HARD/src/hard/DistinctSubsequences.java

fishercoder1534 · fishercoder1534 · commit 82067f3d5b54 · 2016-09-13T23:20:52.000-07:00
diff --git a/HARD/src/hard/DistinctSubsequences.java b/HARD/src/hard/DistinctSubsequences.java
@@ -0,0 +1,34 @@
+package hard;
+
+public class DistinctSubsequences {
+    /**This is a typical DP problem, illustrated in Jiuzhang.
+     * 
+     * I've drawn out the 2d matrix on the whiteboard:
+     * 
+     * 1. initialize a 2d matrix of size (m+1)*(n+1)
+     * 2. initialize row 0, it should be 1,0,0,0,0... this is because when S is an empty string, only when T is empty, it could be a subsequence
+     * 3. initialize column 0, it should be 1,1,1,1,1,1...
+     * 4. starting from (1,1)*/
+
+    public int numDistinct(String s, String t) {
+        int m = s.length(), n = t.length();
+        int[][] dp = new int[m+1][n+1];
+        
+        char[] schar = s.toCharArray();
+        char[] tchar = t.toCharArray();
+        
+        for(int i = 0; i <= m; i++) dp[i][0] = 1;
+        
+        for(int j = 1; j <= n; j++) dp[0][j] = 0;
+        
+        for(int i = 1; i <= m; i++){
+            for(int j = 1; j <= n; j++){
+                if(schar[i-1] == tchar[j-1]) dp[i][j] = dp[i-1][j]+dp[i-1][j-1];
+                else dp[i][j] = dp[i-1][j];
+            }
+        }
+        
+        return dp[m][n];
+    }
+
+}
