JavaScript动态规划实现最长公共子序列

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最大公共子序列是动态规划中非常经典的例子，其规则是找出两个数组序列中顺序相同但不一定连续、最长的公共子序列

我们用JavaScript来实现它：

<script type="text/javascript">var c=new Array(20),b=new Array(20);for (var i=0,len=c.length>b.length?c.length:b.length;i<len;i++) {c[i]=new Array(20);b[i]=new Array(20);}function LCSLength(m,n,x,y){for(var i=1;i<=m;i++)c[i][0]=0;for(var j=0;j<=n;j++)c[0][j]=0;    for(i=1;i<=m;i++){    for (j=1;j<=n;j++) {    if (x[i-1]==y[j-1]) {    c[i][j]=c[i-1][j-1]+1;    b[i][j]=1;    } else if(c[i-1][j]>=c[i][j-1]){    c[i][j]=c[i-1][j];    b[i][j]=2;    }else{    c[i][j]=c[i][j-1];    b[i][j]=3;    }    }    }}function LCS(m,n){if (m==0 || n==0) {return;}if (b[m][n]==1) {LCS(m-1,n-1);console.log(X[m-1]+" "+m);} else if(b[m][n]==2){LCS(m-1,n);}else{LCS(m,n-1);}}var X=["A","B","C","B","D","A","B"];var Y=["B","D","C","A","B","A"];LCSLength(X.length,Y.length,X,Y);//alert(c[X.length][Y.length]);LCS(X.length,Y.length);//alert(b);</script>

输出为：B 2
C 3
B 4
A 6

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