Merge pull request TheAlgorithms#107 from mk9440/master

Maximum_subaray_problem

dynamic_programming/longest common subsequence.py

@@ -3,16 +3,46 @@
 A subsequence is a sequence that appears in the same relative order, but not necessarily continious.
 Example:"abc", "abg" are subsequences of "abcdefgh". 
 """
-def LCS(s1, s2):
-    m = len(s1)
-    n = len(s2)
+def LCS(x,y):
+    b=[[] for j in range(len(x)+1)]
+    c=[[] for i in range(len(x))]
+    for i in range(len(x)+1):
+        b[i].append(0)
+    for i in range(1,len(y)+1):
+        b[0].append(0)
+    for i in range(len(x)):
+        for j in range(len(y)):
+            if x[i]==y[j]:
+                b[i+1].append(b[i][j]+1)
+                c[i].append('/')
+            elif b[i][j+1]>=b[i+1][j]:
+                b[i+1].append(b[i][j+1])
+                c[i].append('|')
+            else :
+                b[i+1].append(b[i+1][j])
+                c[i].append('-')            
+    return b,c
 
-    arr = [[0 for i in range(n+1)]for j in range(m+1)]
 
-    for i in range(1,m+1):
-        for j in range(1,n+1):
-            if s1[i-1] == s2[j-1]:
-                arr[i][j] = arr[i-1][j-1]+1
-            else:
-                arr[i][j] = max(arr[i-1][j], arr[i][j-1])
-    return arr[m][n]
+def print_lcs(x,c,n,m):
+    n,m=n-1,m-1
+    ans=[]
+    while n>=0 and m>=0:
+        if c[n][m]=='/':
+            ans.append(x[n])
+            n,m=n-1,m-1
+        elif c[n][m]=='|':
+            n=n-1
+        else:
+            m=m-1 
+    ans=ans[::-1]
+    return ans                   
+
+
+if __name__=='__main__':
+    x=['a','b','c','b','d','a','b']
+    y=['b','d','c','a','b','a']
+    b,c=LCS(x,y)
+    print('Given \nX : ',x)
+    print('Y : ',y)
+    print('LCS : ',print_lcs(x,c,len(x),len(y)))

dynamic_programming/max_sub_array.py

@@ -0,0 +1,59 @@
+"""
+author : Mayank Kumar Jha (mk9440)
+"""
+
+import time
+import matplotlib.pyplot as plt
+from random import randint
+def find_max_sub_array(A,low,high):
+    if low==high:
+        return low,high,A[low]
+    else :
+        mid=(low+high)//2        
+        left_low,left_high,left_sum=find_max_sub_array(A,low,mid)
+        right_low,right_high,right_sum=find_max_sub_array(A,mid+1,high)
+        cross_left,cross_right,cross_sum=find_max_cross_sum(A,low,mid,high)
+        if left_sum>=right_sum and left_sum>=cross_sum:
+            return left_low,left_high,left_sum
+        elif right_sum>=left_sum and right_sum>=cross_sum :
+            return right_low,right_high,right_sum
+        else:
+            return cross_left,cross_right,cross_sum
+
+def find_max_cross_sum(A,low,mid,high):
+    left_sum,max_left=-999999999,-1
+    right_sum,max_right=-999999999,-1
+    summ=0
+    for i in range(mid,low-1,-1):
+        summ+=A[i]
+        if summ > left_sum:
+            left_sum=summ
+            max_left=i
+    summ=0        
+    for i in range(mid+1,high+1):
+        summ+=A[i]
+        if summ > right_sum:
+            right_sum=summ
+            max_right=i
+    return max_left,max_right,(left_sum+right_sum)
+
+
+if __name__=='__main__':
+    inputs=[10,100,1000,10000,50000,100000,200000,300000,400000,500000]
+    tim=[]
+    for i in inputs:
+        li=[randint(1,i) for j in range(i)]
+        strt=time.time()
+        (find_max_sub_array(li,0,len(li)-1))
+        end=time.time()
+        tim.append(end-strt)
+    print("No of Inputs       Time Taken")    
+    for i in range(len(inputs)):    
+        print(inputs[i],'\t\t',tim[i])
+    plt.plot(inputs,tim)
+    plt.xlabel("Number of Inputs");plt.ylabel("Time taken in seconds ")
+    plt.show()
+
+
+
+