算法奇妙屋(十一)-不同路径问题(动态规划)

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

    public int uniquePathsWithObstacles(int[][] obstacleGrid) {
        // 创建dp表
        int m = obstacleGrid.length;
        int n = obstacleGrid[0].length;
        int[][] dp = new int[m + 1][n + 1];
        // 初始化
        dp[0][1] = 1;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (obstacleGrid[i][j] == 0) {
                    dp[i + 1][j + 1] = dp[i][j + 1] + dp[i + 1][j];
                }
            }
        }
        return dp[m][n];
    }

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

    public int minFallingPathSum(int[][] matrix) {
        // 创建dp表
        int m = matrix.length;
        int n = matrix[0].length;
        int[][] dp = new int[m + 1][n + 2];
        // 初始化dp表
        for (int i = 0; i < m + 1; i++) {
            dp[i][0] = dp[i][n + 1] = Integer.MAX_VALUE;
        }
        // 求dp值
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n ; j++) {
                dp[i][j] = Math.min(dp[i - 1][j], Math.min(dp[i - 1][j - 1], dp[i - 1][j + 1])) + matrix[i - 1][j - 1];
            }
        }
        int ret = dp[m][1];
        for (int j = 2; j <= n; j++) {
            ret = Math.min(ret, dp[m][j]);
        }
        return ret;
    }

    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[][] dp = new int[m + 1][n + 1];
        for (int i = 0; i <= m; i++) {
            dp[i][0] = Integer.MAX_VALUE;
        }
        for (int j = 0; j <= n; j++) {
            dp[0][j] = Integer.MAX_VALUE;
        }
        dp[0][1] = dp[1][0] = 0;
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i - 1][j - 1];
            }
        }
        return dp[m][n];
    }

    public int calculateMinimumHP(int[][] dungeon) {
        int m = dungeon.length;
        int n = dungeon[0].length;
        int[][] dp = new int[m + 1][n + 1];
        for (int i = 0; i <= m; i++) {
            dp[i][n] = Integer.MAX_VALUE;
        }
        for (int j = 0; j <= n; j++) {
            dp[m][j] = Integer.MAX_VALUE;
        }
        dp[m][n - 1] = dp[m - 1][n] = 1;
        for (int i = m - 1; i >= 0; i--) {
            for (int j = n - 1; j >= 0; j--) {
                dp[i][j] = Math.max(1, (Math.min(dp[i][j + 1], dp[i + 1][j]) - dungeon[i][j]));
            }
        }
        return dp[0][0];
    }