Decrease Elements To Make Array Zigzag - Practice Coding Problems

Decrease Elements To Make Array Zigzag - Problem

Array Greedy Medium

Given an array nums of integers, a move consists of choosing any element and decreasing it by 1.

An array A is a zigzag array if either:

Every even-indexed element is greater than adjacent elements, i.e. A[0] > A[1] < A[2] > A[3] < A[4] > ...
OR, every odd-indexed element is greater than adjacent elements, i.e. A[0] < A[1] > A[2] < A[3] > A[4] < ...

Return the minimum number of moves to transform the given array nums into a zigzag array.

Input & Output

Example 1 — Basic Case

$ Input: nums = [1,17,5]

› Output: 2

💡 Note: We can choose pattern where odd indices are peaks: decrease 17→17 (no change), decrease 5→4 (1 move), decrease 1→0 (1 move). Result: [0,17,4] with 2 total moves.

Example 2 — All Equal

$ Input: nums = [2,2,2]

› Output: 1

💡 Note: Make middle element peak: keep [2,2,2] but need one valley. Best is [1,2,1] requiring 2 moves, or [2,2,1] requiring 1 move for pattern with even peaks.

Example 3 — Already Zigzag

$ Input: nums = [1,3,2,4,1]

› Output: 0

💡 Note: Array already follows zigzag pattern with odd indices as peaks: 1 < 3 > 2 < 4 > 1. No moves needed.

Constraints

1 ≤ nums.length ≤ 1000
1 ≤ nums[i] ≤ 1000

Visualization

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Understanding the Visualization

Input

Original array [1,17,5]

Process

Try both zigzag patterns and compare moves

Output

Return minimum moves needed: 2

Key Takeaway

🎯 Key Insight: Only two zigzag patterns exist - test both and choose the one requiring fewer moves

Asked in

G Google 15 a Amazon 12 M Microsoft 8

The key insight is that there are only two possible zigzag patterns: even-indexed peaks or odd-indexed peaks. We calculate moves for both patterns and choose the minimum. Best approach is greedy two-pattern comparison. Time: O(n), Space: O(1)

Common Approaches

Approach	Time	Space	Notes
✓ Greedy - Two Pattern Approach	O(n)	O(1)	Try both zigzag patterns separately and choose minimum moves
Brute Force - Try All Combinations	O(2^n)	O(n)	Generate all possible zigzag arrays and find minimum moves

Greedy - Two Pattern Approach — Algorithm Steps

Calculate moves for even-indexed peaks pattern
Calculate moves for odd-indexed peaks pattern
Return minimum of both patterns

Visualization

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Step-by-Step Walkthrough

Pattern 1

Calculate moves for even-indexed peaks

Pattern 2

Calculate moves for odd-indexed peaks

Choose

Return minimum moves from both patterns

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>

int calculateMoves(int* nums, int numsSize, int peakPattern) {
    int moves = 0;
    
    for (int i = 0; i < numsSize; i++) {
        if (i % 2 == peakPattern) {
            // This should be a peak - no moves needed
            continue;
        } else {
            // This should be a valley
            int leftNeighbor = i > 0 ? nums[i-1] : INT_MAX;
            int rightNeighbor = i < numsSize-1 ? nums[i+1] : INT_MAX;
            int minNeighbor = leftNeighbor < rightNeighbor ? leftNeighbor : rightNeighbor;
            if (nums[i] >= minNeighbor) {
                moves += nums[i] - (minNeighbor - 1);
            }
        }
    }
    return moves;
}

int solution(int* nums, int numsSize) {
    if (numsSize <= 1) return 0;
    
    // Pattern 0: even indices are peaks
    int movesPattern0 = calculateMoves(nums, numsSize, 0);
    
    // Pattern 1: odd indices are peaks
    int movesPattern1 = calculateMoves(nums, numsSize, 1);
    
    return movesPattern0 < movesPattern1 ? movesPattern0 : movesPattern1;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    int nums[1000];
    int numsSize = 0;
    
    char* token = strtok(line + 1, ",]");
    while (token != NULL) {
        nums[numsSize++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    int result = solution(nums, numsSize);
    printf("%d\n", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through array for each pattern, 2×O(n) = O(n)

✓ Linear Growth

Space Complexity

O(1)

Only using constant extra variables for counters

✓ Linear Space

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~15 min Avg. Time

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Greedy - Two Pattern Approach — Algorithm Steps

Visualization

Code -

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