입력 파일 = %s (n = %d)\n", filename, n);
printf("정렬 결과 = ");
for (int i = 1; i <= 10; i++) {
printf("%f ", list_i[i]);
}
printf("\n\t ...\n\t ");
for (int j = n - 9; j <= n; j++) {
printf("%f ", list_i[j]);
}
printf("\n비교 횟수 = %d\n", com_i);
printf("\n========== 퀵정렬 ==========\n"); //정렬된 데이터 출력
printf("입력 파일 = %s (n = %d)\n", filename, n);
printf("정렬 결과 = ");
for (int i = 1; i <= 10; i++) {
printf("%f ", list_q[i]);
}
printf("\n\t ...\n\t ");
for (int j = n - 9; j <= n; j++) {
printf("%f ", list_q[j]);
}
printf("\n비교 횟수 = %d\n", com_q);
printf("\n========== 힙정렬 ==========\n"); //정렬된 데이터 출력
printf("입력 파일 = %s (n = %d)\n", filename, n);
printf("정렬 결과 = ");
for (int i = 1; i <= 10; i++) {
printf("%f ", list_h[i]);
}
printf("\n\t ...\n\t ");
for (int j = n - 9; j <= n; j++) {
printf("%f ", list_h[j]);
}
printf("\n비교 횟수 = %d\n", com_h);
free(list_i); //할당받은 데이터 free시킴
free(list_q);
free(list_h);
}Dataset(d_data1.txt)
1000
34984.1379 34946.5054 34828.1038 34769.0368 34761.348 34749.3474 34731.5817 34711.6811 34630.7671 34625.2033 34548.8834 34538.6211 34530.0604 34494.6243 34477.5488 34457.0416 34450.2868 34328.7218 34276.9021 34266.0823 34190.3322 34179.3518 34124.548 34114.8123 34083.3726 34018.5786 34014.9219 33910.6842 33881.1894 33798.7756 33678.6101 33676.8022 33662.9995 33659.422 33629.1515 33598.6154 33573.6905 33555.8566 33546.5415 33482.6286 33472.5346 33434.1639 33403.9013 33388.4054 33369.3465 33365.5374 33300.0686 33242.6963 33217.5132 33196.0854 33184.8223 33169.7543 33095.6787 33035.4237 32972.0933 32909.5417 32869.2346 32866.5123 32850.8855 32833.5221 32829.544 32748.6088 32708.9312 32701.2116 32659.3833 32654.1624 32645.4747 32556.1553 32555.296 32544.5923 32522.8832 32521.7863 32503.2335 32495.0817 32493.9804 32439.6849 32415.7406 32406.4163 32359.8682 32355.099 32333.515 32289.1398 32193.9461 32188.5866 32177.5961 32175.27 32131.5655 32124.9847 32082.2196 31992.7585 31984.914 31979.7709 31959.0078 31953.0927 31937.7433 31919.3631 31845.5683 31781.0325 31780.0498 31776.1751 31751.6616 31719.8792 31654.3188 31628.174 31608.9936 31500.7565 31429.1147 31381.2457 31323.7399 31322.6232 31219.2117 31169.7116 31068.6522 31043.6769 31026.0139 31023.3791 30978.211 30962.7726 30902.5125 30873.9991 30854.5627 30822.4911 30815.1398 30761.1919 30713.0767 30532.1665 30450.2796 30428.4128 30416.599 30409.8989 30344.7738 30336.4372 30327.7272 30321.9786 30315.7103 30277.1407 30158.228 30147.7367 30124.4044 30123.4164 29997.3033 29993.4296 29981.9295 29965.4695 29920.3926 29859.8419 29812.4622 29778.1756 29631.7497 29597.4946 29552.0487 29488.1655 29481.6219 29478.6534 29465.4852 29379.5436 29371.8821 29318.8163 29232.4432 29227.8242 29073.8916 29004.1813 28955.4252 28906.0191 28891.8091 28880.8897 28838.4435 28737.8177 28707.5025 28643.0224 28629.4522 28624.8643 28622.7034 28617.7527 28506.7816 28475.7383 28432.9103 28391.6075 28349.8145 28324.8449 28296.4104 28272.4787 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5770.0677 5716.5942 5624.9265 5613.5099 5607.6935 5562.6882 5499.6871 5416.5397 5396.2693 5388.8209 5320.8306 5304.7853 5277.8265 5237.892 5210.1878 5167.9469 5154.9334 5114.0936 5113.097 5108.0555 4917.9084 4841.9678 4732.6668 4721.6548 4674.2212 4667.8899 4641.8588 4634.016 4606.6283 4598.0555 4583.7923 4452.0076 4428.0028 4413.385 4357.0185 4340.4168 4331.3694 4317.5591 4309.5811 4299.3132 4198.6259 4102.6255 4050.8155 4010.11 3989.3302 3968.2625 3941.2579 3878.5372 3809.0752 3796.0671 3740.6982 3684.8156 3683.7803 3646.3937 3586.7757 3574.1139 3506.9456 3455.4022 3438.126 3424.9734 3418.7374 3388.3328 3309.2303 3289.9317 3285.7208 3138.7396 3067.3402 3017.7611 2935.1141 2901.4291 2894.7528 2888.8607 2876.1115 2847.0395 2809.9441 2784.5064 2692.9016 2639.8655 2584.4883 2473.8532 2467.432 2425.516 2420.4121 2404.3821 2390.7605 2291.7503 