最短编辑距离

__author__ = 'Jade'
"""
    solve minimum Edit Distance , time is O(nm) , space is O(nm)    
"""

def findAStrtoBStrMinSteps(a_str , b_str):
    a_str_len , b_str_len = len(a_str) , len(b_str)
    dp = [[0 for j in range(b_str_len + 1)] for i in range(a_str_len + 1)]
    for i in range(a_str_len + 1):
        dp[i][0] = i
    for i in range(b_str_len + 1):
        dp[0][i] = i
    operator_list = list()
    for i in range(a_str_len):
        for j in range(b_str_len):
            dp[i + 1][j + 1] = min(dp[i][j + 1] + 1 , dp[i + 1][j] + 1 , dp[i][j] if a_str[i] == b_str[j] else dp[i][j] + 1)
    a_str_index , b_str_index = a_str_len , b_str_len

    while(a_str_index >= 1 or b_str_index >= 1):
        if(dp[a_str_index][b_str_index] == dp[a_str_index][b_str_index - 1] + 1):
            operator_list.append({"type":"add","index":b_str_index,"value":b_str[b_str_index - 1]})
            b_str_index -= 1
        elif(dp[a_str_index][b_str_index] == dp[a_str_index - 1][b_str_index] + 1):
            operator_list.append({"type":"del","index":a_str_index})
            a_str_index -= 1
        else:
            if(dp[a_str_index][b_str_index] == dp[a_str_index - 1][b_str_index - 1] + 1):
                operator_list.append({"type":"update","index":a_str_index,"value":b_str[b_str_index - 1]})
            a_str_index -= 1
            b_str_index -= 1

    operator_list.reverse()
    return operator_list , dp[a_str_len][b_str_len]

def main():
    a_str = input()
    b_str = input()
    operator_list , mininum_steps = findAStrtoBStrMinSteps(a_str , b_str)
    print('%s transform %s need mininum %d steps'%(a_str , b_str , mininum_steps))
    print('operators as follow:')
    for opt in operator_list:
        if(opt.get('type') == "del"):
            print(opt.get('type'),opt.get('index'))
        else:
            print(opt.get('type') , opt.get("index") , opt.get('value'))

def test():
    while True:
        try:
            a_str , b_str = input().split()
            operator_list , minimum_steps = findAStrtoBStrMinSteps(a_str , b_str)
            print(minimum_steps)
        except:
            break

if __name__ == '__main__':
    test()