您现在的位置是：首页 >技术交流 >动态规划问题网站首页技术交流

动态规划：记录前一部分的最优解，与后文进行比较

经典dp问题 力扣62：不同路径https://leetcode.cn/problems/unique-paths/description/

 先初始化第一行第一列路径只有一条，然后dp[i][j] = dp[i - 1][j] + dp[i][j - 1]

    public int uniquePaths(int m, int n) {
        int dp[][] = new int[m][n];
        for(int i = 0; i < n; i++) dp[0][i] = 1;
        for(int i = 0; i < m; i++) dp[i][0] = 1;
        for(int i = 1; i < m; i++){
            for(int j = 1; j < n; j++){
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[m - 1][n - 1];
    }
}

力扣118：杨辉三角https://leetcode.cn/problems/pascals-triangle/description/

    public List<List<Integer>> generate(int numRows) {
        List<List<Integer>> res = new ArrayList<>(); 
        int dp[][] = new int[numRows][numRows];
        for(int i = 0; i < numRows; i++){
            List<Integer> list = new ArrayList<>();
            for(int j = 0; j <= i; j++){
                if(j == 0){
                    dp[i][j] = 1;
                    list.add(1);
                }else{
                    dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j];
                    list.add(dp[i][j]);
                }
            }
            res.add(list);
        }
        return res;
    }

分治法：大事化小，逐一解决

力扣53 最大子数和https://leetcode-cn.com/problems/maximum-subarray/submissions/

    public int maxSubArray(int[] nums) {
        int maxSum = nums[0], thisSum = 0;
        for(int num : nums){
            thisSum += num;
            if(thisSum > maxSum) maxSum = thisSum;
            if(thisSum < 0) thisSum = 0;
        }
        return maxSum;
    }

dp：力扣47 礼物的最大值https://leetcode.cn/problems/li-wu-de-zui-da-jie-zhi-lcof/

    public int maxValue(int[][] grid) {
        int n = grid.length, m = grid[0].length;
        int dp[][] = new int[n+1][m+1];

        for(int i = 0; i < n; i++){
            for(int j = 0;j < m; j++){
                dp[i+1][j+1] = Math.max(dp[i][j+1] + grid[i][j], dp[i+1][j] + grid[i][j]);
            }
        } 
        return dp[n][m];
    }