2266.1776 2251.2834 2249.4104 2241.848 2235.7242 2172.6065 2143.2725 2073.9734 2059.2494 2040.1964 1992.5206 1967.1822 1934.6877 1926.7469 1923.9722 1918.4894 1902.9401 1822.7693 1793.9098 1683.9921 1629.7067 1628.3793 1595.8989 1576.5063 1547.7709 1528.99 1468.1844 1417.8779 1397.0888 1333.8413 1323.3661 1302.1264 1300.3154 1284.2897 1263.2511 1225.9055 1207.527 1206.8174 1193.9081 1165.2129 1158.4547 1155.6021 1079.1032 1056.6033 1011.2735 994.0313 948.8914 927.5855 868.9127 823.1312 822.2888 817.6334 808.0928 771.8399 745.9508 721.9953 694.7522 661.7128 604.1237 576.6119 568.7607 453.0381 357.6539 341.3964 309.1407 272.7945 247.802 232.1264 231.2615 227.3659 219.5062 209.4667 186.6163 177.1573 174.0658 171.5271 163.8831 158.901 109.6181 68.636
Dataset(a_data1.txt)
1000
40.7425 56.7188 61.2118 66.2228 68.2104 134.378 137.5913 155.8475 194.8303 211.1809 218.9985 240.5506 243.263 273.5229 283.7739 300.4666 347.0022 392.2238 446.7525 450.3512 479.7945 492.8313 541.753 565.2784 569.1443 576.572 584.4611 786.3926 829.0853 844.7691 862.4472 887.0393 911.6595 923.2856 938.2637 957.3679 1007.4219 1078.6965 1090.009 1175.1398 1214.9199 1241.5299 1275.7056 1279.2797 1298.9889 1365.2026 1630.5766 1664.2075 1689.6667 1703.1051 1803.3713 1840.7957 1856.7096 1979.576 1997.317 2043.4296 2070.3664 2083.3648 2110.9853 2166.7557 2238.1031 2247.8258 2248.7245 2280.7912 2304.4963 2314.6652 2337.7178 2372.5835 2390.1483 2460.4608 2468.6169 2491.4905 2499.0563 2504.0063 2601.4552 2690.5757 2734.7753 2773.9639 2783.8544 2797.2174 2869.0072 2942.2555 3041.1722 3059.7192 3113.6914 3239.7127 3265.6934 3286.4986 3334.2388 3464.951 3466.0249 3480.1301 3516.9662 3524.4211 3599.9175 3624.3216 3638.0888 3692.1474 3705.1326 3790.956 3880.9784 3937.3957 4097.8119 4098.5495 4110.9716 4145.2685 4229.9082 4273.7039 4351.5755 4432.7521 4450.9142 4468.4166 4561.0127 4583.9007 4648.2891 4676.5557 4684.4211 4746.7001 4767.6984 4786.393 4798.8073 4871.3004 4910.1708 4936.1119 5146.929 5204.4831 5230.5664 5272.6748 5331.2378 5340.6329 5363.6031 5407.0658 5416.2876 5449.593 5454.8399 5464.516 5561.8342 5621.8769 5622.9906 5680.0411 5715.553 5728.1044 5766.4104 5771.4474 5827.2686 5844.1125 5856.8959 5863.4343 5888.0375 5915.5736 5933.6492 5964.2986 5981.9741 6000.6928 6052.1061 6132.1966 6139.7053 6145.4033 6172.0284 6187.3732 6203.3518 6227.9181 6254.328 6272.5763 6291.7237 6319.3123 6324.3823 6339.7917 6386.2634 6408.9064 6434.856 6435.6308 6457.0047 6498.9851 6523.5413 6525.6286 6566.0222 6569.7375 6621.5923 6648.0331 6651.5266 6756.1299 6790.8083 6808.3157 6831.9237 6870.2176 6906.4173 7032.1466 7046.2422 7075.7092 7090.0985 7108.3446 7135.7308 7143.3531 7149.3871 7267.2458 7272.4332 7275.7293 7290.0457 7307.1556 7311.9236 7346.0846 7415.0005 7477.6627 7547.7029 7557.3829 7618.3563 7626.3022 7636.2043 7665.0135 7722.7313 7779.4271 7788.5589 7865.9181 7892.9003 7908.9671 7909.8626 8016.693 8084.0609 8121.3205 8141.7967 8163.3646 8175.2932 8177.2497 8181.5706 8191.4959 8315.9015 8393.5306 8401.5705 8496.1153 8506.6785 8525.9945 8561.3899 8570.9799 8662.9043 8686.3448 8739.5614 8754.1645 8780.6133 8859.3811 8908.3125 8971.3659 9004.4605 9035.0251 9060.1327 9083.5082 9090.1811 9161.9805 9205.4936 9219.7088 9281.553 9294.1883 9307.9311 9326.9856 9409.2713 9424.0302 9429.4886 9447.4432 9454.5476 9463.3987 9479.7162 9643.4253 9677.6001 9752.1145 9773.8938 9848.1399 9879.3036 9898.3744 9924.4602 9928.1735 9933.1752 9962.7593 10058.7255 10107.371 10169.8685 10247.3613 10271.5601 10292.8233 10306.1045 10315.3849 10427.0495 10464.1049 10480.1484 10501.9832 10583.8096 10586.174 10662.5133 10692.1532 10735.7291 10739.7608 10748.8422 10846.4692 10850.7398 10855.5569 10988.2311 11053.6381 11112.5911 11136.4275 11218.4551 11294.5028 11324.5728 11354.5641 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