算法导论(第三版)Problems2(归并插入排序、数列逆序计算）

讨论内容不说明，仅提供相应的程序。

2.1:归并插入排序θ(nlgn)

void mergeInsertionSort(int a[], int l, int r, int k)

{

    int m;

    if(r-l+1 > k)

    {

        m = (l + r) / 2;

        mergeInsertionSort(a, l, m, k);

        mergeInsertionSort(a, m+1, r, k);

        merge(a, l, m, r);

    }

    else if(l < r)

        insertSort(a, l, r);

}



void insertSort(int a[], int l, int r)

{

    int i, j, key;

    j = l;

    for(i=l+1; i<=r; i++)

        if(a[i] < a[j]) j = i;

    if(j > l)

    {

        key = a[j];

        a[j] = a[l];

        a[l] = key;

    }

    for(i=l+2; i<=r; i++)

    {

        key = a[i];

        for(j=i-1; key<a[j]; j--) a[j+1] = a[j];

        a[j+1] = key;

    }

}



void merge(int a[], int l, int m, int r)

{

    int i, j, k;

    int n1 = m - l + 1;

    int n2 = r - m;

    int lArray[n1+1], rArray[n2+1];

    int max = 1000;



    for(i=0; i<n1; i++) lArray[i] = a[l+i];

    for(i=0; i<n2; i++) rArray[i] = a[m+i+1];

    lArray[n1] = max;

    rArray[n2] = max;

    i = 0;

    j = 0;

    for(k=l; k<=r; k++)

    {

        if(lArray[i] <= rArray[j])

        {

            a[k] = lArray[i];

            ++i;

        }

        else

        {

            a[k] = rArray[j];

            ++j;

        }

    }

}

View Code

2.2:冒泡排序

void bubbleSort(int a[], int n)

{

    int i, j, tmp;



    for(i=0; i<n-1; i++)

        for(j=n-1; j>i; j--)

            if(a[j] < a[j-1])

            {

                tmp = a[j];

                a[j] = a[j-1];

                a[j-1] = tmp;

            }

}

View Code

2.3: 多项式计算方法(θ(n))

int horner(int a[], int x, int n)

{

    int i, sum=a[n-1];

    for(i=n-2; i>=0; i--) sum = a[i] + x * sum;

    return sum;

}



int polynomial(int a[], int x, int n)

{

    int i, xArray[n], sum=0;

    xArray[0] = 1;

    for(i=1; i<n; i++) xArray[i] = x * xArray[i-1];

    for(i=0; i<n; i++) sum = sum + a[i] * xArray[i];

    return sum;

}

View Code

 

2.4：计算数列的逆序θ(nlgn)

int mergeCount(int a[], int l, int r)

{

    int m;

    if(l < r)

    {

        m = (l + r) / 2;

        return mergeCount(a, l, m) + mergeCount(a, m+1, r) + merge(a, l, m, r);

    }

    return 0;

}



int merge(int a[], int l, int m, int r)

{

    int i, j, k, cnt=0;

    int n1 = m - l + 1;

    int n2 = r - m;

    int lArray[n1+1], rArray[n2+1];

    int max =10000;



    for(i=0; i<n1; i++) lArray[i] = a[l+i];

    for(j=0; j<n2; j++) rArray[j] = a[m+1+j];

    lArray[n1] = max;

    rArray[n2] = max;

    i = 0;

    j = 0;

    for(k=l; k<=r; k++)

        if(lArray[i] <= rArray[j])

        {

            a[k] = lArray[i];

            ++i;

        }

        else

        {

            a[k] = rArray[j];

            cnt += (m + j - k + 1);

            ++j;

        }

    return cnt;

}

View Code