mark
// 已知lnx+x^2 =0 在（0,1）范围内有解，用数值方法求解, 精度0.0001
// 求二维矩阵从最左上角元素到最右下角元素的最短路径和，只能往右和往下,输出最
// 短路径和对应的路径
// 输入：map = [[2,3,1],[1,9,1],[6,4,2]]
// 输出：2->3->1->1->2
#include <iostream>
#include <vector>
using namespace std;
// 1
// fx = lnx + x^2
// fx’ = (1 / x) + 2 * x
// x(n+1) = x(n) - f(x)/ f(x)'
#include <math.h>
double newton_solve(double x){
double x0 = x;
double x1 = x0 - (log(x0) + pow(x0, 2)) / ((1 / x0) + 2 *x0);
int max_iter = 1000;
int iter = 0;
while(iter < max_iter && abs(x0 - x1) > 1e-4){
x0 = x1;
x1 = x0 - (log(x0) + pow(x0, 2)) / ((1 / x0) + 2 *x0);
iter += 1;
}
return x1;
}
// 2
//
// [[2,3,1],
// [1,9,1],
// [6,4,2]]
vector<int> minPath(vector<vector<int> > map){
// int minPath(vector<vector<int> > map){
int rows = map.size();
int cols = map[0].size();
vector<vector<int> > dp(rows, vector<int>(cols, 0));
int res = 0;
vector<vector<pair<int, int>>> path(rows, vector<pair<int, int>>(cols, {
0, 0}));
//vector<vector<int> > path(rows, vector<int>(cols, 0));
for(int i = 0; i < rows; i++){
for(int j = 0; j < cols; j++){
if(i == 0 && j == 0){
dp[i][j] = map[i][j];
path[i][j] = {
-1, -1};
}else if(i == 0){
dp[i][j] += dp[i][j - 1] + map[i][j];
path[i][j] = {
i, j - 1};
}else if(j == 0){
dp[i][j] += dp[i - 1][j] + map[i][j];
path[i][j] = {
i - 1, j};
}else{
dp[i][j] += min(dp[i - 1][j], dp[i][j - 1]) + map[i][j];
if(dp[i - 1][j] < dp[i][j - 1]){
path[i][j] = {
i - 1, j};
}else{
path[i][j] = {
i, j - 1};
}
}
}
}
// for(auto a : path){
// for(auto b : a){
// cout << b.first << "," << b.second << endl;
// }
// }
pair<int, int> tmp = path[rows - 1][cols - 1];
vector<int> path_all;
path_all.push_back(map[rows - 1][cols - 1]);
while(tmp.first!=-1 && tmp.second!=-1){
path_all.push_back(map[tmp.first][tmp.second]);
// cout << "path_all.size:" << path_all.size() << endl;
// for(auto a : path_all){
// cout << "a:" << a << endl;
// }
tmp = path[tmp.first][tmp.second];
// cout << "tmp:" << tmp.first << "," << tmp.second << endl;
}
// for(auto a : path_all){
// cout << a << endl;
// }
// return dp[rows - 1][cols - 1];
return path_all;
}
int main() {
vector<vector<int> > nums = {
{
2, 3, 1}, {
1, 9, 1}, {
6, 4, 2}};
// int res = minPath(nums);
// cout << "res:" << res << endl;
vector<int> res = minPath(nums);
// cout << "res:" << res << endl;
// for(auto a : res){
// cout << a << endl;
// }
for(int i = res.size() - 1; i>=0; i--){
cout << res[i];
}
double val = newton_solve(0.5);
cout << "val:" << val << endl;
}