standardization

Fenwick_Tree/Fenwick_Tree.cpp

@@ -10,7 +10,7 @@ int lowbit(int x) {
 }
 
 void update(int index, int value) {
-  // add "value" to the index-th element 
+  // add "value" to the index-th element
   for( ; index <= N ; index += lowbit(index)) {
     bit[index] += value;
   }
@@ -26,7 +26,7 @@ int query(int index) {
 }
 
 int main(){
-  
+
   N = 10;
 
   // WARNING: the index of the first element is 1

Fermat_Little_Theorem/Fermat_Little_Theorem.c

@@ -1,19 +1,20 @@
 #include <stdio.h>
 #include <stdbool.h>
+#include <stdlib.h>
 
 int power(int a, unsigned int n, int p)
 {
     int res = 1;
     a = a % p;
-    
+
     while (n>0)
     {
         if (n & 1)
             res = (res*a)%p;
         n = n>>1;
         a = (a*a) % p;
     }
-    
+
     return res;
 }
 
@@ -31,7 +32,7 @@ bool isPrime(unsigned int n, int k)
             return false;
         k--;
     }
-    
+
     return true;
 }
 

Floyd_Warshall_Algorithm/Floyd_Warshall_Algorithm.cpp

@@ -1,22 +1,23 @@
 #include <iostream>
 #include <limits.h>
 #include <iomanip>
+
 #define Infinity INT_MAX
 #define A 4
+
 using namespace std;
 
 void FloydWarshall(int graph[A][A]);
 
 void output(int length[A][A]);
 
-
 void FloydWarshall(int graph[A][A])
-{ int length[A][A],x,y,z;
+{
+  int length[A][A],x,y,z;
   for(x = 0; x < A; x++)
     for(y = 0; y < A; y++)
       length[x][y] = graph[x][y];
-
-
+
   for(z = 0; z < A; z++)
     for(x = 0; x < A; x++)
       for(y = 0; y < A; y++)
@@ -26,19 +27,22 @@ void FloydWarshall(int graph[A][A])
             length[x][y] = length[x][z] + length[z][y];
        }
   output(length);
-} 
+}
 
 void output(int length[A][A])
-{   cout << "The matrix below shows the shortest distances between each pair of vertices\n";
+{
+     cout << "The matrix below shows the shortest distances between each pair of vertices\n";
      for (int x = 0; x < A; x++)
-      {for (int y = 0; y < A; y++)
-        { if (length[x][y] == Infinity)
+      {
+        for (int y = 0; y < A; y++)
+        {
+          if (length[x][y] == Infinity)
            cout << setw(12) << "INFINITY";
           else
            cout << setw(12) << length[x][y];
         }
        cout << endl;
-      } 
+      }
 }
 
 int main() {
@@ -47,7 +51,7 @@ int main() {
                           {Infinity, Infinity, 0,        7},
                           {Infinity, Infinity, Infinity, 0}
                     };
-  FloydWarshall(graph);                
+  FloydWarshall(graph);
   return 0;
 }
 

Floyd_Warshall_Algorithm/Floyd_Warshall_Algorithm.go

@@ -1,5 +1,5 @@
 package main
- 
+
 import (
     "fmt"
     "math"
@@ -31,7 +31,7 @@ func floyd_warshall(graph [][]float64) [][]float64 {
     }
     return dist
 }
- 
+
 func main() {
     graph := [][]float64{
         {0, 5, math.Inf(1), 10},

Floyd_Warshall_Algorithm/Floyd_Warshall_Algorithm.py

@@ -44,7 +44,7 @@ def main():
              [float('inf'), float('inf'), 0, 1],
              [float('inf'), float('inf'), float('inf'), 0]]
 
-    
+
     floyd = FloydWarshall(graph)
     floyd.run()
     floyd.print_distance()

