Analysis on “Container With Most Water ”

　　Container With Most Water Problem：

　　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.

　　Analysis: 

　　The wooden barrel principle, the bucket of water storage depends on the shortest board.     //木桶原理，水桶中的存水量取决于短板。

　　step i: set two pointer istart and iend  to point the current working min and max index of the  array, initialize them as: istart = 0, iend = height.size() - 1;

　　step ii. when the lower index istart is less than the higher index iend, move the "short board" to gain the volume of the new container, likewise: the area = min(height[istart], height[iend]) * (iend - istart); otherwise, return the larger volume between the current max volume and the volume of the new container;

　　step iii.do step ii till istart less than iend; 

　　So the c++sourcecode:

　　#include <vector>//vector

　　using std::vector;

　　#include <limits.h>//INT_MIN

　　#include <windows.h>//min, max

　　int maxArea(vector<int> &height) {

　　int istart = 0, iend = height.size()-1;

　　int result = INT_MIN;

　　while (istart < iend) {

　　　　int area = min(height[istart], height[iend]) * (iend - istart);

　　　　result = max(result, area);     // Error code: int reslut = max(result, area); redefinition the global variable as a Local variable

　　　　if (height[istart] <= height[iend]) {

　　　　　　++istart;

　　　　}else {

　　　　　　--iend;

　　　　}

　　}

　　return result;

　　}

　　What I have learnt from this problem

1. when using global variable, you should be initialize it and must mind where you use it, use it correct. Don't redefinition it as a Local variable, never do it again;
   
2. draw a mind map in your paper to think very clearly before you coding;
3. C++ allow program redefine the variable in the inner scope that have already defined in the outer scope, so this is a trip when you have no idea about the mechanism.