完成第九章

Author: jungor

chap07/quick_sort.c

@@ -7,9 +7,6 @@
 #include "../utils.h"
 #include <stdlib.h>
 
-static int partition(int nums[], int begin, int end);
-static int randomized_partition(int nums[], int begin, int end);
-
 int partition(int nums[], int begin, int end) {
     int small_top = begin;
     int key = nums[end-1];

chap07/quick_sort.h

@@ -1,6 +1,8 @@
 #ifndef QUICK_SORT_H
 #define QUICK_SORT_H
 
+int partition(int nums[], int begin, int end);
+int randomized_partition(int nums[], int begin, int end);
 void randomized_quick_sort(int nums[], int begin, int end);
 void quick_sort(int nums[], int begin, int end);
 

chap09/README.md

@@ -0,0 +1 @@
+# 第九章 中位数和顺序统计量

chap09/order_statistic.c

@@ -0,0 +1,113 @@
+/**
+ * order_statistic.c
+ * 顺序统计量
+ */
+
+#include "order_statistic.h"
+#include "../chap02/insertion_sort.h"
+#include "../chap07/quick_sort.h"
+#include "../utils.h"
+#include <stdlib.h>
+
+int minimum(int nums[], int len) {
+    int min = nums[0];
+    for (int i = 1; i < len; i++) {
+        if (nums[i] < min) {
+            min = nums[i];
+        }
+    }
+    return min;
+}
+
+int maximum(int nums[], int len) {
+    int max = nums[0];
+    for (int i = 1; i < len; i++) {
+        if (nums[i] > max) {
+            max = nums[i];
+        }
+    }
+    return max;
+}
+
+/**
+ * 返回第i小的元素。最小的是第0小
+ * 平均O(n)
+ */
+int randomized_select(int nums[], int begin, int end, int i) {
+    int len = end - begin;
+    if (len == 1) {
+        return nums[begin];
+    }
+    int q = randomized_partition(nums, begin, end);
+    int left_len = q - begin;
+    if (i == left_len) {
+        return nums[q];
+    } else if (i < left_len) {
+        return randomized_select(nums, begin, q, i);
+    } else {
+        return randomized_select(nums, q+1, end, i-left_len-1);
+    }
+}
+/**
+ * 将数组5个一组进行分组，找出每组的中位数，返回这些中位数的中位数的下标
+ */
+int median_of_medians(int nums[], int begin, int end) {
+    int len = end - begin;
+    int parts_count = len / 5;
+    int last_part_len = len % 5;
+    int part[5] = {0};
+    if (last_part_len > 0) {
+        parts_count++;
+    }
+    int *medians = malloc(parts_count * sizeof(int));
+    for (int i = 0; i < parts_count; i++) {
+        for (int j = 0; j < 5; j++) {
+            part[j] = nums[i*5+j];
+        }
+        int part_len = 5;
+        if (i > len / 5) {
+            part_len = last_part_len;
+        }
+        insertion_sort(part, part_len);
+        medians[i] = part[part_len/2];
+    }
+    int mm = linear_select(medians, 0, parts_count, parts_count/2);
+    free(medians);
+    return mm;
+}
+
+/**
+ * 以pivoit作为主元对数组进行partition。返回partition之后主元后的位置
+ */
+int specified_partition(int nums[], int begin, int end, int pivot) {
+    int pivot_index = begin;
+    for (; pivot_index < end; pivot_index++) {
+        if (nums[pivot_index] == pivot) {
+            break;
+        }
+    }
+    swap(nums, end-1, pivot_index);
+    return partition(nums, begin, end);
+}
+
+/**
+ * 最差O(n)， 假设数组的数都是互异的
+ */
+int linear_select(int nums[], int begin, int end, int i) {
+    int len = end - begin;
+    if (len == 1) {
+        return nums[begin];
+    }
+    // index of median_of_medians
+    int imm = median_of_medians(nums, begin, end);
+    int q = specified_partition(nums, begin, end, imm);
+    int left_len = q - begin;
+    if (i == left_len) {
+        return nums[q];
+    } else if (i < left_len) {
+        return linear_select(nums, begin, q, i);
+    } else {
+        return linear_select(nums, q+1, end, i-left_len-1);
+    }
+
+}

chap09/order_statistic.h

@@ -0,0 +1,9 @@
+#ifndef ORDER_STATISTIC_H
+#define ORDER_STATISTIC_H
+
+int minimum(int nums[], int len);
+int maximum(int nums[], int len);
+int linear_select(int nums[], int begin, int end, int r);
+int randomized_select(int nums[], int begin, int end, int r);
+
+#endif

