算法题目---前缀和

1.一维前缀和模板

解法：前缀和

java 复制代码

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int[] array = new int[n + 1];
        int m = scanner.nextInt();
        for (int i = 1; i <= n; i++) {
            array[i] = scanner.nextInt();
        }
        long[] dp=new long[n+1];
        for (int i = 1; i <= n ; i++) {
            dp[i] = dp[i - 1] + array[i];
        }
        for (int i = 0; i < m; i++) {
            int left = scanner.nextInt();
            int right = scanner.nextInt();
            System.out.println(dp[right] - dp[left-1]);
        }
    }

2.二维前缀和模板

【模板】二维前缀和_牛客题霸_牛客网

解法：前缀和

java 复制代码

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int[][] array = new int[n + 1][m + 1];
        int q = scanner.nextInt();
        for (int i = 1; i <= n ; i++) {
            for (int j = 1; j <= m ; j++) {
                array[i][j] = scanner.nextInt();
            }
        }
        long[][] dp = new long[n + 1][m + 1];
        for (int i = 1; i <= n ; i++) {
            for (int j = 1; j <= m ; j++) {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1] - dp[i - 1][j - 1] + array[i][j];
            }
        }
        for (int i = 0; i < q; i++) {
            int x1 = scanner.nextInt();
            int y1 = scanner.nextInt();
            int x2 = scanner.nextInt();
            int y2 = scanner.nextInt();
            long ret = dp[x2][y2] - dp[x1 - 1][y2] - dp[x2][y1 - 1] + dp[x1 - 1][y1 - 1];
            System.out.println(ret);
        }
    }

3.寻找数组的中心下标

724. 寻找数组的中心下标 - 力扣（LeetCode）

解法：前缀和

java 复制代码

    public int pivotIndex(int[] nums) {
        int len=nums.length;
        int[] dp_left=new int[len];
        int[] dp_right=new int[len];
        for (int i = 1; i < len; i++) {
            dp_left[i]=dp_left[i-1]+nums[i-1];
        }
        for (int i = len-2; i >=0; i--) {
            dp_right[i]=dp_right[i+1]+nums[i+1];
        }

        for (int i = 0; i <len ; i++) {
            if (dp_left[i]==dp_right[i]){
                return i;
            }
        }
        return -1;
    }

4.除自身以外数组的乘积

238. 除了自身以外数组的乘积 - 力扣（LeetCode）

解法：前缀积 + 后缀积

java 复制代码

    public int[] productExceptSelf(int[] nums) {
        int len=nums.length;
        //定义前缀积数组
        int[] dp_left=new int[len];
        //定义后缀积数组
        int[] dp_right=new int[len];
        //处理边界情况
        dp_left[0]=1;
        dp_right[len-1]=1;
        for (int i = 1; i <len ; i++) {
            dp_left[i]=dp_left[i-1]*nums[i-1];
        }
        for (int i = len-2; i >=0 ; i--) {
            dp_right[i]=dp_right[i+1]*nums[i+1];
        }
        int[] ret=new int[len];
        for (int i = 0; i < len; i++) {
            ret[i]=dp_left[i]*dp_right[i];
        }
        return ret;
    }

5.和为k的子数组

560. 和为 K 的子数组 - 力扣（LeetCode）

解法：前缀和 + 哈希表

java 复制代码

    public int subarraySum(int[] nums, int k) {
        HashMap<Integer,Integer> hashMap=new HashMap<>();
        int sum=0;
        int count=0;
        //处理细节
        hashMap.put(0,1);
        for (int x:nums) {
            sum+=x;
            count+=hashMap.getOrDefault(sum-k,0);
            hashMap.put(sum,hashMap.getOrDefault(sum,0)+1);
        }
        return count;
    }

6.和可被K整除的子数组

974. 和可被 K 整除的子数组 - 力扣（LeetCode）

解法：前缀和

java 复制代码

    public int subarraysDivByK(int[] nums, int k) {
        HashMap<Integer,Integer> hashMap=new HashMap<>();
        int count=0;
        int sum=0;
        hashMap.put(0%k,1);
        for (int x:nums) {
            sum+=x;
            int r=(sum%k+k)%k;
            count+=hashMap.getOrDefault(r,0);
            hashMap.put(r,hashMap.getOrDefault(r,0)+1);
        }
        return count;
    }

7.连续数组

525. 连续数组 - 力扣（LeetCode）

解法：前缀和

java 复制代码

    public int findMaxLength(int[] nums) {
        HashMap<Integer,Integer> hashMap=new HashMap<>();
        hashMap.put(0,-1);
        int sum=0;
        int len=0;
        for (int i = 0; i < nums.length; i++) {
            sum+=(nums[i]==0?-1:1);
            if (hashMap.containsKey(sum)){
                len=Math.max(len,i-hashMap.get(sum));
            }else{
                hashMap.put(sum,i);
            }
        }
        return len;
    }

8.矩阵区域和

1314. 矩阵区域和 - 力扣（LeetCode）

解法：前缀和

java 复制代码

    public int[][] matrixBlockSum(int[][] mat, int k) {
        int m=mat.length;
        int n=mat[0].length;
        int[][] dp=new int[m+1][n+1];
        for (int i = 1; i <=m ; i++) {
            for (int j = 1; j <=n ; j++) {
                dp[i][j]=dp[i][j-1]+dp[i-1][j]-dp[i-1][j-1]+mat[i-1][j-1];
            }
        }
        int[][] ans=new int[m][n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                int x1=Math.max(0,i-k)+1;
                int y1=Math.max(0,j-k)+1;
                int x2=Math.min(m-1,i+k)+1;
                int y2=Math.min(n-1,j+k)+1;
                ans[i][j]=dp[x2][y2]-dp[x1-1][y2]-dp[x2][y1-1]+dp[x1-1][y1-1];
            }
        }
        return ans;
    }