算法设计与分析(十一).ppt

算法分析BM算法的最坏情况时间复杂度可以达到Θ(n·m)。如P是am而文本是an时。一般情况可以达到O(n)。如果|Σ||P|，算法的平均时间可以达到O(n/m)。这是因为很多字符不在模式中出现，模式经常会因为坏字符滑动m距离。**模式通过自匹配计算π的过程如下算法11.2计算模式的前缀函数πCOMPUTE-PREFIX-FUNCTION(P)//P是已知的模式m←length[P]π[1]←0k←0//k是当前已匹配的前缀长度forq←2tomdowhilek＞0andP[k+1]≠P[q]dok←π[k]repeatifP[k+1]=P[q]thenk←k+1endifπ[q]←krepeatreturnπENDCOMPUTE-PREFIX-FUNCTIONCOMPUTE-PREFIX-FUNCTION(P)m←length[P]π[1]←0k←0forq←2tomdowhilek＞0andP[k+1]≠P[q]dok←π[k]repeatifP[k+1]=P[q]thenk←k+1endifπ[q]←krepeatreturnπENDCOMPUTE-PREFIX-FUNCTION91234510cababaa0678babip[i]π[i]k=091234510cababaa00678babip[i]π[i]k=0，q=2P[0+1]≠P[2],k=0,不进入while循环π[2]=091234510cababaa001678babip[i]π[i]k=0，q=3P[0+1]＝P[3],k=0,不进入while循环P[0+1]＝P[3],k=1π[3]=1COMPUTE-PREFIX-FUNCTION(P)m←length[P]π[1]←0k←0forq←2tomdowhilek＞0andP[k+1]≠P[q]dok←π[k]repeatifP[k+1]=P[q]thenk←k+1endifπ[q]←krepeatreturnπENDCOMPUTE-PREFIX-FUNCTION91234510cababaa0012678babip[i]π[i]k=1，q=4P[1+1]＝P[4],不进入while循环P[1+1]＝P[4],k=1+1=2π[4]=291234510cababaa00123678babip[i]k=2，q=5P[2+1]＝P[5],不进入while循环P[2+1]＝P[5],k=2+1=3π[5]=391234510cababaa00123678bab4ip[i]k=3，q=6P[3+1]＝P[6],不进入while循环P[3+1]＝P[6],k=3+1=4π[6]=4π[i]π[i]COMPUTE-PREFIX-FUNCTION(P)m←length[P]π[1]←0k←0forq←2tomdowhilek＞0andP[k+1]≠P[q]dok←π[k]repeatifP[k+1]=P[q]thenk←k+1endifπ[q]←krepeatreturnπENDCOMPUTE-PREFIX-FUNCTION91234510cababaa00123678bab45ip[i]k=4，q=7P[4+1]＝P[7],不进入while循环P[4+1]＝P[7],k=4+1=5π[7]=591234