最长公共子序列

/** * Longest Common Subsequence *  * f(i, j) = max{f(i-1, j-1), f(i-1, j-1)+1, f(i-1, j), f(i, j-1)} *  * 主要在空间优化，逐行扫描，下一行只依赖与上一行和本行，可以只需要定义2个数组，更好的办法只需要一个数组 * 每次计算出一个新值，先不更新，等下一个求出来之后，再更新前一个。 * O(min{m, n}+1) * */public class LCS {public static int lcs(int[] a, int[] b){assert(true);int[][] v = new int[a.length+1][b.length+1];for(int i=1; i<=a.length; i++){for(int j=1; j<=b.length; j++){int max = v[i-1][j-1];if(a[i-1] == b[j-1]){max++;}int max2 = v[i-1][j] > v[i][j-1] ? v[i-1][j] : v[i][j-1];v[i][j] = max > max2 ? max : max2;}}return v[a.length][b.length];}public static int lcs2(int[] a, int[] b){int longLength = a.length;int shortLength = b.length;int[] longArray = a;int[] shortArray = b;if(a.length < b.length){longLength = b.length;shortLength = a.length;longArray = b;shortArray = a;}int[] v = new int[shortLength+1];for(int i=1; i<=longLength; i++){int pre = 0;for(int j=1; j<=shortLength; j++){int max = v[j-1];if(longArray[i-1] == shortArray[j-1]){max++;}int max2 = pre>v[j] ? pre : v[j];v[j-1] = pre;pre = max>max2 ? max : max2;}v[shortLength] = pre;}return v[shortLength];}/** * @param args */public static void main(String[] args) {int[] a = {1, 3, 9, 6, 2,4,7,5};int[] b = {7,2,4,8,3,5,1,9,0,6};int max = LCS.lcs(a, b);int max2 = LCS.lcs2(a, b);System.out.println(max);System.out.println(max2);}}