update readme

Author: CheYulin

bioinformatics/dynamic_programming/ReadMe.md

@@ -0,0 +1,81 @@
+#Explanation
+##First: Fibonacci
+
+we can use matrix fast pow to compute that.
+
+see [fibonacci.py](fibonacci.py)
+
+##Second: max sum sub arr
+
+I reduce the problem into another one though doing prefix sum computation first.
+
+see [max_sum_sub_arr.py](max_sum_sub_arr.py)
+
+- input 
+
+```zsh
+[1, -2, 3, 10, -4, 7, 2, -5]
+```
+
+- output
+
+```zsh
+input list: [1, -2, 3, 10, -4, 7, 2, -5]
+scan list: [0, 1, -1, 2, 12, 8, 15, 17, 12]
+differ: 18
+sub arr input list lower idx: 2 value: 3
+sub arr input list upper idx: 6 value: 2
+sub arr: [3, 10, -4, 7, 2]
+
+```
+
+##Third: max len incremental sub arr
+
+see [max_len_incre_sub_arr.py](max_len_incre_sub_arr.py)
+
+- input 
+
+```zsh
+[7, 2, 3, 1, 5, 8, 9, 6]
+```
+
+- output
+
+```zsh
+max incre count: 5 
+
+root-1                                            
+ |_2                                              
+   |_3                                            
+     |_5                                          
+       |_8                                        
+         |_9           
+
+```
+
+##Fourth
+
+skip
+
+##Fifth
+
+see [min_sum_path.py](min_sum_path.py)
+
+- input weight matrix
+
+```zsh
+matrix = [[1, 2, 9], [3, 4, 8], [5, 6, 7]]
+```
+
+- output
+
+```zsh
+root[(2, 2)]                                       (3, 3)
+ |_[(2, 1)]                                        (2, 2) weight: 7 min sum: 20
+   |_[(1, 1)]                                      (2, 1) weight: 6 min sum: 13
+     |_[(0, 1)]                                    (1, 1) weight: 4 min sum: 7
+       |_[(0, 0)]                                  (0, 1) weight: 2 min sum: 3
+         |_None                                    (0, 0) weight: 1 min sum: 1
+min sum:20
+
+```

bioinformatics/dynamic_programming/max_len_incre_sub_arr.py

@@ -44,7 +44,8 @@ def dfs_detail(node_ref, node_level):
     max_val = max(map(lambda node: node.max_len, node_arr))
     root_node = Node(-1)
     root_node.next_list = filter(lambda node: node.max_len == max_val, node_arr)
-    print max_val
+
+    print 'max incre count:', max_val, '\n'
     print_tree(root_node)
 
 

bioinformatics/dynamic_programming/max_sum_sub_arr.py

@@ -54,9 +54,13 @@ def max_difference_detail(i, j):
     input_list = [1, -2, 3, 10, -4, 7, 2, -5]
     scan_list = inclusive_scan(input_list)
     scan_list = [0] + scan_list
-    print input_list
-    print scan_list
-    print max_difference(scan_list)
+    print 'input list:', input_list
+    print 'scan list:', scan_list
+    min_idx, max_idx, differ = max_difference(scan_list)
+    print 'differ:', differ
+    print 'sub arr input list lower idx:', min_idx, 'value:', input_list[min_idx]
+    print 'sub arr input list upper idx:', max_idx - 1, 'value:', input_list[max_idx - 1]
+    print 'sub arr:', input_list[min_idx:max_idx]
 
-    scan_list1 = [0, 2, 4, 7, -1, 3, 6, -2, 4]
-    print max_difference(scan_list1)
+    # scan_list1 = [0, 2, 4, 7, -1, 3, 6, -2, 4]
+    # print max_difference(scan_list1)

bioinformatics/dynamic_programming/min_sum_path.py

@@ -54,4 +54,4 @@ def dfs_detail(node_ref, node_level, cur_idx_pair):
 
 if __name__ == '__main__':
     matrix = [[1, 2, 9], [3, 4, 8], [5, 6, 7]]
-    print min_sum(matrix)
+    print 'min sum:' + str(min_sum(matrix))