Triangle Algorithm
The Triangle Algorithm is a geometric-based approach used in various fields such as computer graphics, image processing, and pattern recognition to solve problems like point location, convex hull construction, and mesh generation. The fundamental idea behind the algorithm is to divide a given set of points into a set of non-overlapping triangles, forming a triangulated irregular network (TIN). These networks can be used to approximate surfaces, model terrains, or represent 2D shapes for various applications. The Delaunay triangulation and Voronoi diagram are two popular techniques employed in the triangle algorithm to optimize the distribution and connectivity of triangles, ensuring that they maintain certain desirable properties such as maximal minimum angle or minimal maximum edge length.
The Triangle Algorithm has several advantages due to its simplicity, efficiency, and adaptability. First, the method can be applied to both structured and unstructured data, making it versatile and suitable for a wide range of applications. Second, the algorithm can be easily parallelized, allowing for significant speedup in computation through the use of multi-core processors or GPU hardware. Finally, triangle-based representations can be easily refined or coarsened to meet specific requirements, such as accuracy or computational complexity. This adaptability has led to the widespread adoption of the Triangle Algorithm in various domains, from computer graphics and visualization to geographic information systems and computational geometry.
class Solution {
public:
int minimumTotal(vector<vector<int> > &triangle) {
int level = triangle.size();
vector<int> dp(level + 1, 0);
for (int i = level - 1; i >= 0; i--) {
for (int j = 0; j <= i; j++) {
dp[j] = triangle[i][j] + min(dp[j], dp[j+1]);
}
}
return dp[0];
}
};
