leetcode120. Triangle

120. Triangle

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle[     [2],    [3,4],   [6,5,7],  [4,1,8,3]]The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

解法一

自底向上，动态规划

public class Solution {    public int minimumTotal(List<List<Integer>> triangle) {        if (triangle == null || triangle.size() == 0) {            return -1;        }        if (triangle.get(0) == null || triangle.get(0).size() == 0) {            return -1;        }        // state: f.get(x).get(y) = minimum path value from x,y to bottom        int len = triangle.size();        // initail a new list        List<List<Integer>> minSum = new ArrayList<>();        List<Integer> temp = null；        for (int i = 0; i < len; i++) {            temp = new ArrayList<>();            for (int j = 0; j < triangle.get(i).size(); j++) {                temp.add(j, 0);            }            minSum.add(i, temp);        }        // initial last row        for (int j = 0; j < triangle.get(len - 1).size(); j++) {            minSum.get(len - 1).set(j, triangle.get(len - 1).get(j));        }        // bottom up        for (int i = len - 2; i >= 0; i--) {            for (int j = 0; j < minSum.get(i).size(); j++) {                minSum.get(i).set(j, Math.min(minSum.get(i + 1).get(j), minSum.get(i + 1).get(j + 1))                + triangle.get(i).get(j));            }        }        return minSum.get(0).get(0);    }}

解法二

直接在原list中进行变化。

public class Solution {    public int minimumTotal(List<List<Integer>> triangle) {        if (triangle == null || triangle.size() == 0) {            return -1;        }        if (triangle.get(0) == null || triangle.get(0).size() == 0) {            return -1;        }        // state: f.get(x).get(y) = minimum path value from x,y to bottom        int len = triangle.size();        // bottom up        for (int i = len - 2; i >= 0; i--) {            for (int j = 0; j <= i; j++) {                triangle.get(i).set(j, Math.min(triangle.get(i + 1).get(j), triangle.get(i + 1).get(j + 1))                        + triangle.get(i).get(j));            }        }        return triangle.get(0).get(0);    }}

解法三

up bottom，新初始化一个列表。

public class Solution {    public int minimumTotal(List<List<Integer>> triangle) {        if (triangle == null || triangle.size() == 0) {            return -1;        }        if (triangle.get(0) == null || triangle.get(0).size() == 0) {            return -1;        }        // state: f.get(x).get(y) = minimum path value from x,y to bottom        // initial new list        int len = triangle.size();        List<List<Integer>> minSum = new ArrayList<>();        List<Integer> temp = null;        for (int i = 0; i < len; i++) {            temp = new ArrayList<>();            for (int j = 0; j < triangle.get(i).size(); j++) {                temp.add(j, 0);            }            minSum.add(i, temp);        }        // initial        minSum.get(0).set(0, triangle.get(0).get(0));        for (int i = 1; i < len; i++) {            minSum.get(i).set(0, minSum.get(i - 1).get(0) + triangle.get(i).get(0));            minSum.get(i).set(i, minSum.get(i - 1).get(i - 1) + triangle.get(i).get(i));        }        // up bottom        for (int i = 1; i < len; i++) {            for (int j = 1; j < i; j++) {                minSum.get(i).set(j, Math.min(minSum.get(i - 1).get(j - 1), minSum.get(i - 1).get(j))                        + triangle.get(i).get(j));            }        }        int best = minSum.get(len - 1).get(0);        for (int i = 0; i < len; i++) {            if (minSum.get(len - 1).get(i) < best)                best = minSum.get(len - 1).get(i);        }        return best;    }}

解法四

up bottom基于原列表list

    public int minimumTotal(List<List<Integer>> triangle) {         if (triangle == null || triangle.size() == 0) {            return -1;        }        if (triangle.get(0) == null || triangle.get(0).size() == 0) {            return -1;        }        // state: f.get(x).get(y) = minimum path value from 0,0 to x,y        int len = triangle.size();        // up bottom        for (int i = 1; i < len; i++) {            for (int j = 0; j <= i; j++) {                if (j == 0) {                    triangle.get(i).set(j, triangle.get(i - 1).get(j)                            + triangle.get(i).get(j));                } else if (j == i) {                    triangle.get(i).set(j, triangle.get(i - 1).get(j - 1)                            + triangle.get(i).get(j));                } else {                    triangle.get(i).set(j, Math.min(triangle.get(i - 1).get(j - 1), triangle.get(i - 1).get(j))                            + triangle.get(i).get(j));                }            }        }        int best = triangle.get(len - 1).get(0);        for (int i = 0; i < len; i++) {            if (triangle.get(len - 1).get(i) < best)                best = triangle.get(len - 1).get(i);        }        return best;    }