From 0bbf19a8433eaf8ff650d8d4e2ac036f5874c632 Mon Sep 17 00:00:00 2001
From: unlockable <g@unlockableworld.com>
Date: Tue, 26 Dec 2023 14:18:48 +0800
Subject: [PATCH] 2 WA...

---
 .gitignore              |   3 +-
 2023208/main.cpp        |   8 +--
 2023208/vandermonde.cpp | 124 ++++++++++++++++++++++++++++++++++++++++
 3 files changed, 130 insertions(+), 5 deletions(-)
 create mode 100644 2023208/vandermonde.cpp

diff --git a/.gitignore b/.gitignore
index 397b0c7..3f53dd8 100644
--- a/.gitignore
+++ b/.gitignore
@@ -7,4 +7,5 @@
 *.o
 *.dat
 *.ilk
-*.pdb
\ No newline at end of file
+*.pdb
+*.in
\ No newline at end of file
diff --git a/2023208/main.cpp b/2023208/main.cpp
index 98df10a..250b893 100644
--- a/2023208/main.cpp
+++ b/2023208/main.cpp
@@ -44,7 +44,7 @@ int main() {
     for (int i = 0; i < n; i++) {
         scanf("%lf %lf", &read_x, &read_y);
         for (int j = 0; j < valid_point_num; j++) {
-            if (compare_double(read_x, point_xs[valid_point_num])) {
+            if (compare_double(read_x, point_xs[j])) {
                 found_duplicate = true;
                 break;
             }
@@ -70,11 +70,11 @@ int main() {
         for (int i = 0; i < row; i++) {
             t[row] -= t[i] * get_num(row, i);
         }
-        if (!compare_double(t[row], 0)) {
-            t[row] /= get_num(row, row);
+        if (compare_double(t[row] / 1000, 0)) {
+            t[row] = 0;
         } 
         else {
-            t[row] = 0;
+            t[row] /= get_num(row, row);
         }
     }
 
diff --git a/2023208/vandermonde.cpp b/2023208/vandermonde.cpp
new file mode 100644
index 0000000..d3f3744
--- /dev/null
+++ b/2023208/vandermonde.cpp
@@ -0,0 +1,124 @@
+#include <stdio.h>
+#define EPSILON 1e-6
+struct Point {
+    double x, y;
+};
+
+double A[101][101] = {0};
+Point points[101] = {0};
+int valid_point_num = 0;
+int n = 0, m = 0;
+
+int display_matrix() {
+    for (int i = 0; i < valid_point_num; i++) {
+        for (int j = 0; j < valid_point_num; j++) {
+            printf("%lf ", A[i][j]);
+        }
+        printf("| %lf\n", points[i].y);
+    }
+    printf("\n");
+    return 0;
+}
+
+int display_result_vec() {
+    for (int i = 0; i < valid_point_num; i++) {
+        printf("%lf ", points[i].x);
+    }
+
+    printf("\n");
+    return 0;
+}
+
+bool compare_double(double a, double b) {
+    return (a - b > 0 ? a - b : -(a - b)) < EPSILON;
+}
+
+double evaluate(double x, int highest) {
+    double ans = points[highest].x;
+    for (int i = highest + 1; i < valid_point_num; i++) {
+        ans *= x;
+        ans += points[i].x;
+    }
+    return ans;
+}
+
+int main() {
+    // freopen("lambdaeight19.in", "r", stdin);
+    scanf("%d %d", &n, &m);
+    for (int i = 0; i < n; i++) {
+        bool found_duplicate = false;
+        double read_x, read_y;
+        scanf("%lf %lf", &read_x, &read_y);
+        for (int j = 0; j < valid_point_num; j++) {
+            if (compare_double(read_x, points[j].x)) {
+                found_duplicate = true;
+                break;
+            }
+        }
+
+        if (!found_duplicate) {
+            points[valid_point_num++] = Point {read_x, read_y};
+        }
+
+    }
+    
+    // vandermonde matrix
+    for (int i = 0; i < valid_point_num; i++) {
+        A[i][n - 1] = 1;
+        for (int j = valid_point_num - 2; j >= 0; j--) {
+            A[i][j] = points[i].x * A[i][j + 1];
+        }
+    }
+
+    // display_matrix();
+
+    // Gauss
+    for (int col = 0; col < valid_point_num; col++) {
+        for (int row = col + 1; row < valid_point_num; row++) {
+            if (compare_double(A[col][col], 0)) {
+                continue;
+            }
+            double coeff =  - A[row][col] / A[col][col];
+            A[row][col] = 0;
+            for (int i = col + 1; i < valid_point_num; i++) {
+                A[row][i] += coeff * A[col][i];
+            }
+            points[row].y += coeff * points[col].y;
+        }
+        display_matrix();
+    }
+
+    // Solve for x
+    for (int i = valid_point_num - 1; i >= 0; i--) {
+        for (int j = valid_point_num - 1; j > i; j--) {
+            points[i].y -= points[j].x * A[i][j];
+        }
+        if (compare_double(points[i].y, 0)) {
+            points[i].x = 0;
+        } else {
+            points[i].x = points[i].y / A[i][i];
+        }
+        // display_result_vec();
+    }
+
+    display_result_vec();
+
+    // Find highest
+    int highest = 0;
+    for (int i = 0; i < valid_point_num; i++) {
+        if (!compare_double(points[i].x, 0)) {
+            highest = i;
+            break;
+        }
+    }
+
+    printf("%d\n", valid_point_num - 1 - highest);
+
+    //Evaluate
+    for (int i = 0; i < m; i++) {
+        double to_be_evaled = 0;
+        scanf("%lf", &to_be_evaled);
+        printf("%lf\n", evaluate(to_be_evaled, highest));
+    }
+    return 0;
+}
\ No newline at end of file