🔢 ICPC Style Array Problem Output Explanations in C

🔢 Problem 1: Maximum Subarray Sum

🧾 Output Explanation:

The subarray [4, -1, 2, 1] in the given array sums up to 6, which is the largest sum achievable from any contiguous subarray.

💻 C Code:

#include <stdio.h>

int main() {
    int n, a[100000], maxSum, currSum;
    scanf("%d", &n);
    for (int i = 0; i < n; i++) scanf("%d", &a[i]);

    currSum = maxSum = a[0];
    for (int i = 1; i < n; i++) {
        currSum = (currSum + a[i] > a[i]) ? currSum + a[i] : a[i];
        if (currSum > maxSum) maxSum = currSum;
    }
    printf("%d\n", maxSum);
    return 0;
}

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📉 Problem 2: Count Inversions

🧾 Output Explanation:

Inversions are pairs where a larger number appears before a smaller number.
For the input, the inversions are:

• (2,1) at indices (0,2)
• (4,1) at indices (1,2)
• (4,3) at indices (1,3)

Total inversions = 3.

💻 C Code:

#include <stdio.h>

int main() {
    int n, a[100000], count = 0;
    scanf("%d", &n);
    for (int i = 0; i < n; i++) scanf("%d", &a[i]);

    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            if (a[i] > a[j]) count++;
        }
    }
    printf("%d\n", count);
    return 0;
}

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📦 Problem 3: Prefix Sum Query

🧾 Output Explanation:

Each query asks for the sum of elements between indices L and R.
For example:

• Query 1: sum from 1 to 3 → 1+2+3 = 6
• Query 2: sum from 2 to 4 → 2+3+4 = 9
• Query 3: sum from 3 to 5 → 3+4+5 = 12

💻 C Code:

#include <stdio.h>

int main() {
    int n, q, a[100001], prefix[100001] = {0};
    scanf("%d %d", &n, &q);
    for (int i = 1; i <= n; i++) {
        scanf("%d", &a[i]);
        prefix[i] = prefix[i-1] + a[i];
    }

    while (q--) {
        int l, r;
        scanf("%d %d", &l, &r);
        printf("%d\n", prefix[r] - prefix[l-1]);
    }
    return 0;
}

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🎯 Problem 4: Maximum in Submatrix (2D Array)

🧾 Output Explanation:

The matrix is divided into all possible K×K submatrices.
For each submatrix, the maximum element is printed:

• Top-left 2x2 submatrix max = 5
• Top-right 2x2 submatrix max = 6
• Bottom-left 2x2 submatrix max = 8
• Bottom-right 2x2 submatrix max = 9

💻 C Code:

#include <stdio.h>

int max(int a, int b) { return a > b ? a : b; }

int main() {
    int n, k, a[500][500];
    scanf("%d %d", &n, &k);
    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++)
            scanf("%d", &a[i][j]);

    for (int i = 0; i <= n - k; i++) {
        for (int j = 0; j <= n - k; j++) {
            int mx = a[i][j];
            for (int x = 0; x < k; x++)
                for (int y = 0; y < k; y++)
                    mx = max(mx, a[i + x][j + y]);
            printf("%d\n", mx);
        }
    }
    return 0;
}

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🔁 Problem 5: Matrix Rotation (90 Degrees Clockwise)

🧾 Output Explanation:

Rotating the matrix 90° clockwise means:

• The first row becomes the last column,
• The second row becomes the second last column, and so on.

Example: Input row [1 2 3] becomes the last column from top to bottom.

💻 C Code:

#include <stdio.h>

int main() {
    int n, a[1000][1000];
    scanf("%d", &n);
    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++)
            scanf("%d", &a[i][j]);

    for (int j = 0; j < n; j++) {
        for (int i = n - 1; i >= 0; i--)
            printf("%d ", a[i][j]);
        printf("\n");
    }
    return 0;
}

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