Python/dynamic_programming/max_sub_array.py

"""
author : Mayank Kumar Jha (mk9440)
"""
from __future__ import print_function

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()