main.c

@@ -6,6 +6,8 @@
 #include "chap07/quick_sort.h"
 #include "chap08/counting_sort.h"
 #include "chap08/radix_sort.h"
+#include "chap09/order_statistic.h"
+#include "chap15/cut_rod.h"
 #include <stdio.h>
 #include <stdlib.h>
 #include <time.h>
@@ -14,19 +16,23 @@ int main() {
     srand(time(NULL));
     //int nums[] = {13,-3,-25,20,-3,-16,-23,18,20,-7,12,-5,-22,15,-4,7};
     //int nums[10] = {1, 0, 4, 3, 7, 6, 5, 2, 9, 8};
-    //int nums[100] = {
-    //    71, 57, 79, 0, 60, 56, 89, 92, 87, 18, 43, 53, 86, 26, 15, 51, 73,
-    //    65, 41, 42, 25, 62, 49, 28, 70, 78, 5, 85, 22, 69, 6, 93, 37, 4, 40,
-    //    38, 77, 64, 76, 63, 94, 33, 21, 29, 35, 11, 12, 97, 48, 7, 17, 91, 
-    //    99, 8, 44, 24, 39, 83, 3, 52, 90, 95, 2, 10, 58, 88, 27, 14, 75,
-    //    98, 66, 9, 68, 67, 55, 50, 16, 45, 59, 20, 54, 72, 32, 19, 84, 47,
-    //    1, 80, 13, 36, 34, 96, 81, 31, 46, 30, 61, 23, 74, 82
-    //};
-    int nums[] = {49, 26, 64, 97, 59, 62, 76, 12, 76, 20, 5, 66, 60, 0, 28, 59, 9, 43, 5, 44, 27, 80, 80, 27, 10, 10, 14, 86, 7, 37, 39, 12, 27, 40, 46, 96, 93, 38, 11, 27, 56, 6, 75, 85, 12, 50, 49, 75, 63, 12, 11, 71, 28, 38, 0, 53, 96, 2, 99, 58, 85, 81, 88, 60, 73, 15, 86, 72, 63, 58, 47, 28, 59, 96, 62, 86, 73, 92, 50, 46, 60, 2, 23, 8, 42, 5, 11, 63, 60, 14, 50, 72, 28, 48, 82, 17, 15, 22, 68, 29};
-    print_array(nums, 100);
-    radix_sort(nums, 100);
+    int nums[100] = {
+        71, 57, 79, 0, 60, 56, 89, 92, 87, 18, 43, 53, 86, 26, 15, 51, 73,
+        65, 41, 42, 25, 62, 49, 28, 70, 78, 5, 85, 22, 69, 6, 93, 37, 4, 40,
+        38, 77, 64, 76, 63, 94, 33, 21, 29, 35, 11, 12, 97, 48, 7, 17, 91, 
+        99, 8, 44, 24, 39, 83, 3, 52, 90, 95, 2, 10, 58, 88, 27, 14, 75,
+        98, 66, 9, 68, 67, 55, 50, 16, 45, 59, 20, 54, 72, 32, 19, 84, 47,
+        1, 80, 13, 36, 34, 96, 81, 31, 46, 30, 61, 23, 74, 82
+    };
+    // int nums[] = {49, 26, 64, 97, 59, 62, 76, 12, 76, 20, 5, 66, 60, 0, 28, 59, 9, 43, 5, 44, 27, 80, 80, 27, 10, 10, 14, 86, 7, 37, 39, 12, 27, 40, 46, 96, 93, 38, 11, 27, 56, 6, 75, 85, 12, 50, 49, 75, 63, 12, 11, 71, 28, 38, 0, 53, 96, 2, 99, 58, 85, 81, 88, 60, 73, 15, 86, 72, 63, 58, 47, 28, 59, 96, 62, 86, 73, 92, 50, 46, 60, 2, 23, 8, 42, 5, 11, 63, 60, 14, 50, 72, 28, 48, 82, 17, 15, 22, 68, 29};
+    int price_table[] = {0,1,5,8,9,10,17,17,20,24,30};
+    //print_array(nums, 100);
+    //int s = linear_select(nums, 0, 100, 10);
+    //radix_sort(nums, 100);
     // subarr sa = maximum_subarray(nums, 0, 4);
-    print_array(nums, 100);
+    //print_array(nums, 100);
+    int s = memoized_cut_rod(price_table, 10);
+    printf("%d\n", s);
     //printf("left: %d, right: %d, sum: %d\n", sa.left, sa.right, sa.sum);
     return 0;
 }