Grid Path Count Example Added

Author: Mansour Torabi

.gitignore

@@ -1 +1 @@
-*.png
+*.asv

EVAL.m Fibonacci/EVAL_fibo.mEVAL.m renamed to Fibonacci/EVAL_fibo.m

@@ -5,16 +5,16 @@
 %%
 
 % Using Recursive Method
-tic; Fibo1(40); toc
+tic; Fibo_R(40); toc
 
 % Using Dynamic Programming
-tic; Fibo2(40); toc
+tic; Fibo_DP(40); toc
 
 %%
 
 % Using Dynamic Programming
-tic; Fibo2(10000); toc
+tic; Fibo_DP(10000); toc
 
 % Using Matrix Exponentiation
-tic; Fibo3(10000); toc
+tic; Fibo_M(10000); toc
 

Fibo2.m Fibonacci/Fibo_DP.mFibo2.m renamed to Fibonacci/Fibo_DP.m

@@ -1,4 +1,4 @@
-function F = Fibo2(n)
+function F = Fibo_DP(n)
 %%
 % Author: Mansour Torabi, 
 % Contact: smtoraabi@ymail.com
@@ -10,22 +10,19 @@
 % Time Complexity   : O(n)
 % Space             : O(n)
 
-Memo = [];
-MemoIdx = [];
+Memo = zeros(1,n)*nan;
+
 F = Fibonacci(n);
 
     function f = Fibonacci(n)
-        if any(n == MemoIdx)
+        if ~isnan(Memo(n))
             f = Memo(n); return;
         end
         if n <= 2
-            f = 1;
-            Memo(n) = f;
-            MemoIdx = [MemoIdx, n];
+            f = 1; Memo(n) = f; 
         else
             f = Fibonacci(n-1) + Fibonacci(n-2);
-            Memo(n) = f;
-            MemoIdx = [MemoIdx, n];
+            Memo(n) = f; 
         end
     end
 end

Fibo3.m Fibonacci/Fibo_M.mFibo3.m renamed to Fibonacci/Fibo_M.m

@@ -1,4 +1,4 @@
-function F = Fibo3(n)
+function F = Fibo_M(n)
 %%
 % Author: Mansour Torabi, 
 % Contact: smtoraabi@ymail.com

Fibo1.m Fibonacci/Fibo_R.mFibo1.m renamed to Fibonacci/Fibo_R.m

@@ -1,4 +1,4 @@
-function f = Fibo1(n)
+function f = Fibo_R(n)
 %%
 % Author: Mansour Torabi, 
 % Contact: smtoraabi@ymail.com
@@ -13,5 +13,5 @@
 if n <= 2
     f = 1;
 else
-    f = Fibo1(n-1) + Fibo1(n-2);
+    f = Fibo_R(n-1) + Fibo_R(n-2);
 end

Grid Path/EVAL_grid_path.m

@@ -0,0 +1,18 @@
+clc, clear
+
+% Define Map (Grid Path)
+Map = zeros(15,10);
+Map(3,5) = 1;
+Map(6,7) = 1;
+Map(7,3) = 1;
+
+% Visualize Map (Grid Path)
+MapView(Map)
+%%
+tic;
+N1 = GridPath_R(Map, 1,1)
+toc;
+
+tic;
+N2 = GridPath_DP(Map, 1,1)
+toc;

Grid Path/GridMap.png

@@ -0,0 +1,26 @@
+function N = GridPath_DP(Map, i, j)
+
+[m, n] = size(Map);
+Memo = zeros(m,n)*nan;
+
+N = GridPath(Map, i, j);
+
+    function nn = GridPath(Map, i, j)
+        if i > m || j > n % if out of Map
+            nn = 0; return;
+        end
+        if ~isnan(Memo(i,j)) % if in the Memo
+            nn = Memo(i,j); return;
+        elseif Map(i,j) == 1  % if there is obstacle
+            nn = 0; Memo(i,j) = nn; return;
+        else % if last step of Map
+            if ((i == m-1)&& (j == n)) || ((i == m) && (j == n-1))
+                nn = 1;  Memo(i,j) = nn; return;
+            else
+                nn = GridPath(Map, i+1, j) + GridPath(Map, i, j+1);
+                Memo(i,j) = nn; return;
+            end
+        end
+        
+    end
+end

Grid Path/GridPath_DP.m

@@ -0,0 +1,16 @@
+function N = GridPath_R(Map, i, j)
+
+[m, n] = size(Map);
+
+if i > m || j > n % if out of Map
+    N = 0; return
+elseif Map(i,j) == 1  % if there is obstacle
+    N = 0; return;
+else
+    if ((i == m-1)&& (j == n)) || ((i == m) && (j == n-1))
+        N = 1;    % if last step of Map
+    else
+        N = GridPath_R(Map, i+1, j) + GridPath_R(Map, i, j+1);
+    end
+end
+

Grid Path/GridPath_R.m

@@ -0,0 +1,20 @@
+function MapView(Map)
+
+Mapv = Map; 
+Mapv(1,1) = 2; Mapv(end, end) = 2;
+imagesc(Mapv); 
+
+[m, n] = size(Map);
+
+hold on;
+for ii = 1:n
+    plot([0.5+ii, 0.5+ii],[0.5, m+0.5],'w')
+end
+
+for jj = 1:m
+     plot([0.5, n+0.5],[0.5+jj, 0.5+jj],'w')
+end
+
+axis equal;
+axis off;
+