JavaScript動態規劃實現最長公共子序列

最大公共子序列是動態規劃中非常經典的例子，其規則是找出兩個數組序列中順序相同但不一定連續、最長的公共子序列

我們用JavaScript來實現它：

<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>

輸出爲：B 2  
                C 3 
                B 4  
                A 6