TheAlgorithms
diff --git a/‎Graphs/a_star.py‎
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diff --git a/‎Graphs/basic-graphs.py‎
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+
+grid = [[0, 1, 0, 0, 0, 0],
+        [0, 1, 0, 0, 0, 0],#0 are free path whereas 1's are obstacles
+        [0, 1, 0, 0, 0, 0],
+        [0, 1, 0, 0, 1, 0],
+        [0, 0, 0, 0, 1, 0]]
+
+'''
+heuristic = [[9, 8, 7, 6, 5, 4],
+             [8, 7, 6, 5, 4, 3],
+             [7, 6, 5, 4, 3, 2],
+             [6, 5, 4, 3, 2, 1],
+             [5, 4, 3, 2, 1, 0]]'''
+
+init = [0, 0]
+goal = [len(grid)-1, len(grid[0])-1] #all coordinates are given in format [y,x] 
+cost = 1
+
+#the cost map which pushes the path closer to the goal
+heuristic = [[0 for row in range(len(grid[0]))] for col in range(len(grid))]
+for i in range(len(grid)):    
+    for j in range(len(grid[0])):            
+        heuristic[i][j] = abs(i - goal[0]) + abs(j - goal[1])
+        if grid[i][j] == 1:
+            heuristic[i][j] = 99 #added extra penalty in the heuristic map
+
+
+#the actions we can take
+delta = [[-1, 0 ], # go up
+         [ 0, -1], # go left
+         [ 1, 0 ], # go down
+         [ 0, 1 ]] # go right
+
+
+#function to search the path
+def search(grid,init,goal,cost,heuristic):
+
+    closed = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]# the referrence grid
+    closed[init[0]][init[1]] = 1
+    action = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]#the action grid
+
+    x = init[0]
+    y = init[1]
+    g = 0
+    f = g + heuristic[init[0]][init[0]]
+    cell = [[f, g, x, y]]
+
+    found = False  # flag that is set when search is complete
+    resign = False # flag set if we can't find expand
+
+    while not found and not resign:
+        if len(cell) == 0:
+            resign = True
+            return "FAIL"
+        else:
+            cell.sort()#to choose the least costliest action so as to move closer to the goal
+            cell.reverse()
+            next = cell.pop()
+            x = next[2]
+            y = next[3]
+            g = next[1]
+            f = next[0]
+
+            
+            if x == goal[0] and y == goal[1]:
+                found = True
+            else:
+                for i in range(len(delta)):#to try out different valid actions
+                    x2 = x + delta[i][0]
+                    y2 = y + delta[i][1]
+                    if x2 >= 0 and x2 < len(grid) and y2 >=0 and y2 < len(grid[0]):
+                        if closed[x2][y2] == 0 and grid[x2][y2] == 0:
+                            g2 = g + cost
+                            f2 = g2 + heuristic[x2][y2]
+                            cell.append([f2, g2, x2, y2])
+                            closed[x2][y2] = 1
+                            action[x2][y2] = i
+    invpath = []
+    x = goal[0]
+    y = goal[1]
+    invpath.append([x, y])#we get the reverse path from here
+    while x != init[0] or y != init[1]:
+    	x2 = x - delta[action[x][y]][0]
+        y2 = y - delta[action[x][y]][1]
+        x = x2
+        y = y2
+        invpath.append([x, y])
+
+    path = []
+    for i in range(len(invpath)):
+    	path.append(invpath[len(invpath) - 1 - i])
+    print "ACTION MAP"
+    for i in range(len(action)):
+        print action[i]
+                  
+    return path
+    
+a = search(grid,init,goal,cost,heuristic)
+for i in range(len(a)):
+	print a[i] 
+
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+# Accept No. of Nodes and edges
+n, m = map(int, raw_input().split(" "))
+
+# Initialising Dictionary of edges
+g = {}
+for i in xrange(n):
+    g[i + 1] = []
+
+"""
+--------------------------------------------------------------------------------
+    Accepting edges of Unweighted Directed Graphs
+--------------------------------------------------------------------------------
+"""
+for _ in xrange(m):
+    x, y = map(int, raw_input().split(" "))
+    g[x].append(y)
+
+"""
+--------------------------------------------------------------------------------
+    Accepting edges of Unweighted Undirected Graphs
+--------------------------------------------------------------------------------
+"""
+for _ in xrange(m):
+    x, y = map(int, raw_input().split(" "))
+    g[x].append(y)
+    g[y].append(x)
+
+"""
+--------------------------------------------------------------------------------
+    Accepting edges of Weighted Undirected Graphs
+--------------------------------------------------------------------------------
+"""
+for _ in xrange(m):
+    x, y, r = map(int, raw_input().split(" "))
+    g[x].append([y, r])
+    g[y].append([x, r])
+
+"""
+--------------------------------------------------------------------------------
+    Depth First Search.
+        Args :  G - Dictionary of edges
+                s - Starting Node
+        Vars :  vis - Set of visited nodes
+                S - Traversal Stack
+--------------------------------------------------------------------------------
+"""
+
+
+def dfs(G, s):
+    vis, S = set([s]), [s]
+    print s
+    while S:
+        flag = 0
+        for i in G[S[-1]]:
+            if i not in vis:
+                S.append(i)
+                vis.add(i)
+                flag = 1
+                print i
+                break
+        if not flag:
+            S.pop()
+
+
+"""
+--------------------------------------------------------------------------------
+    Breadth First Search.
