题目描述
给定一个三角形,找出从顶到底的最小路径和,每一步可以从上一行移动到下一行相邻的数字
[
[2],
[3,4],
[6,5,7],
[4,1,8,3]
]
解题思路
递推方程:
f(0,0)=a[0][0]
f(i,0)=a[i][0]+f(i-1,0) (i>0)
f(i,i)=a[i][i]+f(i-1,i-1)(i>0)
f(i,j)=a[i][j]+MIN(f(i-1,j),f(i-1,j-1))
python
import copy
class Solution:
def minimumTotal(self, triangle):
"""
:type triangle: List[List[int]]
:rtype: int
"""
temp = copy.deepcopy(triangle)
for i in range(1,len(temp)):
for j in range(len(temp[i])):
if j==0:
temp[i][j] = triangle[i][j]+temp[i-1][j]
elif j<i:
temp[i][j] = triangle[i][j] + min(temp[i-1][j],temp[i-1][j-1])
elif j==i:
temp[i][j] = triangle[i][j]+temp[i-1][j-1]
return min(temp[-1])
if __name__ == '__main__':
a = Solution()
test = [[1],[2,3],[3,4,5]]
print(a.minimumTotal(test))
应该不是最优雅的写法,算是勉强实现了想法吧。
import java.util.List;
public class Solution {
public int minimumTotal(List<List<Integer>> triangle) {
if (triangle == null || triangle.size() < 1) {
return 0;
}
// 创建数组的第二维度
int[][] minSum = new int[triangle.size()][];
// 创建数组的第一维度
for (int i = 0; i < minSum.length; i++) {
minSum[i] = new int[i + 1];
}
// 设置第一行
minSum[0][0] = triangle.get(0).get(0);
// 设置其它行
for (int i = 1; i < minSum.length; i++) {
List<Integer> line = triangle.get(i);
for (int j = 0; j < minSum[i].length; j++) {
if (j == 0) {
minSum[i][0] = line.get(0) + minSum[i - 1][0];
} else if (i == j) {
minSum[i][j] = line.get(j) + minSum[i - 1][j - 1];
} else if (j < i) {
minSum[i][j] = line.get(j) + Math.min(minSum[i - 1][j], minSum[i - 1][j - 1]);
}
}
}
//找最后一行的最小值就是所求的解
int min = minSum[minSum.length - 1][0];
int length = minSum[minSum.length - 1].length;
for (int i = 1; i < length; i++) {
if (min > minSum[length - 1][i]) {
min = minSum[length - 1][i];
}
}
return min;
}
}