# "Leetcode-Interview algorithm classic-java Implementation" "120-triangle (triangle)"

Source: Internet
Author: User

"120-triangle (triangle)" "leetcode-Interview algorithm classic-java Implementation" "All topics Directory Index" Original Question

Given a triangle, find the minimum path sum from top to bottom. Each step of the 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 one (i.e., `2 + 3 + 5 + 1 = 11` ).
Note:
Bonus Point If you be able to does this using only O (n) extra space, where n is the total number of rows in the triangle.

Main Topic

Given a triangle, find the smallest path from the top to the bottom, and each step can be moved from the previous row to the next row of adjacent numbers

Thinking of solving problems

Recursive equation:
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)) (0

Code Implementation

Algorithm implementation class

``Import java.util.List; Public classSolution { Public int Minimumtotal(list<list<integer>> triangle) {if(Triangle = =NULL|| Triangle.size () <1) {return 0; }//Create the second dimension of the array        int[] Minsum =New int[Triangle.size ()] [];//Create the first dimension of the array         for(inti =0; i < minsum.length; i++) {Minsum[i] =New int[i +1]; }//Set the first lineminsum[0][0] = triangle.Get(0).Get(0);//Set other rows         for(inti =1; i < minsum.length; i++) {list<integer> line = triangle.Get(i); for(intj =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]); }            }        }//Find the minimum value of the last line is the solution        intMin = minsum[minsum.length-1][0];intLength = Minsum[minsum.length-1].length; for(inti =1; i < length; i++) {if(Min > Minsum[length-1][i]) {min = minsum[length-1][i]; }        }returnMin }}``
Evaluation Results

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"Leetcode-Interview algorithm classic-java Implementation" "120-triangle (triangle)"

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