From d4d0020be95cfcead06893d2166c43190797782f Mon Sep 17 00:00:00 2001
From: juan <juancloudcomputing@protonmail.com>
Date: Mon, 28 Nov 2022 16:32:09 +0800
Subject: [PATCH] Add part1 of pset7

---
 semester3/pset7/7-1-Minimum-Spanning-Tree.c | 131 ++++++++++++++++++++
 semester3/pset7/7-2-DFS.c                   |  74 +++++++++++
 2 files changed, 205 insertions(+)
 create mode 100644 semester3/pset7/7-1-Minimum-Spanning-Tree.c
 create mode 100644 semester3/pset7/7-2-DFS.c

diff --git a/semester3/pset7/7-1-Minimum-Spanning-Tree.c b/semester3/pset7/7-1-Minimum-Spanning-Tree.c
new file mode 100644
index 0000000..ee14b6b
--- /dev/null
+++ b/semester3/pset7/7-1-Minimum-Spanning-Tree.c
@@ -0,0 +1,131 @@
+#include <stdio.h>
+#define SIZE 10
+#define INF 9999
+
+void createLine(int mat[SIZE][SIZE], char start, char end, int weight) {
+  mat[start - 'A'][end - 'A'] = weight;
+  mat[end - 'A'][start - 'A'] = weight;
+}
+
+int getMinNode(int* dist, int* visited) {
+  int minDist = INF, minEnd;
+  for (int i = 0; i < SIZE; i++) {
+    if (dist[i] < minDist && !visited[i]) {
+      minDist = dist[i];
+      minEnd = i;
+    }
+  }
+  return minEnd;
+}
+
+int min(int l, int r) {
+  return (l < r)? l : r;
+}
+
+void sort(int* ans, int size) {
+  // init bucket sort
+  int max = -1;
+  for (int i = 0; i < size; i++) {
+    if (ans[i] > max) {
+      max = ans[i];
+    }
+  }
+
+  int bucket[max + 1];
+  for (int i = 0; i < max + 1; i++) {
+    bucket[i] = 0;
+  }
+
+  // bucket sort
+  for (int i = 0; i < size; i++) {
+    bucket[ans[i]]++;
+  }
+
+  int count = 0;
+  int sorted[size];
+  for (int i = 0; i < max + 1; i++) {
+    while (bucket[i]) {
+      sorted[count++] = i;
+      bucket[i]--;
+    }
+  }
+
+  for (int i = 0; i < size; i++) {
+    ans[i] = sorted[i];
+  }
+}
+
+void createGraph(int mat[SIZE][SIZE]) {
+  for (int i = 0; i < SIZE; i++) {
+    for (int j = 0; j < SIZE; j++) {
+      mat[i][j] = INF;
+    }
+  }
+
+  createLine(mat, 'A', 'B', 3);
+  createLine(mat, 'A', 'E', 4);
+  createLine(mat, 'A', 'D', 4);
+  createLine(mat, 'B', 'A', 3);
+  createLine(mat, 'B', 'E', 2);
+  createLine(mat, 'B', 'F', 3);
+  createLine(mat, 'B', 'C', 10);
+  createLine(mat, 'C', 'F', 6);
+  createLine(mat, 'C', 'G', 1);
+  createLine(mat, 'D', 'E', 5);
+  createLine(mat, 'D', 'H', 6);
+  createLine(mat, 'E', 'F', 11);
+  createLine(mat, 'E', 'H', 2);
+  createLine(mat, 'E', 'I', 1);
+  createLine(mat, 'E', 'D', 5);
+  createLine(mat, 'F', 'E', 11);
+  createLine(mat, 'F', 'B', 3);
+  createLine(mat, 'F', 'C', 6);
+  createLine(mat, 'F', 'G', 2);
+  createLine(mat, 'F', 'J', 11);
+  createLine(mat, 'F', 'I', 3);
+  createLine(mat, 'G', 'J', 8);
+  createLine(mat, 'H', 'I', 4);
+  createLine(mat, 'I', 'J', 7);
+}
+
+int main(void) {
+  int mat[SIZE][SIZE];
+  createGraph(mat);
+
+  char start, end;
+  int weight;
+  scanf("%c,%c,%d", &start, &end, &weight);
+  mat[start - 'A'][end - 'A'] = weight; // the matrix is undirectional
+  mat[end - 'A'][start - 'A'] = weight;
+
+  int ans[SIZE - 1];
+  int dist[SIZE] = {};
+  for (int i = 1; i < SIZE; i++) {
+    dist[i] = INF;
+  }
+  int top = 0;
+
+  int cur;
+  int visited[SIZE] = {};
+
+  while (top != SIZE) {
+    cur = getMinNode(dist, visited);
+    visited[cur] = 1;
+
+    ans[top++] = dist[cur];
+
+    for (int j = 0; j < SIZE; j++) {
+      dist[j] = min(dist[j], mat[cur][j]);
+      // printf("%c -> %c: %d\n", cur + 'A', j + 'A', dist[j]);
+    }
+  }
+
+  ans[0] = ans[top - 1]; // top == SIZE
+
+  sort(ans, SIZE - 1);
+  for (int i = 0; i < SIZE - 1; i++) {
+    printf("%d,", ans[i]);
+  }
+
+  return 0;
+}
diff --git a/semester3/pset7/7-2-DFS.c b/semester3/pset7/7-2-DFS.c
new file mode 100644
index 0000000..ac5f136
--- /dev/null
+++ b/semester3/pset7/7-2-DFS.c
@@ -0,0 +1,74 @@
+#include <stdio.h>
+#include <stdlib.h>
+#define SIZE 9
+
+typedef struct stack {
+  int top;
+  int *arr;
+} stack;
+
+stack *newStack() {
+  stack *st = malloc(sizeof(stack));
+  st->top = 0;
+  st->arr = malloc(sizeof(int) * SIZE * 3);
+
+  return st;
+}
+
+void push(stack *st, int i) { st->arr[st->top++] = i; }
+
+int pop(stack *st) { return st->arr[--st->top]; }
+
+int isEmpty(stack *st) { return (st->top == 0); }
+
+int main(void) {
+  int mat[SIZE][SIZE] = {};
+
+  mat[1][2] = 1;
+  mat[1][3] = 1;
+  mat[2][1] = 1;
+  mat[2][4] = 1;
+  mat[2][5] = 1;
+  mat[3][1] = 1;
+  mat[3][6] = 1;
+  mat[3][7] = 1;
+  mat[4][2] = 1;
+  mat[4][8] = 1;
+  mat[5][2] = 1;
+  mat[5][8] = 1;
+  mat[6][3] = 1;
+  mat[6][8] = 1;
+  mat[7][3] = 1;
+  mat[7][8] = 1;
+  mat[8][4] = 1;
+  mat[8][5] = 1;
+  mat[8][6] = 1;
+  mat[8][7] = 1;
+
+  int visited[SIZE] = {};
+
+  int start;
+  scanf("%d", &start);
+
+  stack *st = newStack();
+
+  push(st, start);
+
+  int cur;
+
+  while (!isEmpty(st)) {
+    cur = pop(st);
+    if (!visited[cur]) {
+      visited[cur] = 1;
+      printf("%d,", cur);
+    }
+
+    for (int i = SIZE - 1; i > 0; i--) {
+      if (!visited[i] && mat[cur][i] == 1) {
+	push(st, i);
+      }
+    }
+  }
+
+  return 0;
+}