Ford_Fulkerson_Method/Ford_Fulkerson_Method.cpp

@@ -3,110 +3,111 @@
 #include <limits.h>
 #include <string.h>
 #include <queue>
+
 using namespace std;
- 
+
 // Number of vertices in given graph
 #define V 6
- 
+
 /* Returns true if there is a path from source 's' to sink 't' in
   residual graph. Also fills parent[] to store the path */
 bool bfs(int rGraph[V][V], int s, int t, int parent[])
 {
-    // Create a visited array and mark all vertices as not visited
-    bool visited[V];
-    memset(visited, 0, sizeof(visited));
- 
-    // Create a queue, enqueue source vertex and mark source vertex
-    // as visited
-    queue <int> q;
-    q.push(s);
-    visited[s] = true;
-    parent[s] = -1;
- 
-    // Standard BFS Loop
-    while (!q.empty())
-    {
-        int u = q.front();
-        q.pop();
- 
-        for (int v=0; v<V; v++)
-        {
-            if (visited[v]==false && rGraph[u][v] > 0)
-            {
-                q.push(v);
-                parent[v] = u;
-                visited[v] = true;
-            }
-        }
-    }
- 
-    // If we reached sink in BFS starting from source, then return
-    // true, else false
-    return (visited[t] == true);
+    // Create a visited array and mark all vertices as not visited
+    bool visited[V];
+    memset(visited, 0, sizeof(visited));
+
+    // Create a queue, enqueue source vertex and mark source vertex
+    // as visited
+    queue <int> q;
+    q.push(s);
+    visited[s] = true;
+    parent[s] = -1;
+
+    // Standard BFS Loop
+    while (!q.empty())
+    {
+        int u = q.front();
+        q.pop();
+
+        for (int v = 0; v < V; v++)
+        {
+            if (visited[v]==false && rGraph[u][v] > 0)
+            {
+                q.push(v);
+                parent[v] = u;
+                visited[v] = true;
+            }
+        }
+    }
+
+    // If we reached sink in BFS starting from source, then return
+    // true, else false
+    return (visited[t] == true);
 }
- 
+
 // Returns tne maximum flow from s to t in the given graph
 int fordFulkerson(int graph[V][V], int s, int t)
 {
-    int u, v;
- 
-    // Create a residual graph and fill the residual graph with
-    // given capacities in the original graph as residual capacities
-    // in residual graph
-    int rGraph[V][V]; // Residual graph where rGraph[i][j] indicates 
-                     // residual capacity of edge from i to j (if there
-                     // is an edge. If rGraph[i][j] is 0, then there is not)  
-    for (u = 0; u < V; u++)
-        for (v = 0; v < V; v++)
-             rGraph[u][v] = graph[u][v];
- 
-    int parent[V];  // This array is filled by BFS and to store path
- 
-    int max_flow = 0;  // There is no flow initially
- 
-    // Augment the flow while tere is path from source to sink
-    while (bfs(rGraph, s, t, parent))
-    {
-        // Find minimum residual capacity of the edhes along the
-        // path filled by BFS. Or we can say find the maximum flow
-        // through the path found.
-        int path_flow = INT_MAX;
-        for (v=t; v!=s; v=parent[v])
-        {
-            u = parent[v];
-            path_flow = min(path_flow, rGraph[u][v]);
-        }
- 
-        // update residual capacities of the edges and reverse edges
-        // along the path
-        for (v=t; v != s; v=parent[v])
-        {
-            u = parent[v];
-            rGraph[u][v] -= path_flow;
-            rGraph[v][u] += path_flow;
-        }
- 
-        // Add path flow to overall flow
-        max_flow += path_flow;
-    }
- 
-    // Return the overall flow
-    return max_flow;
+    int u, v;
+
+    // Create a residual graph and fill the residual graph with
+    // given capacities in the original graph as residual capacities
+    // in residual graph
+    int rGraph[V][V]; // Residual graph where rGraph[i][j] indicates
+    // residual capacity of edge from i to j (if there
+    // is an edge. If rGraph[i][j] is 0, then there is not) 
+    for (u = 0; u < V; u++)
+        for (v = 0; v < V; v++)
+            rGraph[u][v] = graph[u][v];
+
+    int parent[V];//This array is filled by BFS and to store path
+
+    int max_flow = 0;//There is no flow initially
+
+    // Augment the flow while tere is path from source to sink
+    while (bfs(rGraph, s, t, parent))
+    {
+        // Find minimum residual capacity of the edhes along the
+        // path filled by BFS. Or we can say find the maximum flow
+        // through the path found.
+        int path_flow = INT_MAX;
+        for (v=t; v!=s; v=parent[v])
+        {
+            u = parent[v];
+            path_flow = min(path_flow, rGraph[u][v]);
+        }
+
+        // update residual capacities of the edges and reverse edges
+        // along the path
+        for (v=t; v != s; v=parent[v])
+        {
+            u = parent[v];
+            rGraph[u][v] -= path_flow;
+            rGraph[v][u] += path_flow;
+        }
+
+        // Add path flow to overall flow
+        max_flow += path_flow;
+    }
+
+    // Return the overall flow
+    return max_flow;
 }
- 
+
 // Driver program to test above functions
 int main()
 {
-    // Let us create a graph shown in the above example
-    int graph[V][V] = { {0, 16, 13, 0, 0, 0},
-                        {0, 0, 10, 12, 0, 0},
-                        {0, 4, 0, 0, 14, 0},
-                        {0, 0, 9, 0, 0, 20},
-                        {0, 0, 0, 7, 0, 4},
-                        {0, 0, 0, 0, 0, 0}
-                      };
- 
-    cout << "The maximum possible flow is " << fordFulkerson(graph, 0, 5);
- 
-    return 0;
+    // Let us create a graph shown in the above example
+    int graph[V][V] = { {0, 16, 13, 0, 0, 0},
+                        {0, 0, 10, 12, 0, 0},
+                        {0, 4, 0, 0, 14, 0},
+                        {0, 0, 9, 0, 0, 20},
+                        {0, 0, 0, 7, 0, 4},
+                        {0, 0, 0, 0, 0, 0}
+                      };
+
+    cout << "The maximum possible flow is " << fordFulkerson(graph, 0, 5);
+
+    return 0;
 }

Ford_Fulkerson_Method/Ford_Fulkerson_Method.java

@@ -4,10 +4,10 @@
 
 
 class Ford_Fulkerson_Method {
-  
+
   //Number of vertices in graph
   static final int V = 6;
-  
+
   /* Returns true if there is a path from source 's' to sink
     't' in residual graph. Also fills parent[] to store the
     path */
@@ -118,7 +118,7 @@ public static void main (String[] args) throws java.lang.Exception
                          m.fordFulkerson(graph, 0, 5));
 
   }
-  
+
 
 }
 /* Output
@@ -127,4 +127,4 @@ public static void main (String[] args) throws java.lang.Exception
 
 
 
-*/
+*/