+        Args :  G - Dictionary of edges
+                s - Starting Node
+        Vars :  vis - Set of visited nodes
+                Q - Traveral Stack
+--------------------------------------------------------------------------------
+"""
+from collections import deque
+
+
+def bfs(G, s):
+    vis, Q = set([s]), deque([s])
+    print s
+    while Q:
+        u = Q.popleft()
+        for v in G[u]:
+            if v not in vis:
+                vis.add(v)
+                Q.append(v)
+                print v
+
+
+"""
+--------------------------------------------------------------------------------
+    Dijkstra's shortest path Algorithm
+        Args :  G - Dictionary of edges
+                s - Starting Node
+        Vars :  dist - Dictionary storing shortest distance from s to every other node
+                known - Set of knows nodes
+                path - Preceding node in path
+--------------------------------------------------------------------------------
+"""
+
+
+def dijk(G, s):
+    dist, known, path = {s: 0}, set(), {s: 0}
+    while True:
+        if len(known) == len(G) - 1:
+            break
+        mini = 100000
+        for i in dist:
+            if i not in known and dist[i] < mini:
+                mini = dist[i]
+                u = i
+        known.add(u)
+        for v in G[u]:
+            if v[0] not in known:
+                if dist[u] + v[1] < dist.get(v[0], 100000):
+                    dist[v[0]] = dist[u] + v[1]
+                    path[v[0]] = u
+    for i in dist:
+        if i != s:
+            print dist[i]
+
+
+"""
+--------------------------------------------------------------------------------
+    Topological Sort
+--------------------------------------------------------------------------------
+"""
+from collections import deque
+
+
+def topo(G, ind=None, Q=[1]):
+    if ind == None:
+        ind = [0] * (len(G) + 1) 		# SInce oth Index is ignored
+        for u in G:
+            for v in G[u]:
+                ind[v] += 1
+        Q = deque()
+        for i in G:
+            if ind[i] == 0:
+                Q.append(i)
+    if len(Q) == 0:
+        return
+    v = Q.popleft()
+    print v
+    for w in G[v]:
+        ind[w] -= 1
+        if ind[w] == 0:
+            Q.append(w)
+    topo(G, ind, Q)
+
+
+"""
+--------------------------------------------------------------------------------
+    Reading an Adjacency matrix
+--------------------------------------------------------------------------------
+"""
+
+
+def adjm():
+    n, a = input(), []
+    for i in xrange(n):
+        a.append(map(int, raw_input().split()))
+    return a, n
+
+
+"""
+--------------------------------------------------------------------------------
+    Floyd Warshall's algorithm
+        Args :  G - Dictionary of edges
+                s - Starting Node
+        Vars :  dist - Dictionary storing shortest distance from s to every other node
+                known - Set of knows nodes
+                path - Preceding node in path
+
+--------------------------------------------------------------------------------
+"""
+
+
+def floy((A, n)):
+    dist = list(A)
+    path = [[0] * n for i in xrange(n)]
+    for k in xrange(n):
+        for i in xrange(n):
+            for j in xrange(n):
+                if dist[i][j] > dist[i][k] + dist[k][j]:
+                    dist[i][j] = dist[i][k] + dist[k][j]
+                    path[i][k] = k
+    print dist
+
+
+"""
+--------------------------------------------------------------------------------
+    Prim's MST Algorithm
+        Args :  G - Dictionary of edges
+                s - Starting Node
+        Vars :  dist - Dictionary storing shortest distance from s to nearest node
+                known - Set of knows nodes
+                path - Preceding node in path
+--------------------------------------------------------------------------------
+"""
+
+
+def prim(G, s):
+    dist, known, path = {s: 0}, set(), {s: 0}
+    while True:
+        if len(known) == len(G) - 1:
+            break
+        mini = 100000
+        for i in dist:
+            if i not in known and dist[i] < mini:
+                mini = dist[i]
+                u = i
+        known.add(u)
+        for v in G[u]:
+            if v[0] not in known:
+                if v[1] < dist.get(v[0], 100000):
+                    dist[v[0]] = v[1]
+                    path[v[0]] = u
+
+
+"""
+--------------------------------------------------------------------------------
+    Accepting Edge list
+        Vars :  n - Number of nodes
+                m - Number of edges
+        Returns : l - Edge list
+                n - Number of Nodes
+--------------------------------------------------------------------------------
+"""
+
+
+def edglist():
+    n, m = map(int, raw_input().split(" "))
+    l = []
+    for i in xrange(m):
+        l.append(map(int, raw_input().split(' ')))
+    return l, n
+
+
+"""
+--------------------------------------------------------------------------------
+    Kruskal's MST Algorithm
+        Args :  E - Edge list
+                n - Number of Nodes
+        Vars :  s - Set of all nodes as unique disjoint sets (initially)
+--------------------------------------------------------------------------------
+"""
+
+
+def krusk((E, n)):
+    # Sort edges on the basis of distance
+    E.sort(reverse=True, key=lambda x: x[2])
+    s = [set([i]) for i in range(1, n + 1)]
+    while True:
+        if len(s) == 1:
+            break
+        print s
+        x = E.pop()
+        for i in xrange(len(s)):
+            if x[0] in s[i]:
+                break
+        for j in xrange(len(s)):
+            if x[1] in s[j]:
+                if i == j:
+                    break
+                s[j].update(s[i])
+                s.pop(i)
+                break