commit changes to gh-pages aug 23

Author: tg123

_includes/_root/palindrome-partitioning-ii/README.md

@@ -1,4 +1,16 @@
+## [Longest Palindromic Substring](../longest-palindromic-substring) + [Word Break](../word-break)
 
-## TODO 
-  * write down thinking
+After running [Longest Palindromic Substring](../longest-palindromic-substring), 
+we got a table `P[len][index]`, that is, we can tell if `s[i..j]` is palindromic
 
+## Apply [Word Break](../word-break)
+
+`M[i]` means the mincut of `s[0..i]`.
+
+When a new char comes, we have 3 choices:
+ 
+ * `M[i + 1] = 0`: if `s[0..i + 1]` is palindromic
+ * `M[i + 1] = M[i] + 1`: cut at `i`, between the old string `s[0..i]` and the new char.
+ * `M[i + 1] = M[j] + 1`: cut at `j`, `j from 0 -> i`, such that `s[j..i+1]` is palindromic, between the `s[0..j]` and `s[j..i + 1]`.
+
+Our job is to find the minimum value among them.

_includes/_root/palindrome-partitioning-ii/Solution.java

@@ -1,48 +1,49 @@
 public class Solution {
-
     public int minCut(String s) {
-        final char[] S = s.toCharArray();
-        final int N = S.length;
+        char[] S = s.toCharArray();
 
-        if(N == 0) return 0;
-        if(N == 1) return 0;
-        if(N == 2) return S[0] == S[1] ? 0 : 1;
+        if(S.length == 0) return 0;
 
-        boolean[][] P = new boolean[N][N];
+        boolean[][] P = new boolean[S.length][S.length];
 
-        for(int i = 0; i < N - 1; i++){
-            P[i][i] = true;
-            P[i][i + 1] = S[i] == S[i + 1];
-        }
+        // len 1
+        Arrays.fill(P[1 - 1], true);
 
-        P[N - 1][N - 1] = true;
+        // len 2
+        for(int i = 0; i < S.length - 1; i++){
+            P[2 - 1][i] = S[i] == S[i + 2 - 1];
+        }
 
-        for(int j = 2; j < N; j++){
-            for(int i = 0; i < j; i++){
-                P[i][j] |= P[i + 1][j - 1] && S[i] == S[j];
+        // len 3 to max
+        for(int len = 3; len <= S.length; len++){
+            
+            for(int i = 0; i < S.length - (len - 1); i++){
+                P[len - 1][i] = P[len - 1 - 2][i + 1] && S[i] == S[i + len - 1];
             }
         }
 
-        
-        int mincut[] = new int[N + 1]; // i -> end
-
-        for(int i = N - 2; i >= 0; i--){
-
-            if(P[i][N - 1]) {
-                mincut[i] = 0;
-            } else {
-                mincut[i] = mincut[i + 1] + 1;
-
-                for(int j = i + 1; j < N; j++){
-                    if(P[i][j]){
-                        mincut[i] = Math.min(1 + mincut[j + 1], mincut[i]);
+        int[] mincut = new int[S.length + 1];
+        
+        mincut[0] = 0;
+        mincut[1] = 0;
+        
+        for(int len = 2; len <= S.length; len++){
+            
+            if(P[len - 1][0]){
+                mincut[len] = 0;
+            }else{
+                
+                mincut[len] = mincut[len - 1] + 1;
+                
+                for(int i = 1; i < len - 1; i++){
+                    
+                    if(P[len - i - 1][i]){
+                        mincut[len] = Math.min(mincut[i] + 1 , mincut[len]);
                     }
                 }
-                //mincut = Math.min(minCut(s.substring(i + 1)) + 1, mincut);
             }
         }
-
-        return mincut[0];
 
+        return mincut[S.length];
     }
-}
+}

_includes/_root/substring-with-concatenation-of-all-words/README.md

@@ -1,4 +1,38 @@
+## [Space-time tradeoff](http://en.wikipedia.org/wiki/Space%E2%80%93time_tradeoff)
 
-## TODO 
-  * write down thinking
+A brute force solution is easy. Yet, obviously, time limited. 
 
+### Check concatenation using count sum
+
+cut a string `S` into N substring, lets say `s1 * 1, s2 * 2, s3 * 1`, 
+that is, `S` could be `s2s1s2s3` or `s3s1s2s2` or some string else.
+
+convert `L` to count sum, which is a map of `string to count`
+
+```
+M = empty Map
+
+for s in L
+  M[s] = M[s] + 1
+  
+
+```
+
+
+check concatenation S by minus count
+
+```
+cut S into substrings by some length
+
+_M = clone of M
+
+for s in substrings
+  
+  if _M[s] == 0
+    Not a concatenation
+ 
+  _M[s] = _M[s] - 1
+  
+
+
+```

palindrome-partitioning-ii/index.md

@@ -1,7 +1,8 @@
 ---
 layout: solution
 title: Palindrome Partitioning II
-date: 2014-07-23 02:42:48 +0800
+date: 2014-08-22 20:14:10 +0800
+eaten: true
 ---
 {% assign leetcode_name = {{page.path | remove: '/index.md'}}  %}
 {% assign leetcode_readme = {{leetcode_name | append: '/README.md' | prepend: '_root/' }}  %}

substring-with-concatenation-of-all-words/index.md

@@ -1,7 +1,8 @@
 ---
 layout: solution
 title: Substring with Concatenation of All Words
-date: 2014-07-23 02:42:48 +0800
+date: 2014-08-23 00:06:08 +0800
+eaten: true
 ---
 {% assign leetcode_name = {{page.path | remove: '/index.md'}}  %}
 {% assign leetcode_readme = {{leetcode_name | append: '/README.md' | prepend: '_root/' }}  %}