anagrams update

Author: zhongn2

Multiply Strings.cpp

@@ -1 +1,2 @@
-//Multiply Strings
+//Multiply Strings
+// we should know how to add two strings together:

Unique Binary Search Trees.cpp

@@ -0,0 +1,24 @@
+//Unique Binary Search Trees
+// f(0) = 1 empty tree
+// f(1) = 1 root
+// f(2) = f(0) * f(1) // 1 as root
+//		+ f(1) * f(0) // 2 as root
+// f(3) = f(0) * f(2) // 1 as root
+//		+ f(1) * f(1) // 2 s root
+//		+ f(2) * f(0) // 3 as root
+// ==> f(i) = sum(f(k - 1) * f(i - k)) ( k = 1 to i)
+
+class Solution {
+public:
+    int numTrees(int n) {
+        vector<int> f(n + 1, 0);
+        f[0] = 1;
+        f[1] = 1;
+        for(int i = 2; i <= n; i++){
+            for(int k = 1; k <= i; k++){
+                f[i] += f[k - 1] * f[i - k];
+            }
+        }
+        return f[n];
+    }
+};

Unique Paths.cpp

@@ -0,0 +1,21 @@
+//Unique Paths 
+//p[i][j] is from[0][0] to i, j 
+//p[i][j] = p[i-1][j] + p[i][j-1];
+class Solution {
+public:
+    int uniquePaths(int m, int n) {
+        int p[m][n];
+         for(int i=0; i < m; i++){
+            p[i][0] = 1;
+        }
+         for(int i=0; i < n; i++){
+            p[0][i] = 1;
+        } 
+        for(int i = 1; i < m; i++){
+            for(int j = 1; j < n; j++){
+                p[i][j] = p[i-1][j] + p[i][j-1];
+            }
+        }
+        return p[m-1][n-1];
+    }
+};

triangle.cpp

@@ -0,0 +1,16 @@
+
+// bottom-up regular method
+// it could be  O(1) space complexcity
+class Solution {
+public:
+    int minimumTotal(vector<vector<int> > &triangle) {
+        int n = triangle.size();
+        if(n == 0) return 0;
+        for(int i = n - 2; i >= 0; i--){
+            for(int j = 0; j <= i; j++){
+                triangle[i][j] = min(triangle[i+1][j], triangle[i+1][j+1]) + triangle[i][j];
+            }
+        }
+        return triangle[0][0];
+    }
+};