refine the comments

Author: haoel

algorithms/largestRectangleInHistogram/largestRectangleInHistogram.cpp

@@ -3,20 +3,52 @@
 // Date   : 2014-07-20
 
 /********************************************************************************** 
-* 
-* Given n non-negative integers representing the histogram's bar height where the width of each bar is 1, 
-* find the area of largest rectangle in the histogram.
-* 
-* Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].
-* 
-* The largest rectangle is shown in the shaded area, which has area = 10 unit.
-* 
-* For example,
-* Given height = [2,1,5,6,2,3],
-* return 10.
-* 
-*               
-**********************************************************************************/
+ * 
+ * Given n non-negative integers representing the histogram's bar height where the width of each bar is 1, 
+ * find the area of largest rectangle in the histogram.
+ * 
+ *                    6          
+ *                  +---+        
+ *               5  |   |        
+ *              +---+   |        
+ *              |   |   |        
+ *              |   |   |        
+ *              |   |   |     3  
+ *              |   |   |   +---+
+ *        2     |   |   | 2 |   |
+ *      +---+   |   |   +---+   |
+ *      |   | 1 |   |   |   |   |
+ *      |   +---+   |   |   |   |
+ *      |   |   |   |   |   |   |
+ *      +---+---+---+---+---+---+
+ *      
+ * Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].
+ *      
+ *      
+ *                    6          
+ *                  +---+        
+ *               5  |   |        
+ *              +-------|        
+ *              |-------|        
+ *              |-------|        
+ *              |-------|     3  
+ *              |-------|   +---+
+ *        2     |-------| 2 |   |
+ *      +---+   |-------|---+   |
+ *      |   | 1 |-------|   |   |
+ *      |   +---|-------|   |   |
+ *      |   |   |-------|   |   |
+ *      +---+---+---+---+---+---+
+ *      
+ * 
+ * The largest rectangle is shown in the shaded area, which has area = 10 unit.
+ * 
+ * For example,
+ * Given height = [2,1,5,6,2,3],
+ * return 10.
+ * 
+ *               
+ **********************************************************************************/
 
 #include <iostream>
 #include <vector>
@@ -132,7 +164,7 @@ void test(int a[], int n)
 
 int main()
 {
-    #define TEST(a) test(a, sizeof(a)/sizeof(int))
+#define TEST(a) test(a, sizeof(a)/sizeof(int))
 
     int a0[] = {2,1,3,1};
     TEST(a0);

algorithms/uniquePaths/uniquePaths.II.cpp

@@ -29,6 +29,7 @@
 #include <vector>
 using namespace std;
 
+//As same as DP solution with "Unique Path I", just need to consider the obstacles.
 int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) {
     vector< vector<int> > v = obstacleGrid;
     unsigned int max=0;

algorithms/uniquePaths/uniquePaths.cpp

@@ -3,25 +3,48 @@
 // Date   : 2014-06-25
 
 /********************************************************************************** 
-* 
-* A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
-* 
-* The robot can only move either down or right at any point in time. The robot is trying to reach 
-* the bottom-right corner of the grid (marked 'Finish' in the diagram below).
-* 
-* How many possible unique paths are there?
-* 
-* Above is a 3 x 7 grid. How many possible unique paths are there?
-* 
-* Note: m and n will be at most 100.
-*               
-**********************************************************************************/
+ * 
+ * A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
+ * 
+ * The robot can only move either down or right at any point in time. The robot is trying to reach 
+ * the bottom-right corner of the grid (marked 'Finish' in the diagram below).
+ *    
+ *    
+ *    start                                                  
+ *    +---------+----+----+----+----+----+                   
+ *    |----|    |    |    |    |    |    |                   
+ *    |----|    |    |    |    |    |    |                   
+ *    +----------------------------------+                   
+ *    |    |    |    |    |    |    |    |                   
+ *    |    |    |    |    |    |    |    |                   
+ *    +----------------------------------+                   
+ *    |    |    |    |    |    |    |----|                   
+ *    |    |    |    |    |    |    |----|                   
+ *    +----+----+----+----+----+---------+                   
+ *                                   finish                  
+ *    
+ * 
+ * How many possible unique paths are there?
+ * 
+ * Above is a 3 x 7 grid. How many possible unique paths are there?
+ * 
+ * Note: m and n will be at most 100.
+ *               
+ **********************************************************************************/
 
 #include <stdio.h>
 #include <stdlib.h>
 
 void printMatrix(int*a, int m, int n);
 
+/*
+ * Dynamic Programming
+ *
+ * We have a dp[i][j] represents  how many paths from [0][0] to hear. So, we have the following DP formuler:
+ *
+ *    dp[i][j] =  1  if i==0 || j==0        //the first row/column only have 1 uniqe path.
+ *             =  dp[i-1][j] + dp[i][j-1]   //the path can be from my top cell and left cell.
+ */
 int uniquePaths(int m, int n) {
     int* matrix = new int[m*n];
     printMatrix(matrix, m, n);
@@ -58,7 +81,7 @@ int main(int argc, char** argv)
         m = atoi(argv[1]);
         n = atoi(argv[2]);
     }
-    
+
     printf("uniquePaths=%d\n", uniquePaths(m,n));
     return  0;
 }