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#!/usr/bin/env python

'''

Leetcode: Container With Most Water

Given n non-negative integers a1, a2, ..., an, where each represents a point at coordinate (i, ai). n vertical lines are drawn such that the two endpoints of line i is at (i, ai) and (i, 0). Find two lines, which together with x-axis forms a container, such that the container contains the most water.

Note: You may not slant the container.

'''

from __future__ import division

import random

# Find i < j to maximize (j-i)*min{ai, aj}, see 2sum

# O(n)

def container_water(a):

i, j = 0, len(a)-1

water = 0

water_i = water_j = None

while i < j:

cur = (j-i)* min(a[i], a[j])

if cur > water: water = cur; water_i = i; water_j = j

if a[i] < a[j]: i += 1

else: j -= 1

print '(%d,%d): %d' % (water_i,water_j,water)

return water

if __name__ == '__main__':

a = [2,1,3,2,4,5,2,3,1,4]

print container_water(a)