1.計算二項式係數（動態規劃）
 
# coding:utf-8
 
# computing C(n,k)
def Binomial_coefficient(n,k):
    if k == 0 or k == n:
        result = 1
    else:
        result = Binomial_coefficient(n-1,k-1)+Binomial_coefficient(n-1,k)
    return result
 
 
print Binomial_coefficient(10,3)
 
 
 
2.Floyd演算法
 
# coding:utf-8
 
 
# floyd
_ = float('inf')
a = [[0,_,3,_],[2,0,_,_],[_,7,0,1],[6,_,_,0]]
 
 
for k in range(4):
    for i in range(4):
        for j in range(4):
            if a[i][j] > a[i][k] + a[k][j]:
                a[i][j] = a[i][k] + a[k][j]
            else:
                pass
 
 
 
print a
 
3.揹包問題
 
# coding:utf-8
 
 
# knapsack_problem
w = [2,1,3,2]
v = [12,10,20,15]
matrix = []
sub_lst = []
for i_i in range(5):
    for j_j in range(6):
        sub_lst.append(0)
    matrix.append(sub_lst)
    sub_lst = []
 
 
for i in range(1,5):
    for j in range(1,6):
        if j >= w[i-1]:
            matrix[i][j] = max(matrix[i-1][j],v[i-1]+matrix[i-1][j-w[i-1]])
        else:
            matrix[i][j] = matrix[i-1][j]
print matrix
 
4.用於計算最小公約數的Euclid演算法
 
# coding:utf-8
 
 
# Euclid
def Euclid(m,n):
    while n != 0:
        r = m % n
        m = n
        n = r
    return m
 
print Euclid(60,24)
 
 
 
5.求一個一維陣列中大小最接近的兩個元素的差
 
# coding:utf-8
 
 
# minDistance
def minDistance(lst):
    dmin = float('inf')
    for i in range(len(lst)):
        for j in range(len(lst)):
            if i < j and abs(lst[i]-lst[j]) < dmin:
                dmin = abs(lst[i] - lst[j])
            else:
                pass
    return dmin
 
 
print minDistance([1,99,5,10,23,80])
 
 
 
6.計算一個十進位制數轉換為二進位制數後的位數
 
# coding:utf-8
 
 
# calculate count of binary
 
 
# method1
def Binary(n):
    count = 1
    while n > 1:
        count += 1
        n = n / 2
    return count
 
 
print Binary(4)
 
 
# method2
def Binary2(n):
    if n == 1:
        return 1
    else:
        return Binary2(n/2)+1
print Binary2(4)
 
7. 選擇排序
 
# coding:utf-8
 
 
# selection_sort
def swap(a,b):
    tmp = a
    a = b
    b = tmp
    return a,b
 
 
def Selection_Sort(lst):
    for i in range(len(lst)-1):
        min = i
        for j in range(1,len(lst)):
            if lst[j] < lst[min]:
                min = j
        lst[i],lst[min] = swap(lst[i],lst[min])
    return lst
 
 
print Selection_Sort([3,1,2])
 
 
 
8.氣泡排序
 
# coding:utf-8
 
 
# BubbleSort
def swap(a,b):
    tmp = a
    a = b
    b = tmp
    return a,b
 
 
def Bubble_sort(lst):
    for i in range(len(lst)-1):
        for j in range(len(lst)-1-i):
            if lst[j+1] < lst[j]:
                lst[j],lst[j+1] = swap(lst[j],lst[j+1])
    return lst
 
 
print Bubble_sort([3,1,2])