数学基础:三、动态规划1(求解编辑距离)
编辑距离
的概念,百度一下你就知道。也有很多文章有所介绍
https://blog.csdn.net/chichoxian/article/details/53944188
做动态规划的题就是根据表格,找出规律,推导出状态转移方程
比如编辑距离
的状态转移方程
如下:
d[i+1, j+1] = min(d[i, j+1] + 1, d[i+1, j] + 1, d[i, j] + r(i, j))
下面这个我是用Java实现的:
public class Lesson9_1 {
public static int getStrDistince(String a, String b) {
if (a == null || b == null) return -1;
int aLength = a.length();
int bLength = b.length();
int[][] d = new int[aLength + 1][bLength + 1];
for (int i = 0; i <= aLength; i++) {
d[i][0] = i;
}
for (int j = 0; j <= bLength; j++) {
d[0][j] = j;
}
//d[i+1, j+1] = min(d[i, j+1] + 1, d[i+1, j] + 1, d[i, j] + r(i, j))
for (int i = 0; i < aLength; i++) {
for (int j = 0; j < bLength; j++) {
// d[i, j+1] + 1
int m = d[i][j + 1] + 1;
// d[i+1, j] + 1
int n = d[i + 1][j] + 1;
int r = a.charAt(i) == b.charAt(j) ? 0 : 1;
// d[i, j] + r(i, j)
int k = d[i][j] + r;
int min1 = Math.min(m, n);
int min2 = Math.min(min1, k);
d[i + 1][j + 1] = min2;
}
}
return d[aLength][bLength];
}
public static void main(String[] args) {
int strDistince = getStrDistince("mou", "mouuse");
System.out.println(strDistince);
}
}