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dynamic_programming/max_sub_array.py

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+"""
+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()
+
+
+
+