public void quickSort(int[] nums, int left, int right) {
if (left >= right)
return;
int i = left - 1, j = right + 1, x = nums[left];
while (i < j) {
do i++; while (nums[i] < x);
do j--; while (nums[j] > x);
if (i < j) {
int temp = nums[i];
nums[i] = nums[j];
nums[j] = temp;
}
}
quickSort(nums, left, j);
quickSort(nums, j + 1, right);
}mergeSort时间复杂度是稳定O(nlogn)，空间复杂度O(n)，稳定的。quickSort时间复杂度平均O(nlogn)，最坏O(n^2)，最好O(nlogn)，空间复杂度O(nlogn)，不稳定的。
public void mergeSort(int[] nums, int left, int right) {
if (left >= right)
return;
int mid = left + (right - left) / 2;
mergeSort(nums, left, mid);
mergeSort(nums, mid + 1, right);
int k = 0, i = left, j = mid + 1;
int[] temp = new int[right - left + 1];
while (i <= mid && j <= right)
if (nums[i] < nums[j])
temp[k++] = nums[i++];
else
temp[k++] = nums[j++];
while (i <= mid)
temp[k++] = nums[i++];
while (j <= right)
temp[k++] = nums[j++];
for (i = left, j = 0; i <= right; i++, j++)
nums[i] = temp[j];
}public int kmp(String text, String pattern) {
int m = pattern.length();
if (m == 0)
return 0;
int n = text.length();
int[] next = new int[m + 1];
for (int i = 2, j = 0; i <= m; i++) {
while (j > 0 && pattern.charAt(i - 1) != pattern.charAt(j))
j = next[j];
if (pattern.charAt(i - 1) == pattern.charAt(j))
j++;
next[i] = j;
}
for (int i = 1, j = 0; i <= n; i++) {
while (j > 0 && text.charAt(i - 1) != pattern.charAt(j))
j = next[j];
if (text.charAt(i - 1) == pattern.charAt(j))
j++;
if (j == m)
return i - m;
}
return -1;
}public static final int SIZE = 26;
public static class TrieNode {
TrieNode[] children = new TrieNode[SIZE];
int times;
TrieNode() {
times = 0;
for (int i = 0; i < SIZE; i++)
children[i] = null;
}
}
public static TrieNode root = new TrieNode();
public static void insert(String word) {
TrieNode node = root;
for (int i = 0; i < word.length(); i++) {
int index = word.charAt(i) - 'a';
if (node.children[index] == null)
node.children[index] = new TrieNode();
node = node.children[index];
}
node.times++;
}
public static int query(String word) {
TrieNode node = root;
for (int i = 0; i < word.length(); i++) {
int index = word.charAt(i) - 'a';
if (node.children[index] == null)
return 0;
node = node.children[index];
}
return node.times;
}朴素并查集
public static int[] p;
public static int find(int x) {
if (p[x] != x)
p[x] = find(p[x]);
return p[x];
}
p[find(a)] = find(b);public class Main{
public static final int INF = 0x3f3f3f3f;
public static int n;
public static int[][] g;
public static int[] dist;
public static boolean[] visit;
public static void main(String[] args) {
Scanner scan = new Scanner(System.in);
n = scan.nextInt();
int m = scan.nextInt();
g = new int[n + 1][n + 1];
dist = new int[n + 1];
visit = new boolean[n + 1];
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++)
if (i == j)
g[i][j] = 0;
else
g[i][j] = INF;
for (int i = 0; i < m; i++) {
int x = scan.nextInt(), y = scan.nextInt(), z = scan.nextInt();
g[a][b] = Math.min(g[a][b], c);
}
int res = dijkstra();
System.out.println(res);
}
}边权不能是负数！ 1.dist[1] = 0, dist[i] = +∞ 2.for i 1 ~ n t <- 不在s中的，距离最近的点 – n2n2 / n s <- t – n 用t更新其他点的距离 – m / mlogn
public static int dijkstra() {
for (int i = 1; i <= n; i++)
dist[i] = INF;
dist[1] = 0;
for (int i = 0; i < n - 1; i++) {
int t = -1;
for (int j = 1; j <= n; j++)
if (!visit[j] && (t == -1 || dist[t] > dist[j]))
t = j;
if (t == n)
break;
for (int j = 1; j <= n; j++)
dist[j] = Math.min(dist[j], dist[t] + g[t][j]);
visit[t] = true;
}
if (dist[n] == INF)
return -1;
return dist[n];
}public static int dijkstra() {
for (int i = 1; i <= n; i++)
dist[i] = INF;
dist[1] = 0;
PriorityQueue<Node> heap = new PriorityQueue<>((node1, node2) -> node1.length - node2.length);
heap.add(new Node(1, 0));
while (!heap.isEmpty()) {
Node top = heap.poll();
int length = top.length, cur = top.node;
if (visit[cur])
continue;
visit[cur] = true;
for (Node next: map.get(cur)) {
int node = next.node, cost = next.length;
if (dist[node] > length + cost) {
dist[node] = length + cost;
heap.add(new Node(node, dist[node]));
}
}
}
if (dist[n] == INF)
return -1;
return dist[n];
}O(nm)
public static int bellman_ford() {
for (int i = 1; i <= n; i++)
dist[i] = INF;
dist[1] = 0;
for (int i = 0; i < k; i++) {
for (int j = 1; j <= n; j++)
backup[j] = dist[j]; // deep copy
for (int k = 0; k < m; k++) {
int x = edges[k].x;
int y = edges[k].y;
int z = edges[k].z;
dist[y] = Math.min(dist[y], backup[x] + z);
}
}
if (dist[n] > INF / 2)
return -1;
else
return dist[n];
}一般O(m)，最坏O(nm)。n表示点数，m表示边数。
public static int spfa() {
for (int i = 1; i <= n; i++)
dist[i] = INF;
dist[1] = 0;
Queue<Integer> queue = new LinkedList<>();
queue.add(1);
visit[1] = true;
while (!queue.isEmpty()) {
int t = queue.poll();
visit[t] = false;
for (Node cur: map.get(t)) {
int node = cur.node, length = cur.length;
if (dist[node] > dist[t] + length) {
dist[node] = dist[t] + length;
if (!visit[node]) {
queue.add(node);
visit[node] = true;
}
}
}
}
return dist[n];
}O(nm)，n表示点数，m表示边数。
public static boolean spfa() {
Queue<Integer> queue = new LinkedList<>();
for (int i = 1; i <= n; i++) {
queue.add(i);
visit[i] = true;
}
while (!queue.isEmpty()) {
int t = queue.poll();
visit[t] = false;
for (Node cur: map.get(t)) {
int node = cur.node, length = cur.length;
if (dist[node] > dist[t] + length) {
dist[node] = dist[t] + length;
count[node] = count[t] + 1;
if (count[node] >= n)
return true;
if (!visit[node]) {
queue.add(node);
visit[node] = true;
}
}
}
}
return false;
}Floyd O(n3)O(n3)
public static void floyd() {
for (int k = 1; k <= n; k++)
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++)
d[i][j] = Math.min(d[i][j], d[i][k] + d[k][j]);
}