《算法导论》学习笔记（1）

引言

所用教材为《算法导论》第三版，下面是前三章中一些算法的代码实现。

插入排序

#define GET_ARRAY_LEN(array) (sizeof(array) / sizeof(array[0]))
#include <stdio.h>

void InsertionSort(int* ary, int len){
    for(int j=1; j<len; j++){
        int key = ary[j];
        int i = j - 1;
        while(i>=0 && ary[i]>key){
            ary[i+1] = ary[i];
            i = i - 1;
        }
        ary[i+1] = key;
    }
}

int main(){
    int ary[] = {4,5,2,4,7,13,42,6,42,34,1,3};
    int len = GET_ARRAY_LEN(ary);
    InsertionSort(ary, len);
    for(int i=0; i<len; i++){
        printf("%d ", ary[i]);
    }
}

冒泡排序

#define GET_ARRAY_LEN(array) (sizeof(array) / sizeof(array[0]))
#include <stdio.h>

void BubbleSort(int* ary, int len){
    for(int j=1; j<len; j++){
        for(int i=j; i>=0; i--){
            if(ary[i-1] > ary[i]){
                int tem = ary[i-1];
                ary[i-1] = ary[i];
                ary[i] = tem;
            }
        }
    }
}

int main(){
    int ary[] = {4,5,2,4,7,13,42,6,42,34,1,3};
    int len = GET_ARRAY_LEN(ary);
    BubbleSort(ary, len);
    for(int i=0; i<len; i++){
        printf("%d ", ary[i]);
    }
}

这个程序有bug，在g++下没问题，在Clang++下就会出现问题，详见关于算法笔记（1）中冒泡排序的bug

归并排序

#define GET_ARRAY_LEN(array) (sizeof(array) / sizeof(array[0]))
#include <stdio.h>
#include <math.h>

void Merge(int* ary, int r, int mid, int p){
    int len1 = mid - p + 1;
    int len2 = r - mid;
    int* temAry1 = new int[len1];
    int* temAry2 = new int[len2];
    for(int i=0; i<len1; i++)
        temAry1[i] = ary[p+i-1];
    for(int i=0; i<len2; i++)
        temAry2[i] = ary[mid+i];

    int i = 0;
    int j = 0;
    int k = p-1;
    while(i < len1 && j < len2){
        if(temAry1[i] <= temAry2[j]){
            ary[k] = temAry1[i];
            i = i + 1;
        }
        else{
            ary[k] = temAry2[j];
            j = j + 1;
        }
        k = k + 1;
    }
    while(i < len1){
        ary[k] = temAry1[i];
        i = i + 1;
        k = k + 1;
    }
    while(j < len2){
        ary[k] = temAry2[j];
        j = j + 1;
        k = k + 1;
    }
}

void MergeSort(int* ary, int r, int p=1){
    if(p<r){
        int mid = floor((r + p) / 2);
        MergeSort(ary, mid, p);
        MergeSort(ary, r, mid+1);
        Merge(ary, r, mid, p);
    }
}

int main(){
    int ary[] = {4,5,2,4,7,13,42,6,42,34,1,3};
    int len = GET_ARRAY_LEN(ary);
    MergeSort(ary, len);
    for(int i=0; i<len; i++){
        printf("%d ", ary[i]);
    }
}

逆序对个数

#define GET_ARRAY_LEN(array) (sizeof(array) / sizeof(array[0]))
#include <stdio.h>
#include <math.h>

int Merge(int* ary, int r, int mid, int p){
    int len1 = mid - p + 1;
    int len2 = r - mid;
    int* temAry1 = new int[len1];
    int* temAry2 = new int[len2];
    for(int i=0; i<len1; i++)
        temAry1[i] = ary[p+i-1];
    for(int i=0; i<len2; i++)
        temAry2[i] = ary[mid+i];

    int i = 0;
    int j = 0;
    int k = p-1;
    int count = 0;
    while(i < len1 && j < len2){
        if(temAry1[i] <= temAry2[j]){
            ary[k] = temAry1[i];
            i = i + 1;
        }
        else{
            ary[k] = temAry2[j];
            j = j + 1;
            count += (len1 - i);
        }
        k = k + 1;
    }
    while(i < len1){
        ary[k] = temAry1[i];
        i = i + 1;
        k = k + 1;
    }
    while(j < len2){
        ary[k] = temAry2[j];
        j = j + 1;
        k = k + 1;
    }
    return count;
}

int CountInversion(int* ary, int r, int p=1){
    if(p<r){
        int mid = floor((r + p) / 2);
        int c = 0;
        c += CountInversion(ary, mid, p);
        c += CountInversion(ary, r, mid+1);
        c += Merge(ary, r, mid, p);
        return c;
    }else
        return 0;
}

int main(){
    int ary[] = {4,5,2,4,7,13,42,6,42,34,1,3};
    int len = GET_ARRAY_LEN(ary);
    printf("Inversion Number: %d", CountInversion(ary, len));
}