基础算法(python)

分治法-最大子数组问题

def FindMaxCrossingSubarray(A,low,mid,high):    leftsum=-float('INF')    su=0    for i in range(mid,low-1,-1):        su+=A[i]        if leftsum<su:            leftsum=su            maxleft=i    rightsum=-float('INF')    su=0    for i in range(mid+1,high+1):        su+=A[i]        if rightsum<su:            rightsum=su            maxright=i    return (maxleft,maxright,leftsum+rightsum)def FindMaximumSubarray(A,low,high):    if low==high:        return (low,high,A[low])    else:        mid=(low+high)/2        (leftlow,lefthigh,leftsum)=FindMaximumSubarray(A,low,mid)        (rightlow,righthigh,rightsum)=FindMaximumSubarray(A,mid+1,high)        (crosslow,crosshigh,crosssum)=FindMaxCrossingSubarray(A,low,mid,high)    if leftsum>=rightsum and leftsum>=crosssum:        return (leftlow,lefthigh,leftsum)    elif rightsum>=leftsum and rightsum>=crosssum:        return (rightlow,righthigh,rightsum)    else:        return (crosslow,crosshigh,crosssum)

归并排序

def MergeSort(A,p,r):    if p<r:        q=(p+r)/2        MergeSort(A,p,q)        MergeSort(A,q+1,r)        Merge(A,p,q,r)def Merge(A,p,q,r):    L=[];R=[]    for i in range(q-p+1):        L.append(A[p+i])    for i in range(r-q):        R.append(A[q+1+i])    i=0;j=0    L.append(float('INF'));R.append(float('INF'))    res=[]    for k in range(p,r+1):        if L[i]<=R[j]:            A[k]=L[i]            i+=1        else:            A[k]=R[j]            j+=1

堆排序

def MaxHeapify(A,i,heapsize):    left=2*i+1;right=2*i+2    if left<heapsize and A[left]>A[i]:        largest=left    else:        largest=i    if right<heapsize and A[right]>A[largest]:        largest=right    if largest!=i:        A[i],A[largest]=A[largest],A[i]        MaxHeapify(A,largest,heapsize)def BuildMaxHeap(A,heapsize):    for i in range((len(A)-1)/2,-1,-1):        MaxHeapify(A,i,heapsize)def HeapSort(A):    heapsize=len(A)    BuildMaxHeap(A,heapsize)    for i in range(len(A)-1,0,-1):        A[0],A[heapsize-1]=A[heapsize-1],A[0]        heapsize-=1        MaxHeapify(A,0,heapsize)

快速排序

def Partition(A,p,r):    x=A[r]    i=p-1    for j in range(p,r):        if A[j]<=x:            i+=1            A[i],A[j]=A[j],A[i]    A[i+1],A[r]=A[r],A[i+1]    return i+1def QuickSort(A,p,r):    if p<r:        q=Partition(A,p,r)        QuickSort(A,p,q-1)        QuickSort(A,q+1,r)

快速排序的Hoare划分

def HoarePartition(A,p,r):    x=A[r]    i=p;j=r    while 1:        while i<r and A[i]<x:            i+=1        while j>p and A[j]>=x:            j-=1        if i<j:            A[i],A[j]=A[j],A[i]        else:            A[r],A[i]=A[i],A[r]            return jdef QuickSort(A,p,r):    if p<r:        q=HoarePartition(A,p,r)        QuickSort(A,p,q)        QuickSort(A,q+1,r)

快速排序的随机化版本

import randomdef Partition(A,p,r):    x=A[r]    i=p-1    for j in range(p,r):        if A[j]<=x:            i+=1            A[i],A[j]=A[j],A[i]    A[i+1],A[r]=A[r],A[i+1]    return i+1def RandomizedPartition(A,p,r):    i=random.randint(p,r)    A[i],A[r]=A[r],A[i]    return Partition(A,p,r)def RandomizedQuickSort(A,p,r):    if p<r:        q=RandomizedPartition(A,p,r)        RandomizedQuickSort(A,p,q-1)        RandomizedQuickSort(A,q+1,r)

计数排序

def CountingSort(A,B,k):    C=[0 for i in range(k+1)]    for i in range(len(A)):        C[A[i]]+=1    for i in range(1,k+1):        C[i]+=C[i-1]    for i in range(len(A)-1,-1,-1):        B[C[A[i]]-1]=A[i]        C[A[i]]-=1

选择算法(找第k小的数)

import randomdef Patition(A,p,r):    x=A[r]    i=p-1    for j in range(p,r):        if A[j]<=x:            i+=1            A[i],A[j]=A[j],A[i]    A[r],A[i+1]=A[i+1],A[r]    return i+1def RandomizedPatition(A,p,r):    i=random.randint(p,r)    A[r],A[i]=A[i],A[r]    return Patition(A,p,r)def RandomizedSelect(A,p,r,i):    if p==r:        return A[p]    q=RandomizedPatition(A,p,r)    k=q-p    if i==k:        return A[q]    elif i<k:        return RandomizedSelect(A,p,q-1,i)    else:        return RandomizedSelect(A,q+1,r,i-k-1)