algorithms/cpp/trappingRainWater/trappingRainWater.cpp

// Source : https://oj.leetcode.com/problems/trapping-rain-water/
// Author : Hao Chen
// Date   : 2014-07-02

/********************************************************************************** 
* 
* Given n non-negative integers representing an elevation map where the width of each bar is 1, 
* compute how much water it is able to trap after raining. 
* 
* For example, 
* Given [0,1,0,2,1,0,1,3,2,1,2,1], return 6.
*   
*     ^                                             
*     |                                             
*   3 |                       +--+                  
*     |                       |  |                  
*   2 |          +--+xxxxxxxxx|  +--+xx+--+         
*     |          |  |xxxxxxxxx|  |  |xx|  |         
*   1 |   +--+xxx|  +--+xxx+--+  |  +--+  +--+      
*     |   |  |xxx|  |  |xxx|  |  |  |  |  |  |      
*   0 +---+--+---+--+--+---+--+--+--+--+--+--+----->
*       0  1   0  2  1   0  1  3  2  1  2  1        
* 
* The above elevation map is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 
* 6 units of rain water (blue section) are being trapped. Thanks Marcos for contributing this image!
*               
**********************************************************************************/

#include <stdio.h>
/*
 * The idea is:
 *    1) find the highest bar.
 *    2) traverse the bar from left the highest bar.
 *       becasue we have the highest bar in right, so, any bar higher than its right bar(s) can contain the water.
 *    3) traverse the bar from right the highest bar.
 *       becasue we have the highest bar in left, so, any bar higher than its left bar(s) can contain the water.
 *
 * The code below is quite clear!
 *
 */
int trap(int a[], int n) {
    int result = 0;

    //find the highest value/position
    int maxHigh = 0;
    int maxIdx = 0;
    for(int i=0; i<n; i++){
        if (a[i] > maxHigh){
            maxHigh = a[i];
            maxIdx = i;
        }
    }

    //from the left to the highest postion
    int prevHigh = 0;
    for(int i=0; i<maxIdx; i++){
        if(a[i] > prevHigh){
            prevHigh = a[i];
        }
        result += (prevHigh - a[i]);
    }

    //from the right to the highest postion
    prevHigh=0;
    for(int i=n-1; i>maxIdx; i--){
        if(a[i] > prevHigh){
            prevHigh = a[i];
        }
        result += (prevHigh - a[i]);
    }

    return result;
}

#define TEST(a) printf("%d\n", trap(a, sizeof(a)/sizeof(int)))
int main()
{
    int a[]={2,0,2};
    TEST(a);
    int b[]={0,1,0,2,1,0,1,3,2,1,2,1};
    TEST(b);
    return 0;
}