Twitter算法面试题详解（Java实现）——Trapping Rain Water

【算法题：求出高低不同的砖中能存多少水】

「Trapping Rain Water」

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.

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. 

 

解法思路：先找出数列中最左和最右的数值最大值，序列号为p、q(若最大值唯一则p、q相同)，然后分三段计算存水量，具体代码如下：

/*
 * 算法题：求高低不同的砖中能存多少水
 */

import java.util.ArrayList;
import java.util.List;

public class FillWater {

    public static void main(String[] args) {

        int num[] = { 0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1 };
        List<Integer> stone = new ArrayList<Integer>();
        for (int i = 0; i < num.length; i++) {
            stone.add(num[i]);
        }
        int result = 0;
        int p = 0, q = 0;// 找出左右最高点序号
        for (int j = 0; j < stone.size(); j++) {
            if (stone.get(j) > stone.get(p)) {
                p = j;
                q = j;
            } else if (stone.get(j) == stone.get(p)) {
                q = j;
            }
            System.out.println("p: " + p + " , q: " + q);
        }
        result += calcL(stone.subList(0, p + 1)) + calcH(stone.subList(p, q + 1))
                + calcR(stone.subList(q, stone.size()));

        System.out.println("result: " + result);
    }

    // 处理中段：p-q
    static int calcH(List<Integer> a) {
        int waterHigh = 0;
        for (int i = 0; i < a.size(); i++) {
            waterHigh += a.get(0) - a.get(i);
        }
        System.out.println("waterHigh: " + waterHigh);
        return waterHigh;
    }

    // 处理左段：0-p
    static int calcL(List<Integer> a) {
        int waterLeft = 0;
        for (int i = 1; i < a.size(); i++) {
            if (a.get(i) < a.get(i - 1)) {
                waterLeft += a.get(i - 1) - a.get(i);
                a.set(i, a.get(i - 1));
            }
        }
        System.out.println("waterLeft: " + waterLeft);
        return waterLeft;
    }

    // 处理右段：q-end
    static int calcR(List<Integer> a) {
        int waterRight = 0;
        for (int i = a.size() - 2; i > 0; i--) {
            if (a.get(i) < a.get(i + 1)) {
                waterRight += a.get(i + 1) - a.get(i);
                a.set(i, a.get(i + 1));
            }
        }
        System.out.println("waterRight: " + waterRight);
        return waterRight;
    }

}