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目录
爬楼梯
cpp
class Solution {
public:
int climbStairs(int n) {
int a = 0, b = 0, c = 1;
for (int i = 1; i <= n; i++)
{
a = b;
b = c;
c = a + b;
}
return c;
}
};杨辉三角
cpp
class Solution {
public:
vector<vector<int>> generate(int numRows) {
vector<vector<int>> res(numRows);
for (int i = 0; i < numRows; i++)
{
res[i].resize(i + 1, 1);
for (int j = 1; j < i; j++)
{
res[i][j] = res[i - 1][j - 1] + res[i - 1][j];
}
}
return res;
}
};打家劫舍
cpp
class Solution {
public:
int rob(vector<int>& nums) {
int n = nums.size();
vector<int> f(n), g(n);
f[0] = nums[0];
for (int i = 1; i < n; i++)
{
f[i] = g[i - 1] + nums[i];
g[i] = max(g[i - 1], f[i - 1]);
}
return max(f[n - 1], g[n - 1]);
}
};完全平方数
这是一个完全背包问题。
cpp
class Solution {
public:
int numSquares(int n) {
int m = sqrt(n);
vector<int> dp(n + 1, 0x3f3f3f3f);
dp[0] = 0;
for (int i = 1; i <= m; i++)
{
for (int j = i * i; j <= n; j++)
{
dp[j] = min(dp[j], dp[j - i * i] + 1);
}
}
return dp[n];
}
};零钱兑换
cpp
class Solution {
public:
int coinChange(vector<int>& coins, int amount) {
const int N = 0x3f3f3f3f;
vector<int> dp(amount + 1, N);
dp[0] = 0;
for (int i = 0; i < coins.size(); i++)
{
for (int j = coins[i]; j <= amount; j++)
{
dp[j] = min(dp[j], dp[j - coins[i]] + 1);
}
}
return dp[amount] >= N ? -1 : dp[amount];
}
};单词拆分
cpp
class Solution {
public:
bool wordBreak(string s, vector<string>& wordDict) {
unordered_set<string> hashset(wordDict.begin(), wordDict.end());
int n = s.size();
s = ' ' + s;
vector<bool> dp(n + 1);
dp[0] = true;
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= i; j++)
{
if (dp[j - 1] && hashset.count(s.substr(j, i - j + 1)))
{
dp[i] = true;
break;
}
}
}
return dp[n];
}
};最长递增子序列
cpp
class Solution {
public:
int lengthOfLIS(vector<int>& nums) {
int n = nums.size();
vector<int> dp(n, 1);
int res = 1;
for (int i = 1; i < n; i++)
{
for (int j = 0; j < i; j++)
{
if (nums[j] < nums[i])
dp[i] = max(dp[i], dp[j] + 1);
res = max(res, dp[i]);
}
}
return res;
}
};贪心解法。
cpp
class Solution {
public:
int lengthOfLIS(vector<int>& nums) {
int n = nums.size();
vector<int> v;
for (auto e : nums)
{
if (v.empty() || e > v.back()) v.push_back(e);
else
{
int l = 0, r = v.size() - 1;
while (l < r)
{
int mid = (r + l) / 2;
if (v[mid] < e) l = mid + 1;
else r = mid;
}
v[l] = e;
}
}
return v.size();
}
};最大子数组和
dp[i] 表示以 i 位置为结尾的所有连续子数组的最大和。
cpp
class Solution {
public:
int maxSubArray(vector<int>& nums) {
int n = nums.size();
vector<int> dp(n + 1);
int res = -0x3f3f3f3f;
for (int i = 1; i <= n; i++)
{
dp[i] = max(dp[i - 1], 0) + nums[i - 1];
res = max(res, dp[i]);
}
return res;
}
};
cpp
class Solution {
public:
int maxSubArray(vector<int>& nums) {
int pre = 0, res = -0x3f3f3f3f;
for (auto e : nums)
{
pre = (pre, 0) + e;
res = max(res, pre);
}
return res;
}
};乘积最大子数组
cpp
class Solution {
public:
int maxProduct(vector<int>& nums) {
int n = nums.size(), res = -0x3f3f3f3f;
vector<int> f(n + 1, 1), g(n + 1, 1);
for (int i = 1; i <= n; i++)
{
int x = nums[i - 1];
int y = x * f[i - 1], z = x * g[i - 1];
f[i] = max(x, max(y, z));
g[i] = min(x, min(y, z));
res = max(res, f[i]);
}
return res;
}
};分割等和子集
cpp
class Solution {
public:
bool canPartition(vector<int>& nums) {
int sum = 0;
for (auto e : nums) sum += e;
if (sum % 2) return false;
sum /= 2;
vector<bool> dp(sum + 1);
dp[0] = true;
for (int i = 0; i < nums.size(); i++)
{
for (int j = sum; j >= nums[i]; j--)
{
dp[j] = dp[j] || dp[j - nums[i]];
}
}
return dp[sum];
}
};最长有效括号
初始化 -1 处理第一个字符就是 ) 的情况，避免栈操作错误。
栈中存储未匹配的
（下标或无效）下标。
cpp
class Solution {
public:
int longestValidParentheses(string s) {
stack<int> st;
st.push(-1);
int len = 0;
for (int i = 0; i < s.size(); i++)
{
if (s[i] == '(') st.push(i);
else
{
st.pop();
if (st.empty()) st.push(i);
else len = max(len, i - st.top());
}
}
return len;
}
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